maxima-aez-notes

Maxima uses Gnuplot for plotting; n.b. the use of $ to show the plot!

plot2d(sin(x), [x,0,2%pi])$

There is an example of how to save a figure in Problem 5.

plot2d([discrete, [1,2,3,4], [2,-3,4,-5]], [style, points])$

• "Most things in Maxima are expressions."
• A comma expression is a sequence of expressions which evaluates to the value of the last one. The syntax is (<exp_1>, <exp_2>, ..., <exp_n>).
• "By default, function names are verbs." I do not understand the significance of nouns and verbs in Maxima.
• There is an automatic simplifier, but you can guide it with functions such as tellsimp.

The block allows you to have local variables, similar to a let or where in Haskell. The first argument should be a list of the variable names that will be local to this expression. The following demonstrates the usage:

print(block([a,b],a:1,b:2,[a+b,numberp(a)]));
print(numberp(a));

: [3, true]
: false

NOTE: As of 2022 I prefer wxMaxima as a notebook style front-end for Maxima.

This tutorial shows how you can set up org-mode to work as a Maxima notebook.

Each cell of the notebook should have the following header #+header: :exports both so that org-mode knows to display the output and then the source block should also have the language specified as maxima and :results output included as well. To actually evaluate a source block use either org-babel-execute-src-block or org-babel-execute-maybe. The latter is just a convenience wrapper around the former. In spacemacs this is bound to SPC m b e.

There is a the example function which can be used to get examples of the usage of a function. There is the ? <function>; to get the documentation for a function.

if cond_1 then expr_1 elseif cond_2 then expr_2 else expr_3;

There are several ways to express for loops.

for variable: initial_value step increment thru limit do body

for variable: initial_value step increment while condition do body

for variable: initial_value step increment unless condition do body

for variable in list do body

To force the evaluation of an expression before binding it to the value of a function use the define function.

define(fdash(x), diff(f(x), x));

restart();
kill(all);

matchdeclare([xx,yy,aa],true)$
tellsimpafter(xx^a*yy^a,(xx*yy)^a)$
tellsimpafter(xx^a/yy^a,(xx/yy)^a)$

print(x^a*y^a);
print(x^a/y^a);
print(x^a*y^a*z^a);
print(x^a*(y^a*z^a));

produces the following output

:      a
: (x y)

:  x a
: (-)
:  y

:  a  a  a
: x  y  z

:        a
: (x y z)

Note the difference between the (%o6) and (%o7) which seems to mean that the tree AST is not a binary tree.

Use the load command to load packages. For example

load("distrib");

to get some useful functions for working with distributions. The f90 package exports the function f90 which will convert an expression into valid Fortran90 which has syntax very close to most of the mainstream languages.

You can use %o<n> to refer to the output named n.

To save sessions there is the stringout function which can take as a mode one of several options: all, input for a verbatim copy of the session, and values and functions for the existing values and functions. To read a file there is batch and batchload, the latter being a silent version of batch.

The simplify_sum package provides the simplify_sum function. This package was used in Problem 4.

The exponentialize function converts circular and hyperbolic functions into expressions consisting of exponentials.

Suppose you are doing an integral and you want to change from Cartesian to polar coordinates. What was for Jacobian in this case again? The following demonstrates how to compute it with Maxima.

Note that we have used the quote on the call to diff to prevent this being evaluated as we are defining the ODE here.

eq : 'diff(y,x) = -y;

ode2(eq, y, x);

sol : ic1(%, x = 1, y = 8);

plot2d(rhs (sol), [x, 0,4], [y, 0, 10]);

This snippet demonstrates some ways to get different expressions for the same quantity. Note how the numerator and denominator can be separated to have different simplification steps applied as in the definition of d.

a : (x* exp(-aa) + y + y * exp(-aa))/ (y*exp(-aa) + x);
b : ratsimp(a);
c : collectterms(expand(num(b)), exp(aa)) / denom(b);
d : block(
  [ea: exp(-aa)],
  collectterms(expand(ea * num(b)), ea) / expand(ea * denom(b))
  );
display(a, b, c, d);

      - aa           - aa
    %e     y + y + %e     x
a = -----------------------
           - aa
         %e     y + x
          aa
       (%e   + 1) y + x
   b = ----------------
                aa
          y + %e   x
          aa
        %e   y + y + x
    c = --------------
                aa
          y + %e   x
        - aa
      %e     (y + x) + y
  d = ------------------
           - aa
         %e     y + x

• Use ctrl k to trigger the auto-complete function.
• To change the pre-amble used during the LaTeX export use Edit > Configure > Export and fill in the desired commands there.
• ctrl 0 starts a new math cell, but ctrl n for n as 1, 2, 3, … provides a bunch of helpful text based cells.
• When I compiled wxMaxima 21.11.0 from source it suddenly wanted to use Portuguese as the language. Far too much searching revealed that the way to solve this is to open .wxMaxima (the configuration file) and change language=153 to language=59 (British English).

• Another problem I hit was wxMaxima not being able to locate the Maxima documentation. The solution was to add the following line to .wxMaxima, unfortunately upon exiting, this seems to loose that configuration, I'm not sure how to correct this.

  helpFile=/usr/share/maxima/5.43.2/doc/html/header.hhp
  

Add the following to your configuration.

(add-to-list 'load-path "<path/to/emacs/maxima/")
(autoload 'maxima-mode "maxima" "Maxima mode" t)
(autoload 'imaxima "imaxima" "Frontend for maxima with Image support" t)
(autoload 'maxima "maxima" "Maxima interaction" t)
(autoload 'imath-mode "imath" "Imath mode for math formula input" t)
(setq imaxima-use-maxima-mode-flag t)
(add-to-list 'auto-mode-alist '("\\.ma[cx]" . maxima-mode))

Start a Maxima session with M-x imaxima. To send a buffer to the REPL use C-c C-b. To send a region C-c C-r or just a single line C-c C-c. To get the potential completions for a variable name M-TAB.