The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert Lewis

Posts: 52
Registered: 7/17/08
Re: Corrected: Solving a system of first-order multi-variable equations
Posted: May 4, 2014 10:03 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Friday, May 2, 2014 7:28:30 PM UTC-4, wrote:
> Hello, are there standard methods for solving systems of multi-variable equations where all variables are of order one, such as the following?:
> + c12.xy + c13.yz + c14.xz + c15.x + c16.y + c17.z = c10
> + c22.xy + c23.yz + c24.xz + c25.x + c26.y + c27.z = c30
> + 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. Of possible importance, a matrix (or multiple matrices of multiple dimensions) of the constants would be sparse. Any references to standard solutions would be greatly appreciated. These might include numerical approaches. Thanks in advance for any help!

Usually the best way to solve systems of polynomial equations symbolically is with resultants, especially the Dixon resultant. It is usually much much better than trying Groebner bases. The resultant is a single polynomial in one of the variables; the others are eliminated. Above, you would eliminate, say, y and z, leaving a polynomial in x.

If you want a fully symbolic solution of the system above, with all 24 parameters, I think that would be doable.

But if you want many more equations, I think a fully symbolic solution is unfeasible. If you mean that most of the parameters will be 0, then there is a good chance for a fully symbolic solution for maybe up to 10 equations.

Robert H. Lewis
Fordham University

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.