Anyone know such application available out there?

Let me explain:

I need some application to solve linear equation "formulas" for me -- i.e output is of the form (A+B)(C+D) or similar (not necessarily optimal, I can simplify it later myself). The main important idea is that it will operate on "symbols" rather than calculate digits.

All equations are solvable for all unknowns (i.e if we put it in a matrix, it has

**n**x

**n** rows and columns).

Why do I need this? I have some points (for the sake of an example, let's say 4 points), at specific locations (known), and I want to find out the coefficients for a function that walks through them.

Note: I might also need functions with multiple arguments (like bilinear function), so 4 points doesn't always mean a 3rd degree polynomial

Here the example equation (^ denotes power):

Ax^3 + Bx^2 + Cx + D = p1
Ay^3 + By^2 + Cy + D = p2
Az^3 + Bz^2 + Cz + D = p3
Aw^3 + Bw^2 + Bw + D = p4

Now I wish to find a formula to find out the

**A,B,C,D** unknowns (coefficients).

**x,y,z,w** and

**p1,p2,p3,p4** are known, and once I have the formula, I can replace them with their values (actually, they're variables

) and calculate the coefficients.

The question is, is such program available out there? (I might possibly need 4th or even higher degree polynomials, for more points, or multi-dimensional functions as well).

A bilinear function example:

Ax + By + Cxy + D = p1
Au + Bv + Cuv + D = p2
Ao + Bp + Cop + D = p3
An + Bm + Anm + D = p4

Again, the unknowns are

**A,B,C,D** and the others are variables with some values stored, and I need some kind of formula for this.

A link to some program would be nice

If there is no such program available, then links to these 2 function examples (or even more functions) with written formulas is welcomed as well. Web page, .pdf, database, whatever

*Yes I know I could solve them myself, but with substitution it's so hard and even Cramer's rule gets complicated on such equations, especially if we move on to higher degrees*