Introduction to (wx)Maxima
Paul Verheyen, Generated with
chmProcessor
and
wxMaxima
<div class="WordSection1"> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <b><span style="LINE-HEIGHT: 115%; FONT-SIZE: 20pt" lang= "EN-US">Introduction to (wx)Maxima</span></b></p> <h1><span lang="EN-US">Maxima is a CAS</span><a name="NODO0" id= "NODO0"></a></h1> <p class="MsoNormal"><span lang="EN-US">A <b>Computer Algebra System</b> (CAS) is a software program that facilitates symbolic mathematics.<br> The core functionality of a CAS is manipulation of mathematical expressions in symbolic form, rather than merely in numerical form, i.e. as numbers. The program Maxima has the capability of manipulating numerical entities quite well, but it is not limited strictly to manipulations of that kind.<br> <br> The Maxima manual gives a short historical view on the origins of Maxima:</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span lang= "EN-US">"Maxima is a CAS, derived from the Macsyma (MAC's SYmbolic MAnipulation) system, developed at MIT (Massachusetts Institute of Technology) in the years 1968 through 1982 as a part of the MAC project (Machine Aided Cognition). MIT turned over a copy of the Macsyma source code to the Department of Energy in 1982; that version is now known as DOE Macsyma. A copy of DOE Macsyma was maintained by Professor <b>William F. Schelter</b> of the University of Texas from 1982 until his death in 2001. In 1998, Schelter obtained permission from the Department of Energy to release the DOE Macsyma source code under the GNU Public License, and in 2000 he initiated the Maxima project at SourceForge to maintain and develop DOE Macsyma, now called Maxima."</span></p> <p class="MsoNormal"><span lang="EN-US"><br> Maxima is written in Common Lisp ([List processing], see http://en.wikipedia.org/wiki/Lisp_(programming_language)) and runs on different platforms such as Mac OS X, Unix and GNU/Linux as well as under Microsoft Windows.<br> Todays version is maintained by an independent group of users and developers (see http://sourceforge.net/projects/maxima/).<br> Since Maxima is distributed under the GNU-GLP license, it is a free and open source CAS.<br> <br></span></p> <p class="MsoNormal"><span lang="EN-US">In this document we describe the Windows implementation of Maxima and wxMaxima<br> (using the versions Maxima 5.27.0 and wxMaxima 12.04.0).<br> The Windows executable (see http://sourceforge.net/projects/maxima/files/), not only installs the kernel but also a collection of packages that simplify the working environment. The outcome includes a text console (MSDOS mode) and two graphical environments: xMaxima (with permanent help on screen, but only useful in command mode) and wxMaxima.<br> This last is the most advisable one, since it allows to work in screen mode, incorporates a text editor and includes a wide collection of displayable menus as well as shortcuts and buttons to do a lot of mathematical computations without using commands.<br> Besides, two modules of graphical representation are included: gnuplot and openmath.</span></p> <p class="comment"><span lang="EN-US">This introduction is based on information available using the links on<br> <a href= "http://maxima.sourceforge.net/documentation.html" target= "_blank">http://maxima.sourceforge.net/documentation.html</a> ,<br> <a href= "http://andrejv.github.com/wxmaxima/help.html" target= "_blank">http://andrejv.github.com/wxmaxima/help.html</a> ,<br> <a href= "http://statmath.wu.ac.at/~leydold/maxima/" target= "_blank">http://statmath.wu.ac.at/~leydold/maxima/</a> ,<br> and<br> <a href= "http://www.time2010.uma.es/Proceedings/Papers/A043_Paper.pdf" target= "_blank">http://www.time2010.uma.es/Proceedings/Papers/A043_Paper.pdf</a>,<br> [an article in the Proceedings of TIME 2010 (Technology and its Integration into Mathematics Education)]<br> <br> Download and study the examples in<br> <a href= "http://andrejv.github.com/wxmaxima/tutorials/10minute.zip" target= "_blank">http://andrejv.github.com/wxmaxima/tutorials/10minute.zip</a> ,<br> <a href= "http://andrejv.github.com/wxmaxima/tutorials/wxmaxima.zip" target= "_blank">http://andrejv.github.com/wxmaxima/tutorials/wxmaxima.zip</a> ,<br> <a href= "http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript.pdf" target= "_blank">http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript.pdf</a> .<br> You can also find installation information and more at the site of Paul Lutus<br> <a href= "http://arachnoid.com/maxima/installing_testing.html" target= "_blank">http://arachnoid.com/maxima/installing_testing.html</a> .</span></p> <h1><span lang="EN-US">1 First meetings in (wx)Maxima's universe</span> <a name="NODO1" id="NODO1"></a></h1> <h2><span lang="EN-US">wxMaxima is a GUI to Maxima</span><a name= "NODO2" id="NODO2"></a></h2> <p class="comment"><b><span lang="EN-US">Maxima</span></b> <span lang="EN-US">is a CAS (Computer Algebra System) similar to systems like<br> Mathematica, Maple and others. Maxima, however, is a commandline<br> application, which makes it harder to use than its younger cousins.<br> Here is where <b>wxMaxima</b> comes in - it's a <b>GUI</b> (Graphical User Interface)<br> for Maxima, made to make using Maxima simpler and more enjoyable.<br> wxMaxima is developed by Andrej Vodopivec, University of Ljubljana, Slovenia.</span></p> <p class="image"><i><span lang="EN-US">Figure 1: The wxMaxima screen</span></i> <span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_0.png" width="582" height="298"></p> <p class="comment"><span lang="EN-US">Unlike 'commandline Maxima', which works in a simple input-output manner, wxMaxima introduces the concept of a live mathematical document, in which you mix text, calculations and plots.<br> Each wxMaxima document consists of a number of so called '<b>cells</b>'. Cells are the basic building blocks of a wxMaxima document. Each cell has a bracket on the left border of the document, indicating where the cell begins and ends. Cells are of different types, e.g. a 'title cell', a 'text cell', ...<br> The most important cell type is an 'input cell'. An input cell holds Maxima code and can be evaluated with Shift+Enter. The code entered in this cell will be sent to Maxima when you press Shift+Enter. Before wxMaxima sends code to Maxima, it checks if the contents of an input cell ends with a '<b>;</b>' or a '<b>$</b>' - if it doesn't, wxMaxima adds a ';' at the end. Maxima requires that lines end with either ';' or '$'. A '$' means the output will be internally executed, but not be shown on screen.<br> <br> <br></span></p> <h2><span lang="EN-US">Evaluate by Shift+Enter</span><a name= "NODO3" id="NODO3"></a></h2> <p class="comment"><span lang="EN-US">Let's start with some simple calculation examples!<br> Below is an input cell with a simple addition. Place the cursor in it and press <b>Shift+Enter</b> to evaluate it.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">1+20;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_1.png" width="94" height="20"></p> <p class="comment"><span lang="EN-US">Remember: you have to use Shift+Enter to evaluate a cell in wxMaxima!<br></span><span style= "COLOR: red" lang="EN-US">By default <b>Shift+Enter</b> is used to evaluate commands, while <b>Enter</b> is used for multiline input.</span> <span lang="EN-US"><br> <br> This behaviour can be changed in '<b>Edit > Configure</b>' dialog by checking 'Enter evaluates cells'. This switches the roles of these two key commands.<br> <br> Any output wxMaxima gets from Maxima will be attached into the output part of the input cell.<br> Input and output will be numbered by Maxima’s console as respectively (%i#) and (%o#).<br> <br></span></p> <h2><span lang="EN-US">Variables and functions</span><a name= "NODO4" id="NODO4"></a></h2> <p class="comment"><span lang="EN-US">You can also use variables:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">x+x;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_2.png" width="99" height="21"></p> <p class="comment"><span lang="EN-US">In this respect it is important to know that</span> <span style="COLOR: red" lang= "EN-US">the use of '*' is required for multiplication</span><span lang="EN-US">. Refer to the following two examples.<br> Moreover variable (and other)</span> <b><span style="COLOR: red" lang="EN-US">names are case sensitive</span></b><span lang= "EN-US">.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">x+2x;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_3.png" width="442" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">x+2*x;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_4.png" width="99" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">x+2*X;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_5.png" width="127" height="21"></p> <p class="comment"><span lang="EN-US">You can send multiple "lines" to Maxima:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">sqrt(2 * %pi);</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class="input1">float(%);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_6.png" width="244" height="45"></p> <p class="comment"><span lang="EN-US">We use '<b>sqrt</b>' for the function square root.<br> To type the constant "pi" you use '<b>%pi</b>'.<br> If you installed the proper font, Greek symbols can be shown.<br> See<br> <a href= "http://arachnoid.com/maxima/installing_testing.html" target= "_blank">http://arachnoid.com/maxima/installing_testing.html</a><br> or<br> <a href= "http://andrejv.github.com/wxmaxima/help.html" target= "_blank">http://andrejv.github.com/wxmaxima/help.html</a> .<br> To test the ability of wxMaxima to render correctly, type examples of Greek characters in wxMaxima using this notation:<br> <br> %Omega;<br> %omega;<br> <br> The expression "float(%);" contains the "%" symbol and "float".<br> This symbol "<b>%</b>" always holds the result of the last evaluated line<br> (this is not necessarily the cell immediately preceding).<br> "<b>float</b>" refers to the numerical representation of the result.<br> wxMaxima always uses exact calculations so sin(%pi) will evaluate<br> to 0 but sin(3) will not be simplified. In order to get a decimal approximation for sin(3)<br> there are several techniques that can be used:<br> <br> 1) Right-click on the output expression and choose "To Float" from the menu.<br> 2) Enter float(%) in the Input box. Note that % refers to the previously entered expression.<br> 3) Use decimal numbers such as 3.0 instead of 3.<br> <br> Note also that the result of "1/3" and "1.0/3.0" differ.<br> That's because Maxima, unlike numerical matrix packages (Matlab etc.), tries to keep calculations precise - it does not evaluate expressions like 1/3 or sqrt(2) unless asked to. In "1.0/3.0" we used floating point numbers, so Maxima didn't leave the expression unevaluated.<br> <br> Numbered symbols "%o1", "%o2" ... hold the results as they appear when input cells are evaluated.<br> It is possible to refer to the output by referencing using (%o#).<br> When saving a document as a wxMaxima document, extension "wxm", and opening it later, only the input cells are shown. You can use the menu option "<b>Cell > Evaluate all cells</b>" to evaluate all of them. It is possible the numbering of output cells is different after working<br> with the document, so referencing by (%o#) must be used carefully.