interfaces/xmaxima/intro.html

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   7                  <h1 align=center>Maxima Primer</h1>
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   9 <body  BGCOLOR=#ffffff TEXT=#000000 LINK=#244C21>
  10
  11
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  13 <p>Maxima is a computer program for doing mathematics calculations,
  14 symbolic manipulations, numerical computations and graphics.
  15 Procedures can be programmed and then run by Maxima to
  16 do complex tasks.  Much of the syntax for other languages such as
  17 Maple was copied from Maxima.</p>
  18
  19 <h2>Project and documentation links</h2>
  20 <p>The <em>Help</em> menu in Xmaxima gives you access to the following documents:</p>
  21 <ul>
  22 <li>Maxima reference manual</li>
  23 <li>Xmaxima reference manual</li>
  24 <li>Maxima home page, https://maxima.sourceforge.io</li>
  25 <li>Maxima project page, https://sourceforge.net/projects/maxima</li>
  26 </ul>
  27
  28 <h2>Getting started</h2>
  29
  30 <p>To do basic operations, a line is typed, followed by a
  31 semicolon, and then entered.  This can be done in the window above.
  32 Alternately you may edit the blue portions in this buffer, and click
  33 on them, to see the result evaluated above and/or inserted in
  34 this window, depending on what was specified in the html source for this
  35 file.
  36 For example clicking below
  37 <br>
  38 <ul><li>
  39 <eval program=maxima doinsert=0
  40 >integrate(1/(1+x^3),x)</eval>
  41 </ul>
  42 You may double click the above formula, and the integral will be substituted into the Maxima evaluation in the other window.
  43
  44 There are <a href="examples.html">examples</a> which you may also look at
  45 <a href="plotmaxima.html">3d plotting </a>
  46 If you wish to have your plots appear in a separate window, go to the
  47 preferences button under file, and select separate.
  48 You may also go to the <http://www.ma.utexas.edu/users/wfs/netmath/netmath.html>
  49 netmath page </a> to see some more capabilities.
  50
  51
  52 <p>Here are some examples from basic calculus.  To have Maxima
  53 evaluate the derivative of the function below, click on this line.
  54 <ul><li>
  55 <eval program=maxima doinsert=1> diff(cos(x),x);</eval> returns <result modified>result</result>.
  56 </ul>
  57
  58 <p>Maxima can calculate <b>indefinite integrals</b>.
  59 <ul>
  60 <li><eval program=maxima doinsert=1> integrate( x/(1+x^3),x );</eval> returns <result modified>result</result>
  61
  62 <li>...and definite integrals with respect to x from 0 to 1.
  63 <br><eval program=maxima doinsert=1> integrate( 1/(1+x^2), x,  0, 1 ); </eval> returns <result modified>result</result>
  64 <li><eval program=maxima doinsert=0> plot2d(sin(x),[x,0,2*%pi])</eval>
  65 <li><eval program=maxima doinsert=0> plot3d(x^2-y^2,[x,-2,2],[y,-2,2],[grid,12,12])</eval>
  66 </ul>
  67 <ul>
  68 <li>Also, limits can be evaluated as x goes to infinity:
  69 <br><eval program=maxima doinsert=1> limit( (2*x+1)/(3*x+2),  x,inf );</eval> produces <result modified>result</result>
  70
  71 <li><eval program=maxima doinsert=1> limit( sin(3*x)/x,  x,0);</eval> evaluates to <result modified>result</result>
  72 </ul>
  73
  74 <p>Maxima can perform calculations to arbitrary precision.  The
  75 following example computes Pi to one hundred decimal places.
  76 <ul><li><eval program=maxima doinsert=1>block([fpprec:100],bfloat(%pi))</eval> yields <result modified>result</result>
  77 if we took sin of this we would get 0 to to within 100 decimal places..
  78 <li><eval program=maxima doinsert=1>block([fpprec:100],sin(bfloat(%pi)))</eval> gives <result modified>result</result>
  79
  80 <p>Maxima can solve equations.  Click this line to solve the system.
  81 <li><eval program=maxima doinsert=1> solve([x+y+z=5,3*x-5*y=10,y+2*z=3],[x,y,z]);</eval> returns <result modified>result</result>
  82
  83 <li><eval program=maxima doinsert=1> solve(x^2-5*x+6 =0,x);</eval> produces <result modified>result</result>
  84 </ul>
  85 <h5>Linear Algebra</h5>
  86 <p>
  87 For example, matrices can be
  88 entered and manipulated.  Click these two lines.
