notes/software/maxima.md

Startup file

rmaxima  --init-mac='~/.maxima_startup' --init-lisp='~/.maxima_startup.lisp'

Commands

addcol
addrow
diag -- construct block diagonal matrix

zeromatrix(2,5)
zerofor(M)

display2d : false
tex()

Simplification using hyperbolic functions

This function must be added to the startup file

hypsimp(x,M):= ratsimp(subst(x/%i,x,demoivre(subst(x*%i,x,M))));

Usage:

(%i7) expr: (%e^(a*b) - %e^-(a*b))/2;

                              a b     - a b
                            %e    - %e

(%o7) ---------------

                                   2

(%i8) hypsimp(a*b, expr);

(%o8) sinh(a b)

Discretization of a system

load("diag");
Ad: mat_function(exp, A*T);
Bd: expand(integrate(mat_function(exp, A*t), t, 0, T).B);

Matrix exponential

load("diag");
A : matrix([2,1],[0,2]);
mat_function(exp, A);

Cross product

load("vect");
express([1,2,3]~[4,5,6]);

Jacobian

f1: x + y;
f2: sin(y);
f3: x + z;
J: jacobian ([f1, f2, f3], [x, y, z]);