</span></p> <p class="image"><i><span lang="EN-US">Figure 2: Cell > Evaluate all cells</span></i> <span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_7.png" width="536" height="340"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">%Omega;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_8.png" width="86" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">%omega;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_9.png" width="84" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">sin(3);</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">float(%);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_10.png" width="234" height="44"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">sin(3),numer;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_11.png" width="234" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">sin(3.0);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_12.png" width="234" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">1/3 ;</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class="input1">1.0/3.0;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_13.png" width="234" height="64"></p> <p class="comment"><span lang="EN-US">Another option is to select the Numeric menu on the top tool bar and then selecting the "Toggle numeric output" to have all output numerically approximated as a floating point number.<br> !!!! To end this mode select the menu again and choose the numeric mode option again. !!!!</span></p> <p class="comment"><span lang="EN-US">Here is a list of <b>common constants</b> in Maxima, which you should be aware of:<br> <br> %e : Euler's number<br> %pi : the number pi<br> <br> inf : real positive infinity<br> minf or -inf : real minus infinity<br> <br> %i : complex imaginary unit<br> infinity : complex infinity</span></p> <p class="comment"><span lang="EN-US">It is possible to simplify using e.g. "ratsimp":</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">(a+b)^2;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_14.png" width="135" height="28"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ratsimp((a+b)^2);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_15.png" width="184" height="26"></p> <p class="comment"><span lang="EN-US">The preceding could more easily be found by using "expand":</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">expand((a+b)^2);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_16.png" width="184" height="26"></p> <p class="comment"><span lang="EN-US">As you see, Maxima ordens variables in reverse lexicographical order.<br> This ordering can be changed by using ordergreat or orderless, but as you notice in the following this is not the case for products.<br> <br> Note: to get help on any function, just click on the function name and press F1.<br> Try it on ordergreat below.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ordergreat(a,b);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_17.png" width="114" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">expand((a+b)^2);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_18.png" width="184" height="26"></p> <p class="comment"><span lang="EN-US">Sometimes the output is rather long:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">expand((a+b)^20);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_19.png" width="790" height="110"></p> <p class="comment"><span lang="EN-US">You can hide the output by clicking into the empty triangle at the top of the bracket of the input cell above. The output can be shown again<br> by clicking again into the triangle. A full triangle indicates that the cell's output is hidden.</span></p> <p class="comment"><span lang="EN-US">Sometimes Maxima needs additional information to evaluate an expression and asks us a question. A cursor appears automatically, indicating<br> you need to answer a question. Write an answer below the cell and send it to Maxima with Shift+Enter.<br> <br> Below is an integral with a question.<br> Note: instead of answering with "positive;", you can only type "p".</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">integrate( 1 / (x^2 + a), x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_20.png" width="310" height="98"></p> <p class="comment"><span lang="EN-US">We can also inform Maxima beforehand using the function "assume".<br> To revert an assumption, use "forget".<br> (Remember:</span> <span style="COLOR: red" lang="EN-US">to get help on any function, just click on the function name and press F1</span><span lang="EN-US">. Try it.)</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">assume(a > 0)$</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class="input1">integrate( 1 / (x^2 + a), x);</span><br> <span class="input1">forget(a > 0)$</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_21.png" width="155" height="74"></p> <h1><span lang="EN-US">2 Editing and saving</span> <a name="NODO5" id="NODO5"></a></h1> <p class="comment"><span lang="EN-US">Editing cells is easy - to modify the contents of a cell, click into it.<br> A cursor should appear and the left cell bracket should turn red, to indicate that the cell is being edited.<br> <br> Note however that once you move the cursor past the beginning, a horizontal line appears between cells. Think of this line as a horizontal cursor. Pressing any key will insert a new input cell, while pressing ShiftT+UP/DOWN will select cells in that direction.<br> Activating the horizontal cursor is also possible by clicking between cells; click-dragging will result in a cell selection.</span></p> <p class="comment"><span lang="EN-US">When you have a selection of cells, pressing backspace or delete key will delete the selection. You can also cut, copy and paste cells using<br> menu commands.</span></p> <p class="comment"><span lang="EN-US">When the horizontal cursor is active, typing will result in a new input cell. If you want to insert a cell of some other type, go to the Cell<br> menu or use the respective key shortcut.</span></p> <p class="image"><i><span lang="EN-US">Figure 3: Part of the Cell menu</span></i> <span lang="EN-US"><br></span><img border="0" alt= "Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_22.png" width="159" height="90"></p> <p class="comment"><span lang="EN-US">Important<br> =========<br></span><span style="COLOR: red" lang="EN-US">You can use extra spaces or more lines to make your input more readable</span><span lang="EN-US">!<br> E.g.<br> expand((a+b)^2);<br> is the same as<br> expand(<br> (a + b)^2<br> );</span></p> <p class="comment"><span lang="EN-US">When you're satisfied with the document you've created, save it using <b>File > Save</b> menu command (or Ctrl+S key command). By default the extension is <b>wxm</b>.<br> Note that the output parts of input cells will not be saved. When you load your document you can evaluate all cells by the 'Cell > Evaluate all cells' menu command (as mentioned above) or respective key command.<br> <br> When you save a document as 'wxMaxima XML document', not only your input and text commentaries, but also the outputs of your calculations are saved. Moreover, you can also insert pictures in such a <b>wxmx</b> document.</span></p> <h1><span lang="EN-US">3 Symbolical and numerical math</span> <a name="NODO6" id="NODO6"></a></h1> <h2><span lang="EN-US">3.1 Solving equations</span> <a name="NODO7" id="NODO7"></a></h2> <h4><span lang="EN-US">Solve</span><a name="NODO8" id= "NODO8"></a></h4> <p class="comment"><span lang="EN-US">You can solve equations using solve:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(3*x+2=0, x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_23.png" width="145" height="42"></p> <p class="comment"><span lang="EN-US">The brackets [] in the output refer to the fact that Maxima gives this result as a "<b>list</b>".<br> A list is any ordered array of items. In Maxima , lists are enclosed in<br> a pair of square brackets [ ] , and the items in a list are separated by commas.<br> <br> If you do not use "=" in the command solve, Maxima assumes you mean "=0".</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(x^2-4,x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_24.png" width="196" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(x^2-4=5,x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_25.png" width="196" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(a*x^2 + b*x + c = 0, x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_26.png" width="383" height="52"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y=5,3*x-y=1], [x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_27.png" width="209" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Assigning labels</span><a name="NODO9" id= "NODO9"></a></h4> <p class="comment"><span lang="EN-US">It is possible to <b>assign a label</b> to e.g. equations or an output.<br> <br> Maxima uses some nonintuitive syntax for assigning a value to a label. Here are the rules:<br> <br> Use ":" to assign a value to a variable: a : 3;, a : b; etc.<br> <br> Use "=" to compare values for equality: a = 3;,a = b; etc.,<br> also "<" (less than),">" (greater than) and "#" (unequal)<br> <br> Use ":=" to define a function: f(x) := x^2;<br> <br> When an expression has been assigned to some variable, then it remains persistent until it is killed (or Maxima is stopped).<br> <br> Use "kill(name);" to erase a previous assignment of a variable or function: kill(a);, kill(f);<br> <br> Use "kill(all);" to erase all assignments.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">eq1: x+2*y=5;</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class="input1">eq2: 3*x-y=1;</span><br> <span class="input1">solve([eq1,eq2], [x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_28.png" width="209" height="67"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_29.png" width="114" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">a:3;</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">b:100;</span><br> <span class="input1">a+b;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_30.png" width="104" height="64"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">The function “is()”</span><a name="NODO10" id="NODO10"></a></h4> <p class="comment"><span lang="EN-US">You can <b>compare</b> expressions or numbers:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">is(a=b);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_31.png" width="124" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">is(a<b);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_32.png" width="114" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_33.png" width="114" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">is(a<b);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_34.png" width="144" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Lists</span><a name="NODO11" id= "NODO11"></a></h4> <p class="comment"><span lang="EN-US">As mentioned above, Maxima gives the output of e.g. solve as a "list"<br> (see the Maxima manual, 5. Data Types and Structure).<br> If you label this output, you can access the list by way of an index:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">sol: solve(x^2-4=0,x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_35.png" width="196" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">sol[1];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_36.png" width="122" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">sol[2];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_37.png" width="110" height="21"></p> <p class="comment"><span lang="EN-US">If you want to use this output, you can use the function <b>ev</b>():</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ev(x^2-4,sol[2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_38.png" width="84" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">subst;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_39.png" width="124" height="21"></p> <p class="comment"><span lang="EN-US">You can also extract the right hand side of equations using <b>rhs</b>():</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">rhs(sol[2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_40.png" width="84" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_41.png" width="114" height="21"></p> <h2><span lang="EN-US">3.2 Numerical versus exact solutions</span> <a name="NODO12" id="NODO12"></a></h2> <h4><span lang="EN-US">allroots()</span><a name="NODO13" id= "NODO13"></a></h4> <p class="comment"><span lang="EN-US">As is well known, there are no closed form solutions for the roots of polynomials of degree 5 or larger.