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| Solving Polynomial equations with parameter coefficients https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1439 |
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| Author: | Dursun [ Thu Aug 11, 2005 5:33 pm ] |
| Post subject: | Solving Polynomial equations with parameter coefficients |
I was wondering whether it is possible to solve a system of polynomial equations with parameter coeffiecients in terms of the parameter coefficients using one of the libraries of Singular. Dursun. email: bulutoglu.dursun@afit.edu Posted in old Singular Forum on: 2005-06-12 21:05:45+02 |
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| Author: | greuel [ Mon Aug 29, 2005 9:23 am ] |
| Post subject: | |
The question is what you mean by "solving" in this context. Assume that the system is 0-dimensional where the parameters belong to the ground field (e.g. a,b parameters, x,y,z variables: ring r=(0,a,b),(x,y,z),lp; ) Then the library 'triang.lib' provides routines for computing triangular systems (analog of row-echelon form for polynomial equations). Each system contains one univariate polynomial with coefficient being rational functions in the parameters, a second polynomial depending on two varaible, etc. This does, in principle, allow an analysis of the solution set in terms of the parameters. Caveats: - The polynomials (and coefficients) are usually quite big. - During Groebner bases computations, Singular extracts and forgets the content of the coefficients. Hence the dependence on the parameters is only generically true. - A further symbolic analysis would require algebraic extensions of coefficient fields containing parameters which is not implemented. email: greuel@mathematik.uni-kl.de Posted in old Singular Forum on: 2005-07-28 18:26:54+02 |
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