Maxima

Robert P. Munafo, 2007 Jan 27.

Maxima, originally known as MACSYMA, is a symbolic-math package comparable to Mathematica, Maple and MATLAB, but available free of charge in open-source, GPL form.

For more information, go here.

To perform the math work shown in the Brown Method, lemniscates, R2.1/3a and other pages, I used SBCL 0.9.14 and maxima-5.9.3 running on a MacOS X system.

Following are some examples of operations performed with maxima, based on this tutorial by Zdzislaw Meglicki at Indiana University:

limit(x/x, x, 0); calculate a limit

expand((a+b)^3);

solve(a*x^2=4, x); solve an equation

solve([a+b=10, 2*a+b=12], [a,b]); solve a system of equations in two variables

rectform(ev(%e^%i, numer)); convert exponents of complex numbers to actual complex numbers

allroots(x^6+4*x^5+6*x^4+10*x^3+11*x^2+9*x+4=0); find real and/or complex roots of an arbitrary-order polynomial (uses numerical methods)

integrate(x^2*sin(alpha*x), x, 0, beta); perform an integral (Maxima will ask three questions — answer positive; positive; negative;)

7 * 27 / 1.43;

200!;

factor(%);

(2^30/3^20)*sqrt(3);

ev(%, numer);

sum((1+i)/(1+i^4), i, 1, 10);

sum(1/k^2,k,1,inf);

%, simpsum;

sum(1/k^2,k,1,1000),numer;

%pi^2/6, numer;

product(((i^2+3*i-11)/(i+3)), i, 0, 10);

a : (3+5*%i)/(7+4*%i);

rectform(a);

polarform(a);

abs(a);

carg(a);

realpart(a);

imagpart(a);

carg(-1);

b : (x+y)^15;

expand(b);

factor(%);

c : cos(x)^5 + sin(x)^4 + 2*cos(x)^2 - 2*sin(x)^2 - cos(2*x);

trigexpand(c);

trigsimp(%);

d : 2*cos(x/2)^2 * cos(x)^4;

trigrat(d);

trigexpand(%);

trigsimp(%);

e: ezgcd(x^3-y^3, x^2+x-y-y^2);

e[1]*e[2];

expand(%);

expand(e[1]*e[3]);

e2 : (x^3-y^3) / (x^2+x-y-y^2);

factor(e2);

ev(e2, x=1, y=2);

at(e2, [x=1, y=2]);

f(x) := x^2 + 1/2;

functions;

define(g(x), x^2 + 1/2);

f(x) := x * sin(a*x) + b*x^2;

diff(f(x),x);

diff(f(x), x, 2);

'diff(f(x),x);

ev(%, diff);

g(x) := 'diff(f(x),x);

g(x);

g(x), diff;

g(x) := diff(f(x),x);

g(x);

at(g(x), [a=1, b=2, x=3]);

for i:1 thru 16 step 1 do block(display(N(i)));

divisors(100); builtin function that returns an array

for i in divisors(100) do display(i); iterates over the array returned by divisors

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index

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