<br> The command '<b>allroots</b>' may be used to get at least a numerical approximation of the roots.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(x^5-x^4+2*x^3+x^2-x+5, x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_42.png" width="311" height="26"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class= "input1">allroots(x^5-x^4+2*x^3+x^2-x+5);</span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><br> <img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_43.png" width="695" height="67"></p> <p class="comment"><span lang="EN-US">Some of these solutions are so called complex non-real numbers.<br> The d'Alembert-Gauss theorem expresses the fact that every non-constant polynomial with complex coefficients has a root in the field of the complex numbers.<br> Consequently, every non-constant polynomial of degree n with complex coefficients, has exactly n roots (counted with their multiplicities).<br> It implies that a non-constant polynomial of degree n with real coefficients, has at most n roots (counted with their multiplicities).</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(x^2+x+1=0,x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_44.png" width="321" height="45"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">allroots(x^2+x+1);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_45.png" width="634" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">realroots()</span><a name="NODO14" id= "NODO14"></a></h4> <p class="comment"><span lang="EN-US">You can use <b>realroots</b>(expr) or realroots(eqn) to find rational approximations of the real roots of the polynomial expr or polynomial equation eqn of one variable.<br> Coefficients of expr or eqn must be literal numbers; symbol constants such as %pi are rejected.<br> All coefficients are converted to rational equivalents before searching for roots, and computations are carried out by exact rational arithmetic.<br> Even if some coefficients are floating-point numbers, the results are rational.<br> This is done within a tolerance of bound, which you can set yourself in realroots(expr,bound). Maxima uses a standard tolerance bound if you omit this bound.<br> <br> We use realroots on the 5-th degree polynomial from the example above.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class= "input1">realroots(x^5-x^4+2*x^3+x^2-x+5);</span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><br> <img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_46.png" width="208" height="42"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class= "input1">realroots(x^5-x^4+2*x^3+x^2-x+5), numer;</span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><br> <img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_47.png" width="306" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Real number results may seem to be complex numbers</span><a name="NODO15" id="NODO15"></a></h4> <p class="comment"><span lang="EN-US">While it is quite convenient Maxima performs many of its computation over the field of complex numbers, for many applications it may be annoying when we are interested in purely real solutions.<br> The situation may become even worse as the following example demonstrates.<br> Here the solution is computed by means of Cardano’s formula. It looks like complex numbers.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">opl: solve(x^3-x+1/3=0,x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_48.png" width="776" height="198"></p> <p class="comment"><span lang="EN-US">However, all three solutions are real numbers. You can try to transform these complex numbers into Cartesian form, i.e. into the representation a + b %i where a and b are real (the so-called real and imaginary part, respectively).<br> '<b>rectform</b>(expr) returns an expression a + b %i equivalent to expr, such that a and b are purely real.<br> You then can try to reduce the imaginary part to 0 by means of the command' <b>trigsimp</b>'.<br> If you do not use trigsimp or if it is not possible to reduce the imaginary part to 0, then a tiny imaginary part might remain when converting the solutions to floating point numbers due to round-off errors. It can be transformed to a purely real solution by using their real parts. However, you must be confident that the solution is not a complex number.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">trigsimp(rectform(opl));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_49.png" width="685" height="68"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(trigsimp(rectform(opl)));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_50.png" width="696" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(rectform(opl));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_51.png" width="756" height="54"></p> <p class="comment"><span lang="EN-US">Using realroots, you obtain three solutions. This also shows all three solutions are real numbers.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">realroots(x^3-x+1/3);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_52.png" width="432" height="42"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(realroots(x^3-x+1/3));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_53.png" width="696" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">reset()</span><a name="NODO16" id= "NODO16"></a></h4> <p class="comment"><span lang="EN-US">The option <b>reset()</b> resets many global variables and options, and some other variables, to their default values.<br> Sometimes you need this resetting apart from kill(all).</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">reset();</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_54.png" width="797" height="67"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Remark</span><a name="NODO17" id= "NODO17"></a></h4> <p class="comment"><span lang="EN-US">For non-polynomial equations, the result is sometimes not found or you only get one solution:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([cos(x)=1],[x]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_55.png" width="502" height="65"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([cos(x)=0],[x]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_56.png" width="502" height="85"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([cos(x)=sin(x)],[x]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_57.png" width="228" height="23"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">allroots(cos(x)-sin(x));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_58.png" width="522" height="45"></p> <h2><span lang="EN-US">3.3 Solving sytems of equations</span> <a name="NODO18" id="NODO18"></a></h2> <h4><span lang="EN-US">solve()</span><a name="NODO19" id= "NODO19"></a></h4> <p class="comment"><b><span lang="EN-US">solve ([eqn_1, ..., eqn_n], [x_1, ..., x_n])</span></b> <span lang="EN-US">solves a system of simultaneous (linear or non-linear) polynomial equations (by respectively calling linsolve or algsys) and returns a list of the solution lists in the variables.<br> In the case of linsolve this list would contain a single list of solutions. It takes two lists as arguments. The first list represents the equations to be solved; the second list is a list of the unknowns to be determined.<br> If the total number of variables in the equations is equal to the number of equations, the second argument-list may be omitted.<br> The symbols %r1, %r2, …, are introduced as needed to represent arbitrary parameters in the solution.<br> These variables %r# are also appended to the list %rnum_list, which you can clear using reset().</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y=5,x-2*y=-4],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_59.png" width="209" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y=5,x-2*y=-4]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_60.png" width="209" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x-y=2,x^2+y^2=4],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_61.png" width="346" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x-y=2,x^2+y^2=4]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_62.png" width="346" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">No solutions</span><a name="NODO20" id= "NODO20"></a></h4> <p class="comment"><span lang="EN-US">There are no solutions for the following:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y=1,2*x+2*y=3],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_63.png" width="96" height="20"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Infinitely many solutions</span><a name= "NODO21" id="NODO21"></a></h4> <p class="comment"><span lang="EN-US">Sometimes there are an infinite number of solutions:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y=1, 2*x+2*y=2],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_64.png" width="422" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y=1, 2*x+2*y=2],[x]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_65.png" width="422" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[x,y,z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_66.png" width="442" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_67.png" width="442" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[y,z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_68.png" width="442" height="65"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[x,z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_69.png" width="442" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[x]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_70.png" width="442" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_71.png" width="442" height="65"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+2*y-z=1, 2*x+4*y-2*z=2, -x-2*y+z=-1],[z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_72.png" width="442" height="43"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">[</span><br> <span class="input1">x_1-x_2+x_3 -1=0,</span><br> <span class= "input1"> x_3+x_4 = 1,</span><br> <span class="input1">x_1-x_2 -x_4=0</span><br> <span class="input1">],</span><br> <br> <span class="input1">[x_1,x_2,x_3,x_4]</span><br> <span class="input1">);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_73.png" width="536" height="43"></p> <p class="comment"><span lang="EN-US">Be carefull by choosing the variables you want to solve for:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y-z=-1, x+y+z=1],[x,y,z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_74.png" width="311" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y-z=-1, x+y+z=1],[x,z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_75.png" width="221" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y-z=-1, x+y+z=1],[y,z]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_76.png" width="221" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y-z=-1, x+y+z=1],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_77.png" width="96" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x+y-z=-1, x+y+z=1]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_78.png" width="492" height="132"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">reset();</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_79.png" width="777" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Remark</span><a name="NODO22" id= "NODO22"></a></h4> <p class="comment"><span lang="EN-US">Solve does not always find (all) solutions of an arbitrary system of equations. Then an empty list is returned.