This is the second in a sequence of posts about the open source CAS Axiom. The first can be found at http://amca01.wordpress.com/2008/05/25/an-introduction-to-axiom-1/
Axiom variables are created using the “colon equals” method of many other computer languages, and user defined functions with a double equals:
Note that for the last example, the expression involving radicals can be simplified directly, but it requires playing around with types.
Expansion, factorization and simplification of all sorts of expressions can be accomplished easily:
Axiom has powerful algorithms to solve polynomial equations, systems of polynomials, and linear system. There are in fact several different solve functions:
- Basic solve function: will produce real solutions. The precision of the solution can be adjusted by including an extra parameter
- The complex version of solve – will produce complex solutions, also with an adjustable numerical precision
- As its name implies, solutions in the form of radicals, if such can be found.
Note that solve will in general produce numeric solutions, unless the equations are linear. When the precision is given, the list of variables need not be given explicitly, as, according to the documentation: “The list of variables would be redundant information since there can be no parameters for the numerical solver.”