Demo of MathAction.

Axiom

On this web site you can enter Axiom commands and see the output

in proper mathematical form. These commands can also be typed directly into Axiom installed on your own computer.

You must enclose each set of Axiom commands in a '!begin{axiom} end{axiom}' section. For example:

!\begin{axiom}
[1/2, 3/4, 2/3]
\end{axiom}

When you save the changes you make to a page, Axiom processes the contents of each section you have marked and the Axiom output is displayed.

Try this command:

begin{axiom} [1/7, 3/4, 5/6]? end{axiom}

Let's see if we can perform a finite window Fourier inversion.

begin{axiom} simplify(integrate(exp(%i*_omega*t) * exp(-%i*_omega * _tau), _omega=-_Omega .. _Omega)) end{axiom}

Try this integrating this

begin{axiom} 2*x/sin(x)^2 end{axiom}

begin{axiom} integrate(%,x) end{axiom}

Now differentiate it begin{axiom} D(%,x) simplify(%) end{axiom}

Expressions (5) and (8) are really that same.

begin{axiom} simplify(%%(3) - %%(6)) end{axiom}

begin{axiom} D(x^x,x) end{axiom}

See, that was easy!

Here are some more things to try.

begin{axiom} integrate(log(sin(x)),x=0..%pi) end{axiom}

begin{axiom} limit(sum(1/i^2,i=1..n),n=%plusInfinity) end{axiom}

Can you explain these results?

More here: http://www.dcs.st-and.ac.uk/~mnd/documentation/axiom_tutorial/axiom.html

Maxima

Maxima commands are entered like this:

!\begin{maxima}
command;
\end{maxima}

Each such pseudo-environment is saved in a temporary file and executed via the Maxima 'batch("filename")' command.

First test: begin{maxima} 1+2; 2+3; end{maxima}

We are able to separate out the LaTeX? code and display it nicely.

Ordinary differential equations begin{maxima} depends(y,x); diff(y,x)=(4-2*x)/(3*y^2-5); ode2(%,y,x); end{maxima}

Programming begin{maxima} s:0; for i:1 while i<=10 do s:s+i; done; s; fib[0]:0; fib[1]:1; fib[n]?:=fib[n-1]?+fib[n-2]?; fib[20]?; end{maxima}

Reduce

not installed

begin{reduce} coeff(X**3 + 3*X**2*Y + 3*X*Y**2 + Y**3,x); gcd(X**2 + 4*X + 3,X**2 - 2*X - 3); resultant(X**2 + 4*X + 3,X**2 - 2*X - 3,x); decompose(x**6+6x**4+x**3+9x**2+3x-5); factorize(x**6+6x**4+x**3+9x**2+3x); roots(x**6+6x**4+x**3+9x**2+3x-5); interpol({0,7,26,63},z,{1,2,3,4}); end{reduce}