<br> In the following example the “obvious” solution [x=1,y=1], or more generally x=y, is not found.<br> If you use integer exponents, all solutions are found.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x^(-1/2)*y^(1/2)=1, x^(1/2)*y^(-1/2)=1], [x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_80.png" width="96" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ev([x^(-1/2)*y^(1/2)-1, x^(1/2)*y^(-1/2)-1], [x=1,y=1]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_81.png" width="132" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ev([x^(-1/2)*y^(1/2)-1, x^(1/2)*y^(-1/2)-1], [x=a,y=a]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_82.png" width="132" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([x^(-1)*y^(1)=1, x^(1)*y^(-1)=1], [x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_83.png" width="422" height="43"></p> <p class="comment"><span lang="EN-US">Non-polynomial equations cause problems.<br> You can easily manually solve the following system of equations by the substitution and combination method.<br> Explicitly giving commands in Maxima leads to one particular solution, but not to the general solution.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">eq1:cos(x)+sin(y)=1;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_84.png" width="231" height="23"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">eq2:cos(x)-sin(y)=1;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_85.png" width="229" height="23"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve([eq1,eq2],[x,y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_86.png" width="96" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">/* Combine the equations: add eq1 and eq2 */</span></span><span style= "COLOR: blue" lang="EN-US"><br> <span class="input1">eq1nieuw:eq1+eq2;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_87.png" width="172" height="23"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">/* Solve the new equation */</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class="input1">solve(eq1nieuw);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_88.png" width="502" height="65"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">/* Resubstitute in eq2 */</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">subst(0,x,eq2);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_89.png" width="182" height="23"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">/* Solve eq2 after back substitution */</span></span><span style= "COLOR: blue" lang="EN-US"><br> <span class="input1">solve([%], [y]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_90.png" width="502" height="65"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);reset();</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_91.png" width="619" height="44"></p> <h2><span lang="EN-US">3.4 Linear algebra</span> <a name="NODO23" id="NODO23"></a></h2> <h4><span lang="EN-US">matrix() and 'Algebra > Enter matrix...'</span><a name="NODO24" id="NODO24"></a></h4> <p class="comment"><span lang="EN-US">Use "<b>matrix</b>" to create matrices: this takes the row vectors of the matrix as its arguments. These must have the same length.<br> Matrices can contain non-number expressions.<br> The wxMaxima menu 'Algebra > Enter matrix...' can be used to enter a matrix. 'Algebra > Generate matrix...' generates, for instance,<br> its entries from a general term.<br> Note that not every command is defined in a pop-up menu.</span></p> <p class="image"><i><span lang="EN-US">Figure 4: Algebra > Enter matrix...</span></i> <span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_92.png" width="411" height="281"></p> <p class="image"><i><span lang="EN-US">Figure 5: Enter the type of matrix</span></i> <span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_93.png" width="222" height="206"></p> <p class="image"><i><span lang="EN-US">Figure 6: Fill in the form</span></i> <span lang="EN-US"><br></span><img border="0" alt= "Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_94.png" width="439" height="177"></p> <p class="image"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Calculations with matrices: invert() and</span> <span style="COLOR: black" lang= "EN-US">"."</span><a name="NODO25" id="NODO25"></a></h4> <p class="comment"><span style="COLOR: red" lang="EN-US">Use "<b>invert</b>" to calculate an inverse<br> and "<b>.</b>" for matrix multiplication.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">A: matrix([1,2],[3,4]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_95.png" width="112" height="56"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">invert(A);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_96.png" width="131" height="77"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">invert(matrix([1,2],[3,4]));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_97.png" width="131" height="77"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">invert(matrix([1,2],[3,6]));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_98.png" width="492" height="42"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">A: matrix([a,b],[c,d]);</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">B: invert(A);</span><br> <span class="input1">/* Remark: this result assumes A is invertible (see the output)</span><br> <span class="input1">A similar assumption applies to solve(a*x=0,x) : you get as only solution [x=0] */</span><br> <span class="input1">A.B;</span><br> <span class="input1">ratsimp(A.B);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_99.png" width="308" height="320"></p> <p class="comment"><span lang="EN-US">In the last line we used "ratsimp" to simplify the result of "A.B".<br> Maxima has a lot of different simplification functions, depending on what kind of simplification you want. Simplification is a complex<br> topic and if you don't know anything about it, using "ratsimp" may be your best shot.</span></p> <p class="comment"><span lang="EN-US">!!! You can use * and ^ for matrices but it gives you a</span> <b><span style="COLOR: red" lang="EN-US">pointwise</span></b> <span style="COLOR: red" lang= "EN-US">multiplication and exponentiation</span><span lang= "EN-US">, respectively.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A*A;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_100.png" width="128" height="66"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A^3;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_101.png" width="128" height="66"></p> <p class="comment"><span lang="EN-US">!!!</span> <span style= "COLOR: red" lang="EN-US">Always use . and ^^ for matrix multiplication and exponentiation</span><span lang="EN-US">, respectively.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A.A;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_102.png" width="204" height="66"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A^^2;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_103.png" width="204" height="66"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A^^-1;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_104.png" width="210" height="100"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Components of a matrix</span><a name= "NODO26" id="NODO26"></a></h4> <p class="comment"><span lang="EN-US">You can obtain the values of the components of a matrix as demonstrated below:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A[1,2];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_105.png" width="84" height="21"></p> <p class="comment"><span lang="EN-US">Since in Lisp, a matrix is similar to a list of lists, you can show rows as follows:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A[1];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_106.png" width="132" height="21"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A[2];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_107.png" width="132" height="21"></p> <p class="comment"><span lang="EN-US">Consequently, A[1,2] equals A[1][2]:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A[1][2];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_108.png" width="84" height="21"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Inconsistency when working with vectors</span><a name="NODO27" id="NODO27"></a></h4> <p class="comment"><u><span lang="EN-US">Important</span></u> <span lang="EN-US"><br> Vector are usually printed as row vectors. However,</span> <span style="COLOR: red" lang="EN-US">Maxima is quite inconsistent when treating vectors</span><span lang="EN-US">. Depending on the given expression it is interpreted as row vector or as column vector. This is very important when you multiply matrices.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">X:matrix([1,2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_109.png" width="112" height="28"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A.X;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_110.png" width="126" height="58"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">X.A;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_111.png" width="180" height="29"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">Y:matrix([1],[2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_112.png" width="92" height="56"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">Z:transpose(X);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_113.png" width="92" height="56"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">is(X=Y);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_114.png" width="124" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">is(Y=Z);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_115.png" width="114" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">A.Y;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_116.png" width="126" height="58"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">Y.A;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_117.png" width="622" height="42"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_118.png" width="114" height="21"></p> <h1><span lang="EN-US">4 Plotting</span> <a name="NODO28" id= "NODO28"></a></h1> <h2><span lang="EN-US">4.1 The commands plot2d and wxplot2d</span> <a name="NODO29" id="NODO29"></a></h2> <h4><span lang="EN-US">Plotting a function</span><a name="NODO30" id="NODO30"></a></h4> <p class="comment"><span lang="EN-US">In Maxima you can plot curves, surfaces ... by using the commands <b>plot2d</b>, plot3d, .... (see the Maxima manual, 12.3 Functions and Variables for Plotting).<br> The plot is shown in an <i>external window</i>, so when using "Cell > Evaluate all cells", all followingup calculations are suspended until you close the graph window.<br> In the graph window, you can use a crosshair to see the coordinates of points, rotate a 3d-graph and you can set some Options.<br> The graphs use by default Gnuplot, but you can change this behavior with the wxMaxima menu "Plot > Plot Format ...".<br> <br> The x range for the graph must be specified:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">plot2d([sin(x), cos(x)], [x,0, 2*%pi]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_119.png" width="74" height="21"></p> <p class="comment"><span lang="EN-US">If you use the prefix wx with this Maxima command, i.e. you use <b>wxplot2d</b>,<br> the graph is shown by default in the wxMaxima document.<br> When using the wMaxima menu "Plot > Plot2d", this command wxplot2d is used by default.