Solution of Systems of Polynomial Equations

Given a system of equations of rational functions with exact coefficients
```     p1(x1,...,xn)
.
.
pm(x1,...,xn)
```
Axiom can find numeric or symbolic solutions. The system is first split into irreducible components, then for each component, a triangular system of equations is found that reduces the problem to sequential solutions of univariate polynomials resulting from substitution of partial solutions from the previous stage.
```     q1(x1,...,xn)
.
.
qm(xn)
```
Symbolic solutions can be presented using "implicit" algebraic numbers defined as roots of irreducible polynomials or in terms of radicals. Axiom can also find approximations to the real or complex roots of a system of polynomial equations to any user specified accuracy. The operation solve for systems is used in a way similar to solve for single equations. Instead of a polynomial equation, one has to give a list of equations and instead of a single variable to solve for, a list of variables. For solutions of single equations see Solution of a Single Polynomial Equation Use the operation solve if you want implicitly presented solutions.