GroebnerSolve(lv, F, R)

groebsol.spad line 1 [edit on github]

• lv: List Symbol

• F: GcdDomain

• R: GcdDomain

Author : P.Gianni, Summer '88, revised November '89 Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.

genericPosition: (List DistributedMultivariatePolynomial(lv, F), List OrderedVariableList lv) -> Record(dpolys: List DistributedMultivariatePolynomial(lv, F), coords: List Integer)

genericPosition(lp, lv) puts a radical zero dimensional ideal in general position, for system lp in variables lv.

groebSolve: (List DistributedMultivariatePolynomial(lv, F), List OrderedVariableList lv) -> List List DistributedMultivariatePolynomial(lv, F)

groebSolve(lp, lv) reduces the polynomial system lp in variables lv to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type DMP.

testDim: (List HomogeneousDistributedMultivariatePolynomial(lv, F), List OrderedVariableList lv) -> Union(List HomogeneousDistributedMultivariatePolynomial(lv, F), failed)

testDim(lp, lv) tests if the polynomial system lp in variables lv is zero dimensional.