<br> Moreover, the dialog box makes it possible to change some options and the format of the plot (inline, ...), so the graph can be shown in an external window (see the Maxima manual, 12.4 Plotting Options).</span></p> <p class="image"><i><span lang="EN-US">Figure 7: The Plot menu</span></i> <span lang="EN-US"><br></span><img border="0" alt= "Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_120.png" width="527" height="85"></p> <p class="image"><i><span lang="EN-US">Figure 8: Plot 2d dialog box</span></i> <span lang="EN-US"><br></span><img border="0" alt= "Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_121.png" width="482" height="298"></p> <h4><span lang="EN-US">Plotting more than one function</span><a name="NODO31" id="NODO31"></a></h4> <p class="comment"><span lang="EN-US">It is possible to <b>plot more than one function</b>:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x), cos(x)], [x,0, 2*%pi]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_122.png" width="574" height="325"></p> <h4><span lang="EN-US">Set size ratio, set zeroaxis in gnuplot_preamble</span><a name="NODO32" id="NODO32"></a></h4> <p class="comment"><span lang="EN-US">One of the options in this "Plot > Plot2d" menu sets the aspect ratio to 1 (i.e. you use the same units on the horizontal and vertical axis).<br> In the menu, at the same time the option "<b>Set zeroaxis</b>" is used.<br> Adding these details involves inserting a "<b>gnuplot_preamble</b>" which is a list of options not available directly in the wxplot2d command.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x), cos(x)], [x,0, 2*%pi],</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class="input1">[gnuplot_preamble, "set size ratio 1; "]</span><br> <span class="input1">);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_123.png" width="574" height="325"></p> <table style="WIDTH: 380.25pt" class="MsoNormalTable" border="0" cellpadding="0" width="507"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x), cos(x)], [x,0, 2*%pi],</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class="input1"><b>[gnuplot_preamble, "set size ratio 1; set zeroaxis;"]</b></span><br> <br> <span class="input1">);</span></span></p> </td> </tr> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"></td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"></td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_124.png" width="574" height="325"></p> <h4><span lang="EN-US">Labeling both the horizontal and vertical axis</span><a name="NODO33" id="NODO33"></a></h4> <p class="comment"><span lang="EN-US">As you probably noticed, the horizontal axis is labeled x. You should</span> <span style= "COLOR: red" lang="EN-US">label both the horizontal and the vertical axis</span><span lang="EN-US">. This can be done resp. by setting <b>xlabel</b> and <b>ylabel</b> using e.g. [xlabel, string], where string labels the horizontal (=first) axis and [ylabel, string], where string now labels the vertical (=second) axis.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x), cos(x)], [x,0, 2*%pi],</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> [gnuplot_preamble, "set size ratio 1; "],</span><br> <br> <span class= "input1"> [xlabel, "X"],</span><br> <span class= "input1"> [ylabel, "Y"]</span><br> <span class="input1">);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_125.png" width="574" height="325"></p> <h4><span lang="EN-US">More gnuplot_preamble options</span><a name= "NODO34" id="NODO34"></a></h4> <p class="comment"><span lang="EN-US">The "gnuplot_preamble" can also be used to show a grid, to move the legend and to set a title.<br> The key (legend) moves to the bottom left in the following example. It could be set at bottom center, bottom left, bottom right, left center, right center, and so forth.<br> Note the <b>syntax</b>. All Gnuplot options are part of a list, with gnuplot_preamble as the first item in this list. All options are between double quotation marks. Each item ends with a semicolon. Text entries are within single quotation marks.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x),cos(x)], [x,0, 2*%pi],</span></span> <span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> [xlabel, "X"], [ylabel, "Y"],</span><br> <span class= "input1"> [legend, "sin", "cos"],</span><br> <br> <span class= "input1"> [gnuplot_preamble,</span><br> <span class="input1">"</span><br> <span class= "input1"> <b>set grid;</b></span> <b><br> <span class= "input1"> set key bottom left;</span><br> <span class= "input1"> set title 'Two graphs'</span></b><span class="input1">;</span><br> <span class="input1">"</span><br> <span class= "input1"> ]</span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_126.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x), cos(x)], [x,0, 2*%pi],</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> [xlabel, "X"], [ylabel, "Y"],</span><br> <br> <span class= "input1"> [legend, "sin", "cos"],</span><br> <br> <span class= "input1"> [gnuplot_preamble, "<b>set size ratio 1</b>;</span><br> <span class= "input1"> set grid;</span><br> <span class= "input1"> set key bottom left;</span><br> <span class= "input1"> set title 'Two Graphs Aspectratio 1';"]</span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_127.png" width="574" height="325"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Style</span><a name="NODO35" id= "NODO35"></a></h4> <p class="comment"><span lang="EN-US">You can alter the appearance of continuous lines by by applying "style" and using the form [lines,[thickness,color]].<br> The first option, thickness, represents the thickness of the lines to be plotted.<br> The larger the value of this first parameter the larger the individual line thickness.<br> The second option, color, represents the color of the lines with default values:<br> <br> 1-blue 2-red 3-magenta 4-orange 5-brown 6-lime 7-aqua<br> <br> The sequence of colors repeat after the number 7, i.e., 8 will be blue, 9 red, etc.<br> <br> We illiustrate [style,[lines,1,2],[lines,3,4]]:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x), cos(x)], [x,0, 2*%pi],</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> <b> [style,[lines,1,2],[lines,3,4]]</b>,</span><br> <br> <span class= "input1"> [gnuplot_preamble, "set size ratio 1; "],</span><br> <br> <span class= "input1"> [xlabel, "X"], [ylabel, "Y"]</span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_128.png" width="574" height="325"></p> <h4><span lang="EN-US">Limiting the values on the vertical axis</span><a name="NODO36" id="NODO36"></a></h4> <p class="comment"><span lang="EN-US">If the functions grows too fast, it might be necessary to limit the values in the vertical axis using the y option.<br> Compare the following two examples:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d (sec(x), [x, -2, 2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_129.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d (sec(x), [x, -2, 2], <b>[y, -20, 20]</b>);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_130.png" width="574" height="347"></p> <h4><span lang="EN-US">Remarks on scale</span><a name="NODO37" id= "NODO37"></a></h4> <p class="comment"><span lang="EN-US">As above, one might want to control the y axis as well as the x axis.<br> Consider the following function, which draws a circle using two explicit functions.<br> The figure below raises two issues regarding the presentation of the functions, the question of scale and the definition of a legend to identify individual functions.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_131.png" width="782" height="369"></p> <p class="comment"><span lang="EN-US">Two aspects of this graph warrant concern. Most obviously, the "circle" looks decidedly non-spherical. Second, a legend has appeared, one that we might want to make more informative. A legend appears automatically whenever more than one function is being plotted.<br> The first problem relates to the fact that Maxima does not assume that x and y axis have the same units, and it stretches the figure so that the a centimeter along the vertical axis accounts for more units that a centimeter does along the horizontal axis.<br> To avoid this distortion, instruct wxplot2d to produce a square graph.<br> Another option for removing the distortion appears below.<br> To add content to the legend, add a legend option.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5],</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> [<b>legend</b>, "UpperSemiCircle", "LowerSemiCircle"]</span><br> <span class= "input1"> ),</span><br> <span class= "input1"> <b>wxplot_size=[400,400]</b>;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_132.png" width="782" height="469"></p> <p class="comment"><span lang="EN-US">Suppose we want a cleaner display. We could suppress the legend, as below.<br> Also, it is possible to make both halves of the circle having the same color.<br> Furthermore,we can remove the box around the circle and the information about units, as well as the axis labels (although this is not a good working style).</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5],</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> [legend, false],</span><br> <span class= "input1"> [box,false],</span><br> <span class= "input1"> [xlabel, ""], [ylabel, ""]),</span><br> <span class= "input1"> wxplot_size=[400,400];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_133.png" width="782" height="469"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5],</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> [legend, false],</span><br> <span class= "input1"> [box,false],</span><br> <span class= "input1"> [xlabel, "X"], [ylabel, "Y"]),</span><br> <span class= "input1"> wxplot_size=[400,400];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_134.png" width="782" height="469"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5],</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> [legend, false],</span><br> <br> <span class= "input1"> [xlabel, "X"], [ylabel, "Y"]),</span><br> <span class= "input1"> wxplot_size=[400,400];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_135.png" width="782" height="469"></p> <p class="comment"><span lang="EN-US">"Squaring" a display, can also be done by using the gnuplot_preamble "set size ratio 1".</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5],</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> [legend, false],</span><br> <span class= "input1"> [gnuplot_preamble, "set title 'Another way to make a circle appear spherical';</span><br> <span class= "input1"> set size ratio 1;"] );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_136.png" width="782" height="369"></p> <p class="comment"><span lang="EN-US">Using line styles, you can obtain the same colors for both semicircles:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sqrt(4-x^2),-sqrt(4-x^2)], [x,-2.5,2.5],[y,-2.5,2.5],</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> [style,[lines,4,1],[lines,4,1]],</span><br> <span class= "input1"> [legend, false], [xlabel, "X"], [ylabel, "Y"]),wxplot_size=[400,400];</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_137.png" width="782" height="469"></p> <p class="comment"><span lang="EN-US">Sometimes the plot does not show the horizontal axis:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x)+5], [x,0, 2*%pi]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_138.png" width="574" height="325"></p> <p class="comment"><span lang="EN-US">To resolve, use e.g. the y option:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x)+5], [x,0, 2*%pi],[y,0,6.5]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_139.