FGLMIfCanPackage(R, ls)

zerodim.spad line 1 [edit on github]

• R : GcdDomain
• ls : List(Symbol)

This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type Polynomial R by the FGLM algorithm if this is possible (i.e. if the input system generates a zero-dimensional ideal).

fglmIfCan : List(Polynomial(R)) -> Union(List(Polynomial(R)), "failed")

fglmIfCan(lq1) returns the lexicographical Groebner basis of lq1 by using the FGLM strategy, if zeroDimensional?(lq1) holds.

groebner : List(Polynomial(R)) -> List(Polynomial(R))

groebner(lq1) returns the lexicographical Groebner basis of lq1. If lq1 generates a zero-dimensional ideal then the FGLM strategy is used, otherwise the Sugar strategy is used.

zeroDimensional? : List(Polynomial(R)) -> Boolean

zeroDimensional?(lq1) returns true iff lq1 generates a zero-dimensional ideal w.r.t. the variables of ls.