Solution of a Single Polynomial Equation

Axiom can solve polynomial equations producing either approximate or exact solutions. Exact solutions are either members of the ground field or can be presented symbolically as roots of irreducible polynomials. This returns one rational root along with an irreducible polynomial describing the other solutions

If you want solutions expressed in terms of radicals you would use this instead.

The solve command always returns a value but radicalSolve returns only the solutions that it is able to express in terms of radicals. If the polynomial equation has rational coefficients you can ask for approximations to its real roots by calling solve with a second argument that specifies the "precision" epsilon. This means that each approximation will be within plus or minus epsilon of the actual result. Notice that the type of second argument controls the type of the result.

If you give a floating point precision you get a floating point result. If you give the precision as a ration number you get a rational result.

If you want approximate complex results you should use the command complexSolve that takes the same precision argument epsilon.

Each approximation will be within plus or minus epsilon of the actual result in each of the real and imaginary parts.

Note that if you omit the = from the first argument Axiom generates an equation by equating the first argument to zero. Also, when only one variable is present in the equation, you do not need to specify the variable to be solved for, that is, you can omit the second argument. Axiom can also solve equations involving rational functions. Solutions where the denominator vanishes are discarded.