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot2d([sin(x)+5], [x,0, 2*%pi],[y,0,6.5],</span></span><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">[gnuplot_preamble, "set size ratio 1; "]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_140.png" width="574" height="325"></p> <h2><span lang="EN-US">4.2 3-dimensional plots using (wx)plot3d</span> <a name="NODO38" id="NODO38"></a></h2> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><b><span lang= "EN-US">wxplot3d</span></b></span><span class="input1"><span lang= "EN-US">( x*y, [x,-2,2],[y,-2,2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_141.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxplot3d(x*y, [x,-2,2], [y,-2,2],</span></span><span style= "COLOR: blue" lang="EN-US"><br> <span class= "input1"> <b>[gnuplot_preamble, "set hidden3d"]</b>);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_142.png" width="574" height="325"></p> <p class="comment"><span lang="EN-US">If you want to insert a comment in an input cell, you can use<br> <b>/* */</b></span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><b><span lang="EN-US">/* This Maxima commands opens an external window.</span></b></span><b><span style="COLOR: blue" lang= "EN-US"><br> <span class="input1">By keeping the left mouse button pressed, you can rotate the graph.</span><br> <span class="input1">*/</span></span></b><span style="COLOR: blue" lang="EN-US"><br> <span class="input1">plot3d( x*y, [x,-2,2],[y,-2,2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_143.png" width="74" height="21"></p> <h2><span lang="EN-US">4.3 Contours (level curves)</span> <a name= "NODO39" id="NODO39"></a></h2> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><b><span lang= "EN-US">wxcontour_plot</span></b></span><span class= "input1"><span lang="EN-US">(x*y, [x,-2,2],[y,-2,2]);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_144.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxcontour_plot(x*y, [x,-2,2],[y,-2,2],</span></span><span style="COLOR: blue" lang= "EN-US"><br> <br> <span class= "input1"> [<b>legend,false]</b>,</span><br> <br> <span class= "input1"> <b>[gnuplot_preamble,"set cntrparam levels 9"]</b></span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_145.png" width="714" height="505"></p> <h2><span lang="EN-US">4.4 The package draw</span> <a name="NODO40" id="NODO40"></a></h2> <h4><span lang="EN-US">Packages</span><a name="NODO41" id= "NODO41"></a></h4> <p class="comment"><span lang="EN-US">Maxima provides a basic set of core commands and offers a variety of <b>add-on packages</b> for special tasks. This makes it possible to extend the capabilities of the system. Such packages are either automatically loaded on demand or the packages have to be explicitly loaded. For the latter we have to load the corresponding files by using "load(package)". The loaded functions are added to the list of user-defined functions and can be displayed and removed using "functions" and "kill(all)", respectively.<br> <br> To see a list of the packages available in Maxima, launch the <b>Maxima Manual</b> by using the menu item "Help > Maxima Help", and click on the Contents tab. Then, scroll down until you pass all the chapters that start with an upper-case letter. The Maxima packages correspond to those chapters that start with a lower-case letter.<br> <br></span></p> <h4><span lang="EN-US">‘draw’</span><a name="NODO42" id= "NODO42"></a></h4> <p class="comment"><span lang="EN-US">The abilities of Maxima’s plot command are restricted and do not satisfy all needs. Package 'draw' provides a more powerful and flexible plotting (and drawing) tool. However, it only supports the Gnuplot plotting routine, and as such draw is a Maxima–Gnuplot interface. Before you can use the package in Maxima it must be loaded by using "load(draw)" as described above.<br> When you use the corresponding wxMaxima command, the package is automatically loaded.<br> <br> See the Maxima manual:<br> 12. Plotting<br> 48.1 Introduction to draw.</span></p> <p class="image"><i><span lang="EN-US">Figure 9: The Help menu to view the Maxima manual</span></i> <span lang="EN-US"><br> </span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_146.png" width="580" height="222"></p> <p class="image"><i><span lang="EN-US">Figure 10: Information about the draw package in the Maxima manual</span></i> <span lang= "EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_147.png" width="1013" height="592"></p> <p class="comment"><span lang="EN-US">Remark: if you want to insert a comment in an input cell, you can use /* */</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">/* The following command must be given when using e.g. the draw command in Maxima.</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class="input1"> It is not needed when only using wxMaxima commands, in which case the command is</span><br> <span class="input1"> automatically loaded. */</span><br> <span class="input1"><b>load(draw)</b>;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_148.png" width="704" height="21"></p> <p class="comment"><span lang="EN-US">The Maxima command "draw()" plots a series of <b>scenes</b>; its arguments are <b>gr2d</b> and/or <b>gr3d </b>objects, which are 2- or 3-dimensional scenes,<br> together with some options, or lists of scenes and options.<br> If more than one scene is described, a multiplot will be generated.<br> If only one scene is build, then <b>draw2d</b>(...) and <b>draw3d</b>(...) can be used as these are equivalent to draw(gr2d(...)) and draw(gr3d(...)), respectively.<br> <br> Options for these functions (graphics options) are given as key=value pairs, e.g. <b>xaxis=true</b> or <b>xlabel="X"</b>.<br></span><span style="COLOR: red" lang= "EN-US"><br> Scenes in the gr2d and gr3d constructor are interpreted sequentially: graphic options affect those graphic objects placed on its right.</span><span lang="EN-US"><br> Some graphic options affect the global appearance of the scene and may be located at any position or given to the draw command (global options).</span></p> <p class="comment"><span lang="EN-US">Two dimensional scenes can be build by means of the gr2d scene constructor.<br> For plotting graphs of functions the following options are available:<br> <br> • <b>explicit</b>: the function is given in terms of the input values, e.g. f(x):=xˆ2.<br> <br> • <b>implicit</b>: the function is implicitly given by the solution of an equation of the form F(x, y) = 0, e.g, xˆ2+yˆ2-1=0.<br> <br> • <b>parametric</b>: the plotted curve is given as a path in a two dimensional space, e.g. [cos(t),sin(t)].<br> <br> Besides these there are some other graphic objects for adding lines or annotating graphs.<br> <br> <b>explicit(fcn,var,minval,maxval)</b> plots an explicit function fcn, with variable var taking values from minval to maxval:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><b><span lang= "EN-US">wxdraw(</span></b></span> <span class= "input1"><b><span style="COLOR: red" lang= "EN-US">gr2d</span></b></span> <span class="input1"><span style= "COLOR: red" lang="EN-US">(</span></span> <span class= "input1"><span lang="EN-US">explicit(x^2,x,-1,3)</span></span> <span class="input1"><span style="COLOR: red" lang= "EN-US">)</span></span> <span class="input1"><span lang= "EN-US"><b>)</b>;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_149.png" width="574" height="325"></p> <p class="comment"><span lang="EN-US">draw2d is the same as draw(gr2d). In wxMaxima the corresponding is true for wxdraw2d:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><b><span lang= "EN-US">wxdraw2d</span></b></span><span class="input1"><span lang= "EN-US">( explicit(x^2,x,-1,3) );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_150.png" width="574" height="325"></p> <h4><span lang="EN-US">Global and local options</span><a name= "NODO43" id="NODO43"></a></h4> <p class="comment"><span lang="EN-US">You can use lots of options:<br> xrange=[-1,3], yrange=[-1,10] are <b>global options</b>;<br> color=green, line_width = 5 are <b>local options</b>.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw2d( xlabel="X",</span></span><span style= "COLOR: blue" lang="EN-US"><br> <span class= "input1"> ylabel="Y",</span><br> <span class= "input1"> xrange=[-1,3],</span><br> <span class= "input1"> yrange=[-1,10],</span><br> <br> <span class= "input1"> color=green,</span><br> <span class= "input1"> line_width = 5,</span><br> <span class= "input1"> explicit(x^2,x,-1,3) );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_151.png" width="574" height="325"></p> <p class="comment"><b><span lang="EN-US">Options are applied to the graphic objects to the right of the option</span></b><span lang= "EN-US">:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw2d( xlabel="X",</span></span><span style= "COLOR: blue" lang="EN-US"><br> <span class= "input1"> ylabel="Y",</span><br> <span class= "input1"> xrange=[-1,3],</span><br> <span class= "input1"> yrange=[-1,10],</span><br> <span class= "input1"> xaxis=true,</span><br> <span class= "input1"> yaxis=true,</span><br> <br> <span class= "input1"> color=green,</span><br> <span class= "input1"> line_width = 5,</span><br> <span class= "input1"> explicit(x^2,x,-1,4),</span><br> <br> <span class= "input1"> color=blue,</span><br> <span class= "input1"> line_width = 3,</span><br> <span class= "input1"> explicit(4-2*x,x,0,2)</span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_152.png" width="574" height="325"></p> <p class="comment"><span lang="EN-US">If you use more than one gr2d, the plots are placed in one column by default:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw(</span></span> <span style="COLOR: blue" lang= "EN-US"><br> <span class= "input1"> gr2d(color=green,</span><br> <span class= "input1"> line_width = 5,</span><br> <span class= "input1"> explicit(x^2,x,-1,4)) ,</span><br> <br> <span class= "input1"> gr2d(color=blue,</span><br> <span class= "input1"> line_width = 3,</span><br> <span class= "input1"> explicit(4-2*x,x,0,2))</span><br> <br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_153.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw(</span></span> <span style="COLOR: blue" lang= "EN-US"><br> <span class= "input1"> gr2d(color=green,</span><br> <span class= "input1"> line_width = 5,</span><br> <span class= "input1"> xlabel="X",ylabel="Y",</span><br> <span class= "input1"> explicit(x^2,x,-1,4)) ,</span><br> <br> <span class= "input1"> gr2d(color=blue,</span><br> <span class= "input1"> line_width = 3,</span><br> <span class= "input1"> explicit(4-2*x,x,0,2)),</span><br> <br> <span class= "input1"> <b>columns=2</b></span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_154.png" width="574" height="325"></p> <h4><span lang="EN-US">Contour plotting using ‘draw’</span><a name= "NODO44" id="NODO44"></a></h4> <p class="comment"><span lang="EN-US">This package also facilitates contour plotting in 3-D:</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw3d( <b>enhanced3d = true</b>,</span></span><span style="COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> explicit(x*y, x,-2,2, y,-2,2),</span><br> <br> <span class= "input1"> <b>contour=both</b>,</span><br> <span class= "input1"> <b>contour_levels=9</b></span><br> <span class= "input1"> );</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_155.