roger.d.engineer wrote: > >Hello, are there standard methods for solving systems of >multi-variable equations where all variables are of order one, >such as the following?: > >c11.xyz + c12.xy + c13.yz + c14.xz + c15.x + c16.y + c17.z = c10 >c21.xyz + c22.xy + c23.yz + c24.xz + c25.x + c26.y + c27.z = c30 >c31.xyz + c32.xy + c33.yz + c34.xz + c35.x + c36.y + c37.z = c30 > >There are always an equal number of equations and variables, >which in my application may be dozens of variables.
You can use Grobner basis methods to eliminate all but one unknown, yielding one nonlinear polynomial equation in one unknown.
The CAS programs Maple and Mathematica both have built-in support for Grobner basis methods.
If you post a simple numerical example (with say 3 unknowns), I'll show the Maple commands (using Maple's Grobner basis package) which can be used to solve the system.
>(Apologies quasi, for posting incorrect equations earlier, >thank you for your help.)