6. Geometric Solve

6.1 Introduction

This package provides the main functionalities of Kronecker. The verbose flag is GeometricSolveVerbose.

6.2 Verbosity

intrinsic: KroneckerInformations ()

It displays informations about Kronecker package: version, author, date...

intrinsic: KroneckerVersion () -> MonStgElt

intrinsic: KroneckerSetVerbose (l::RngIntElt)

Make Kronecker verbose. Argument l is an integer between 0 and 5.

intrinsic: KroneckerSetVerbose ()

Set to default verbosity 2.

intrinsic: KroneckerSetMathMLVerbose ()

Make Kronecker verbose via MathML.

intrinsic: KroneckerUnsetMathMLVerbose ()

Stop Kronecker verbose via MathML.

6.3 Geometric solve functionalities

intrinsic: GeometricSolve (equations::SeqEnum, inequations::SeqEnum, K: GenericLinearChangeOfVariables:= true, RemoveMultipleComponents:=false) -> Rec

• equations.
• inequations.
• K, field.

It returns a sequence of sequences llf of lifting fibers. llf describes the variety defined by the equations outside the inequations, if everything goes right. The computations are performed over K.
Error condition: Since the algorithm is probabilistic an error can be raised.

intrinsic: GeometricSolve (equations::SeqEnum, inequations::SeqEnum) -> Rec

intrinsic: GeometricSolve (equations::SeqEnum) -> Rec