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw3d( enhanced3d = true,</span></span><span style= "COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> <b>xlabel="X",ylabel="Y",zlabel="Z",</b></span><b><br> <span class= "input1"> xtics=1,ytics=1,ztics=2,</span></b><br> <span class= "input1"> explicit(x*y,x,-2,2,y,-2,2),</span><br> <br> <span class= "input1"> contour = both,</span><br> <span class= "input1"> contour_levels = 9,</span><br> <br> <span class= "input1"> surface_hide = true,</span><br> <br> <span class= "input1"> <b>colorbox=false</b></span><br> <br> <span class= "input1"> ) ;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_156.png" width="574" height="325"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw3d(enhanced3d = true,</span></span><span style= "COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> xlabel="X",ylabel="Y",zlabel="Z",</span><br> <span class= "input1"> xtics=1,ytics=1,ztics=2,</span><br> <span class= "input1"> explicit(x*y,x,-2,2,y,-2,2),</span><br> <span class= "input1"> contour = both,</span><br> <br> <span class= "input1"> <b>contour_levels = {-3, -2, -1, 0, 1, 2,3},</b></span><br> <br> <span class= "input1"> surface_hide = true,</span><br> <br> <span class= "input1"> colorbox=false) $</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_157.png" width="574" height="302"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw3d(enhanced3d = true,</span></span><span style= "COLOR: blue" lang="EN-US"><br> <br> <span class= "input1"> xlabel="X",ylabel="Y",zlabel="Z",</span><br> <span class= "input1"> xtics=1,ytics=1,ztics=2,</span><br> <span class= "input1"> explicit(x*y,x,-2,2,y,-2,2),</span><br> <span class= "input1"> contour = both,</span><br> <br> <span class= "input1"> <b>contour_levels = [-3, 1, 3]</b>,</span><br> <br> <span class= "input1"> surface_hide = true,</span><br> <br> <span class= "input1"> colorbox=false) $</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_158.png" width="574" height="302"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw3d( <b>user_preamble="unset key"</b>,</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> enhanced3d = true,</span><br> <span class= "input1"> xlabel="X",ylabel="Y",zlabel="Z",</span><br> <span class= "input1"> xtics=1,ytics=1,ztics=2,</span><br> <span class= "input1"> explicit(x*y,x,-2,2,y,-2,2),</span><br> <span class= "input1"> contour = both,</span><br> <span class= "input1"> contour_levels = [-3, 1, 3],</span><br> <br> <span class= "input1"> surface_hide = true,</span><br> <span class= "input1"> colorbox=false) $</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_159.png" width="574" height="302"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">wxdraw3d( user_preamble="unset key",</span></span><span style="COLOR: blue" lang="EN-US"><br> <span class= "input1"> enhanced3d = true,</span><br> <span class= "input1"> xlabel="X",ylabel="Y",zlabel="Z",</span><br> <span class= "input1"> xtics=1,ytics=1,ztics=2,</span><br> <span class= "input1"> explicit(x*y,x,-2,2,y,-2,2),</span><br> <span class= "input1"> contour = both,</span><br> <span class= "input1"> contour_levels = [-3, 1, 3],</span><br> <br> <span class= "input1"> surface_hide = true,</span><br> <span class= "input1"> colorbox=false,</span><br> <span class= "input1"> <b>xyplane=0</b> ) $</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_160.png" width="574" height="302"></p> <h1><span lang="EN-US">5 Menu and Panes</span> <a name="NODO45" id= "NODO45"></a></h1> <p class="comment"><span lang="EN-US">Some common (wx)Maxima commands are available through Maxima, Equations, Algebra, Calculus, Simplify, Plot and Numeric menus. All menu entries ending with '...' will open a dialog, to help you formulate the command. The resulting command will be inserted at horizontal cursor's position or below the currently active cell. The command will also be evaluated.</span></p> <p class="image"><i><span lang="EN-US">Figure 11: The wxMaxima menu options</span></i> <span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_161.png" width="461" height="47"></p> <p class="comment"><span lang="EN-US">An optional button panel can be shown in the wxMaxima window using Maxima > Panes. It works in a similar manner as the menus.</span></p> <p class="image"><i><span lang="EN-US">Figure 12: Show or hide Button Pannels</span></i> <span lang="EN-US"><br> </span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_162.png" width="461" height="281"></p> <p class="image"><i><span lang="EN-US">Figure 13: The Statistics and General Math panes</span></i> <span lang="EN-US"><br> </span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_163.png" width="189" height="634"></p> <p class="comment"><span lang="EN-US">Note also that if you have a selection before you use a button panel command or a menu command, that selection will be used as the main<br> (or only) argument to the command. Selection of a previous output or part of an input will work in a similar manner.</span></p> <h1><span lang="EN-US">6 Some caveats</span> <a name="NODO46" id= "NODO46"></a></h1> <h4><span lang="EN-US">Syntax</span><a name="NODO47" id= "NODO47"></a></h4> <p class="comment"><span lang="EN-US">The <b>common arithmetic operations</b> are<br> <br> + addition<br> <br> - subtraction<br> <br> * scalar multiplication<br> <br> / division<br> <br> ^ or ** exponentiation<br> <br> . matrix multiplication<br> <br> and <b>some functions</b> are<br> <br> sqrt square root<br> <br> sin sine<br> cos cosine<br> tan tangent<br> cot cotangent<br> sec secant<br> csc cosecant<br> <br> asin inverse sine<br> acos inverse cosine<br> atan inverse tangent<br> acot inverse cotangent<br> asec inverse secant<br> acsc inverse cosecant<br> <br> exp exponential<br> log natural logarithm<br> <br> sinh hyperbolic sine<br> cosh hyperbolic cosine<br> tanh hyperbolic tangent<br> asinh hyperbolic asin<br> acosh hyperbolic acos<br> atanh hyperbolic atan<br> <br> floor integer below<br> ceiling integer above<br> fix integer part<br> <br> float convert to floating point<br> <br> abs absolute value</span></p> <h4><span lang="EN-US">Output</span><a name="NODO48" id= "NODO48"></a></h4> <p class="comment"><b><span lang="EN-US">Maxima's output is characterized by exact (rational) arithmetic.</span></b><span lang= "EN-US"><br> If irrational numbers are involved in a computation, they are kept in symbolic form.<br> However, it is often useful to express a result in decimal notation. This may be accomplished by following the expression you want expanded by "<b>,numer</b>". You can also use "<b>float</b>". Both give by default 16 significant figures, of which the last is often unreliable.<br> <br> However, Maxima can offer arbitrarily high precision by using the <b>bfloat</b> function.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">5*sqrt(2) + 41;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_164.png" width="153" height="23"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">5*sqrt(2) + 41 ,numer;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_165.png" width="244" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(5*sqrt(2) + 41);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_166.png" width="244" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">bfloat(5*sqrt(2) + 41);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_167.png" width="264" height="20"></p> <p class="comment"><span lang="EN-US">Remember:<br> <br> %pi; (this is how to identify the number "pi" to Maxima,<br> this will appear as a Greek letter only if a Greek font has been installed)<br> <br> float(%pi); (means "give me the numerical value")<br> <br> bfloat(): converts all numbers and functions of numbers in expr to bigfloat numbers.<br> <br> The number of significant digits in the resulting bigfloats is specified by the global variable <b>fpprec</b>.<br> <br> fpprec:1000; (increase the "floating point precision" or "fpprec")<br> fpprec is the number of significant digits for arithmetic on bigfloat numbers (default 16).<br> fpprec does not affect computations on ordinary floating point numbers.<br> <br> <b>set_display(ascii);</b> (this is a special wxMaxima setting that forces all the digits to be printed out)<br> <br> <b>set_display(xml);</b> (return to the default way of displaying things)<br> <br> The "fpprec" and "set_display(ascii)" settings only affect floating-point numbers, integers are always printed out fully.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">%pi;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_168.png" width="83" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(%pi);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_169.png" width="244" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">bfloat(%pi);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_170.png" width="264" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">fpprec:1000;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_171.png" width="114" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">bfloat(%pi);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_172.png" width="794" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">set_display(ascii);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_173.png" width="422" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">bfloat(%pi);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_174.png" width="792" height="284"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">set_display(xml);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_175.png" width="104" height="21"></p> <p class="comment"><span lang="EN-US">Remember:<br> <br> If you want to list all the digits of a floating-point value, use "set_display(ascii);".<br> If you want wxMaxima to render equations and functions in a pretty way, use "set_display(xml);".<br> <br> Use fpprec to set 'big float precision'.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">fpprec:16;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_176.png" width="94" height="20"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">The natural logarithm log()</span><a name= "NODO49" id="NODO49"></a></h4> <p class="comment"><span style="COLOR: red" lang="EN-US">Maxima only offers the natural logarithm function "<b>log</b>"</span><span lang="EN-US">. So do not use "ln".</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">log(10);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_177.png" width="139" height="22"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(log(10));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_178.png" width="244" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">log(%e);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_179.png" width="84" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ln(%e);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_180.png" width="129" height="22"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">float(ln(%e));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_181.png" width="279" height="22"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">log(%e^2)/log(%e);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_182.png" width="84" height="20"></p> <p class="comment"><span lang="EN-US">log10 is not available by default but you can define it yourself as shown below, although some results like log10(100) can be simplified.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1">log10(x):= log(x)/log(10);</span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><br> <img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_183.png" width="235" height="47"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">log10(10);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_184.png" width="84" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">log10(100);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_185.png" width="143" height="46"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ratsimp(log10(100));</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_186.png" width="143" height="46"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">kill(all);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_187.png" width="114" height="21"></p> <p class="comment"><span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt" lang="EN-US">Reserved Words</span></span><span lang="EN-US"><br> ==============<br> The following are reserved words in Maxima and cannot be used as variable names:<br> <br> integrate next from diff in at limit sum for<br> and else if then else do or if unless<br> product while thru step</span></p> <h1><span lang="EN-US">7 Help</span> <a name="NODO50" id= "NODO50"></a></h1> <h4><span lang="EN-US">F1</span><a name="NODO51" id= "NODO51"></a></h4> <p class="comment"><span lang="EN-US">The menu has an option 'Help'.