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.
- 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.
Posted in old Singular Forum on: 2005-07-28 18:26:54+02