  89 <ul>
  90 <li><eval program=maxima doinsert=1> A:matrix([1,2],[3,4]);</eval> gives <result modified>result</result>
  91
  92
  93 <li><eval program=maxima doinsert=1> B:matrix([1,1],[1,1]);</eval> gives <result modified>result</result>
  94
  95 <p>The matrices can then be added, for example:
  96 <li><eval program=maxima doinsert=1>  A + B ;</eval> returns the sum <result modified>result</result>
  97
  98 ...and multiplied.
  99 <li><eval program=maxima doinsert=1>  A . B ;</eval> gives the product<result modified>result</result>
 100
 101
 102 <li><eval program=maxima doinsert=1>  A^^-1</eval> evaluates to the inverse: <result modified>result</result>
 103
 104 <li><eval program=maxima doinsert=1>determinant(matrix([a,b],[c,d]))</eval> gives <result modified>result</result>
 105 <li><eval program=maxima doinsert=0
 106 >      Fib[0] : 0;
 107        Fib[1] : 1;
 108        Fib[n] := Fib[n-1] + Fib[n-2];
 109 </eval>
 110 </ul>
 111 Then the procedure can be called. <eval program=maxima doinsert=1> Fib[8];</eval> gives <result>21</result>
 112
 113
 114 <p>Maxima can solve ordinary differential equations analytically and numerically.  Click the
 115 following line for an example of an analytic solution.
 116
 117
 118 <ul><li>
 119 <eval program=maxima doinsert=1>ode2('diff(y,x)+3*x*y = sin(x)/x,  y,x)</eval> returns <result modified>result</result>
 120 <li><eval program=maxima doinsert=1>ode2('diff(y,x) -y = 1, y,x)</eval> returns <result modified>result</result>
 121 <li>
 122 <eval program=maxima doinsert=1> ode2('diff(y,x,2) - y = 1, y,x)</eval> gives <result modified>result</result>
 123 </ul>
 124
 125 <h4 align=left>Defining a Function</h4>
 126
 127
 128   <p>The standard form is
 129
 130 <ul>
 131 <li>
 132 <eval program=maxima doinsert=1>f(3)</eval> gives <result>f(3)</result>
 133
 134 <li>
 135 <eval program=maxima doinsert=0>f(x):=x+2</eval>
 136 <li>now     <eval program=maxima doinsert=1>f(3)</eval> gives <result>5</result>
 137 </ul>
 138 <p>Local variables:
 139
 140 <p>The <b>block</b>  construct lets us introduce local variables, and also lets
 141 us have a sequence of statements:
 142
 143     <pre>block([v1:val1,v2:val2,v3,v4:val4],stmt1,stmt2,... stmtn)</pre>
 144 the value is the value of the last statement.   During the execution the
 145 variables v1,v2,... will have the values indicated.   If no value is given
 146 for v3 then it will just evaluate to itself:
 147
 148 <p>Thus if we set v3 globally to be 7,
 149 <ul><li><eval program=maxima doinsert=1>v3:7</eval> produces <result>7</result>
 150 <li> , then <eval program=maxima doinsert=1>block([v3],v3)</eval> gives <result>v3</result>.
 151  </ul>
 152 An example in a function:
 153
 154 <ul>
 155 <li><eval program=maxima doinsert=0>g(x):=block([u:x+3,w], u:u^2, w:(y+2)^2, u+w);</eval>
 156
 157
 158
 159 <li><eval program=maxima doinsert=1>g(2)</eval> yields <result><pre>
 160                                         2
 161                                  (y + 2)  + 25
 162 </pre></result>
 163 Using <b>if</b>:
 164
 165
 166
 167 <li><eval program=maxima doinsert=0>h(x):=block([u:x+3,w], u:u^2,
 168               if (u&lt;3) then  w:(y+2)^2 else w:(y+2)^2+1,
 169               u+w);
 170 </eval>
 171
 172
 173
 174 <li><eval program=maxima doinsert=1>[h(3),h(2)]</eval> gives <result><pre>
 175                                 2              2
 176                         [(y + 2)  + 37, (y + 2)  + 26]
 177 </pre></result>
 178
 179   </ul>
 180 Using for:
 181
 182
 183 <ul>
 184 <li><eval program=maxima doinsert=1> block([w:0], for i:1 thru 10 do (w:w+i^2))</eval> gives <result>done</result>
 185 </ul>
 186 <p>a for loop always returns 'done as its value.  To get the value you want
 187 add the w.
 188
 189
 190 <ul>
 191 <li><eval program=maxima doinsert=1> block([w:0], for i:1 thru 10 do (w:w+i^2),w)</eval> gives <result>385</result>
 192 </ul>
 193
 194 The function <b>describe(</b><i>s</i><b>)</b>
 195 returns documentation on all functions whose names include the string <i>s</i>.
 196 For example, if the string is "log",
 197 <br><eval program=maxima doinsert=1>describe("log");all</eval> prints <result modified>this output</result>