</span></p> <p class="comment"><span lang="EN-US">To get help on any function, just click on the function name and press F1. Try it for the following examples.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">solve(3*x+2=0, x);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_188.png" width="145" height="42"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">log(2);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_189.png" width="129" height="22"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">fpprec;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_190.png" width="94" height="20"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">ln(2);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_191.png" width="119" height="22"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">“? name”</span><a name="NODO52" id= "NODO52"></a></h4> <p class="comment"><span lang="EN-US">To get help with a name used by Maxima, just type "<b>? name</b>" or "describe(name)".<br></span><span style="COLOR: red" lang= "EN-US">Do not forget the space between ? and solve</span> <span lang="EN-US">!!!!!</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">? solve;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">“?? name”</span><a name="NODO53" id= "NODO53"></a></h4> <p class="comment"><span lang="EN-US">If you only know part of the name, just type "<b>?? name</b>".<br> Maxima gives you a choice list: you need to make a selection.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">?? solve;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_193.png" width="682" height="550"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">“apropos(name)”</span><a name="NODO54" id= "NODO54"></a></h4> <p class="comment"><span lang="EN-US">If you turn the part of the name you know into a string , and use apropos(), you get a list of Maxima names which have appearing anywhere within them.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">apropos("solve");</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_194.png" width="792" height="89"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang="EN-US">? apropos;</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_195.png" width="712" height="438"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">'example()'</span><a name="NODO55" id= "NODO55"></a></h4> <p class="comment"><span lang="EN-US">Some examples can be obtained using 'example':<br> <br> 'example (<topic>)' displays some examples of <topic>, which is a symbol or a string. To get examples for operators like 'if', 'do', or 'lambda' the argument must be a string, e.g. 'example ("do")'.<br> 'example' is not case sensitive. Most topics are function names.<br> <br> 'example()' returns the list of all recognized topics.</span></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">example(solve);</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_196.png" width="682" height="1003"></p> <table class="MsoNormalTable" border="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="prompt1"><span lang= "EN-US">--></span></span></p> </td> <td style= "PADDING-BOTTOM: 2.85pt; PADDING-LEFT: 2.85pt; PADDING-RIGHT: 2.85pt; PADDING-TOP: 2.85pt" valign="top"> <p class="MsoNormal"><span class="input1"><span lang= "EN-US">example();</span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_197.png" width="798" height="412"></p> <h1><span lang="EN-US">8 Configuration options</span> <a name= "NODO56" id="NODO56"></a></h1> <p class="comment"><span lang="EN-US">The menu '<b>Edit > Configure</b>' leads to a dialog box in which you can change some options and styles.</span></p> <p class="image"><i><span lang="EN-US">Figure 14: Edit > Configure</span></i> <span lang="EN-US"><br></span><img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_198.png" width="290" height="348"></p> <p class="comment"><span lang="EN-US">In particular, the following options can be changed:<br> if you want to change the behaviour of 'Shift+Enter' to evaluate a cell in wxMaxima to 'Enter',<br> check '<b>Enter evaluates cells</b>'. This switches the roles of these two key commands,<br> if you do not like the default behaviour where matching parentheses are automatically inserted,<br> uncheck '<b>Match parenthesis in text controls</b>'.</span></p> <p class="image"><i><span lang="EN-US">Figure 15: Configuration Options<br></span></i> <img border="0" alt="Result" src= "../../../../../Cursus2012/Ba2_Opbel/wxMaxima/wxmx_html/CHMproce/wxMaxima_intro_img/wxMaxima_intro_199.png" width="606" height="487"></p> <h1><span lang="EN-US">9 Further reading</span> <a name="NODO57" id="NODO57"></a></h1> <p class="comment"><span lang="EN-US">At<br> <a href= "http://statmath.wu.ac.at/~leydold/maxima/" target= "_blank">http://statmath.wu.ac.at/~leydold/maxima/</a><br> you should download and study the tutorial by <i>Josef Leydold</i> and <i>Martin Petry</i>. See the links at this page for:<br> a pdf file MaximaSkript.pdf using the link<br> Introduction to Maxima for Economics (<a href= "http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript.pdf" target= "_blank">http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript.pdf</a>),<br> a wxMaxima notebook with all examples from the Introduction to Maxima for Economics (<a href= "http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript.wxm" target= "_blank">http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript.wxm</a>)<br> and the Maxima code for answers to the exercises (<a href= "http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript-sol.wxm">http://statmath.wu.ac.at/~leydold/maxima/MaximaSkript-sol.wxm</a>).<br> <br> See also the links to examples on:<br> <a href="http://math.hawaii.edu/wxmaxima/" target="_blank">http://math.hawaii.edu/wxmaxima/</a><br> <br> and the Maxima book by <i>Gilberto E. Urroz</i><br> (a comprehensive overview, each chapter organized by mathematical area):<br> <a href= "http://www.neng.usu.edu/cee/faculty/gurro/Maxima.html" target= "_blank">http://www.neng.usu.edu/cee/faculty/gurro/Maxima.html</a><br> <br> For more information on plotting and graphics, see<br> <a href= "http://www.austromath.at/daten/maxima/zusatz/Graphics_with_Maxima.pdf" target= "_blank">http://www.austromath.at/daten/maxima/zusatz/Graphics_with_Maxima.pdf</a><br> and <i>Mario Rodríguez Riotorto</i>'s site:<br> <a href= "http://riotorto.users.sourceforge.net/index.html" target= "_blank">http://riotorto.users.sourceforge.net/index.html</a> ,<br> <a href= "http://riotorto.users.sourceforge.net/gnuplot/func2d/index.html" target= "_blank">http://riotorto.users.sourceforge.net/gnuplot/func2d/index.html</a> .<br> <br> A somewhat older but very good description of Maxima’s capabilities can be found<br> at the site of <i>Edwin Woollet</i>:<br> <a href="http://www.csulb.edu/~woollett/" target="_blank">http://www.csulb.edu/~woollett/</a><br> and in the Maxima book by <i>P. de Souza, R. Fateman, J. Moses, C. Yapp</i><br> <a href= "http://maxima.sourceforge.net/docs/maximabook/maximabook-19-Sept-2004.pdf" target= "_blank">http://maxima.sourceforge.net/docs/maximabook/maximabook-19-Sept-2004.pdf</a> .</span></p> <div style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <hr align="center" size="2" width="100%"></div> <p style="MARGIN-BOTTOM: 12pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 10pt" lang="EN-US">Created with</span> <span lang="EN-US"><a href= "http://wxmaxima.sourceforge.net/"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 10pt">wxMaxima</span></a></span><span style="LINE-HEIGHT: 115%; FONT-SIZE: 10pt" lang="EN-US">.</span> <span lang="EN-US"><br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br></span></p> </div> <!-- And the content tree: --> <ul id="contentsTree" class="contentTree"> <li><a href="1.htm#NODO0">Maxima is a CAS</a></li> <li><a href="1.htm#NODO1">1 First meetings in (wx)Maxima's universe</a> <ul> <li><a href="1.htm#NODO2">wxMaxima is a GUI to Maxima</a></li> <li><a href="1.htm#NODO3">Evaluate by Shift+Enter</a></li> <li><a href="1.htm#NODO4">Variables and functions</a></li> </ul> </li> <li><a href="1.htm#NODO5">2 Editing and saving</a></li> <li><a href="1.htm#NODO6">3 Symbolical and numerical math</a> <ul> <li><a href="1.htm#NODO7">3.1 Solving equations</a> <ul> <li><a href="1.htm#NODO8">Solve</a></li> <li><a href="1.htm#NODO9">Assigning labels</a></li> <li><a href="1.htm#NODO10">The function “is()”</a></li> <li><a href="1.htm#NODO11">Lists</a></li> </ul> </li> <li><a href="1.htm#NODO12">3.2 Numerical versus exact solutions</a> <ul> <li><a href="1.htm#NODO13">allroots()</a></li> <li><a href="1.htm#NODO14">realroots()</a></li> <li><a href="1.htm#NODO15">Real number results may seem to be complex numbers</a></li> <li><a href="1.htm#NODO16">reset()</a></li> <li><a href="1.htm#NODO17">Remark</a></li> </ul> </li> <li><a href="1.htm#NODO18">3.3 Solving sytems of equations</a> <ul> <li><a href="1.htm#NODO19">solve()</a></li> <li><a href="1.htm#NODO20">No solutions</a></li> <li><a href="1.htm#NODO21">Infinitely many solutions</a></li> <li><a href="1.htm#NODO22">Remark</a></li> </ul> </li> <li><a href="1.htm#NODO23">3.4 Linear algebra</a> <ul> <li><a href="1.htm#NODO24">matrix() and 'Algebra > Enter matrix...'</a></li> <li><a href="1.htm#NODO25">Calculations with matrices: invert() and "."</a></li> <li><a href="1.htm#NODO26">Components of a matrix</a></li> <li><a href="1.htm#NODO27">Inconsistency when working with vectors</a></li> </ul> </li> </ul> </li> <li><a href="1.htm#NODO28">4 Plotting</a> <ul> <li><a href="1.htm#NODO29">4.1 The commands plot2d and wxplot2d</a> <ul> <li><a href="1.htm#NODO30">Plotting a function</a></li> <li><a href="1.htm#NODO31">Plotting more than one function</a></li> <li><a href="1.htm#NODO32">Set size ratio, set zeroaxis in gnuplot_preamble</a></li> <li><a href="1.htm#NODO33">Labeling both the horizontal and vertical axis</a></li> <li><a href="1.htm#NODO34">More gnuplot_preamble options</a></li> <li><a href="1.htm#NODO35">Style</a></li> <li><a href="1.htm#NODO36">Limiting the values on the vertical axis</a></li> <li><a href="1.htm#NODO37">Remarks on scale</a></li> </ul> </li> <li><a href="1.htm#NODO38">4.2 3-dimensional plots using (wx)plot3d</a></li> <li><a href="1.htm#NODO39">4.3 Contours (level curves)</a></li> <li><a href="1.htm#NODO40">4.4 The package draw</a> <ul> <li><a href="1.htm#NODO41">Packages</a></li> <li><a href="1.htm#NODO42">‘draw’</a></li> <li><a href="1.htm#NODO43">Global and local options</a></li> <li><a href="1.htm#NODO44">Contour plotting using ‘draw’</a></li> </ul> </li> </ul> </li> <li><a href="1.htm#NODO45">5 Menu and Panes</a></li> <li><a href="1.htm#NODO46">6 Some caveats</a> <ul> <li><a href="1.htm#NODO47">Syntax</a></li> <li><a href="1.htm#NODO48">Output</a></li> <li><a href="1.htm#NODO49">The natural logarithm log()</a></li> </ul> </li> <li><a href="1.htm#NODO50">7 Help</a> <ul> <li><a href="1.htm#NODO51">F1</a></li> <li><a href="1.htm#NODO52">“? name”</a></li> <li><a href="1.htm#NODO53">“?? name”</a></li> <li><a href="1.htm#NODO54">“apropos(name)”</a></li> <li><a href="1.htm#NODO55">'example()'</a></li> </ul> </li> <li><a href="1.htm#NODO56">8 Configuration options</a></li> <li><a href="1.htm#NODO57">9 Further reading</a></li> </ul>
