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Topic: Corrected: Solving a system of first-order multi-variable equations
Replies: 3   Last Post: May 4, 2014 10:03 PM

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quasi

Posts: 10,450
Registered: 7/15/05
Re: Corrected: Solving a system of first-order multi-variable equations
Posted: May 2, 2014 8:34 PM
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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.)


No problem.

quasi



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