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# groebnerWalk(...,Strategy=>...) -- specify the algorithm for groebnerWalk

- Usage:
    `H = groebnerWalk(G, R, Strategy => Generic)`

## Description

Choose which algorithm to use for the Groebner walk. Options are Standard for the original algorithm of Collart, Kalkbrener, and Mall and Generic for the generic walk of Fukuda, Jensen, Lauritzen, and Thomas. The default option is Standard.

    i1 : KK = ZZ/32003;

    i2 : R1 = KK[x,y,z,u,v, MonomialOrder=>Eliminate 3];

    i3 : I1 = ideal(3 - 2*u + 2*u^2 - 2*u^3 - v + u*v + 2*u^2*v^3 - x,
                    6*u + 5*u^2 - u^3 + v + u*v + v^2 - y,
                    -2 + 3*u - u*v + 2*u*v^2 - z);

    o3 : Ideal of R1

    i4 : R2 = KK[x,y,z,u,v, MonomialOrder=>Weights=>{0,0,0,1,1}];

    i5 : groebnerWalk(I1, R2, Strategy=>Generic)

    o5 = GroebnerBasis[status: done; S-pairs encountered up to degree 0]

    o5 : GroebnerBasis

## See also

- GroebnerWalk -- Compute Groebner bases via the Groebner walk
- groebnerWalk -- convert a Groebner basis

## Functions with optional argument named Strategy:

- `addHook(...,Strategy=>...)` -- see addHook -- add a hook function to an object for later processing
- annihilator(...,Strategy=>...) (missing documentation)
- `basis(...,Strategy=>...)` -- see basis -- basis or generating set of all or part of a ring, ideal or module
- `mingens(...,Strategy=>...)` -- see Complement -- a Strategy option value
- `trim(...,Strategy=>...)` -- see Complement -- a Strategy option value
- `compose(Module,Module,Module,Strategy=>...)` -- see compose -- composition as a pairing on Hom-modules
- decompose(Ideal,Strategy=>...) (missing documentation)
- determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `dual(MonomialIdeal,List,Strategy=>...)` -- see dual(MonomialIdeal,Strategy=>...)
- `dual(MonomialIdeal,RingElement,Strategy=>...)` -- see dual(MonomialIdeal,Strategy=>...)
- dual(MonomialIdeal,Strategy=>...)
- `End(...,Strategy=>...)` -- see End -- module of endomorphisms
- exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `gb(...,Strategy=>...)` -- see gb -- compute a Gröbner basis
- `GF(...,Strategy=>...)` -- see GF -- make a finite field
- `groebnerBasis(...,Strategy=>...)` -- see groebnerBasis -- Gröbner basis, as a matrix
- groebnerWalk(...,Strategy=>...) -- specify the algorithm for groebnerWalk
- `Hom(...,Strategy=>...)` -- see Hom -- module of homomorphisms
- `homomorphism'(...,Strategy=>...)` -- see homomorphism' -- get the element of Hom from a homomorphism
- `hooks(...,Strategy=>...)` -- see hooks -- list hooks attached to a key
- `intersect(Ideal,Ideal,Strategy=>...)` -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
- `intersect(Module,Module,Strategy=>...)` -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
- isPrime(Ideal,Strategy=>...) (missing documentation)
- `match(...,Strategy=>...)` -- see match -- regular expression matching
- minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- normalCone(Ideal,RingElement,Strategy=>...) (missing documentation)
- normalCone(Ideal,Strategy=>...) (missing documentation)
- `parallelApply(...,Strategy=>...)` -- see parallelApply -- apply a function to each element in parallel
- `pushForward(...,Strategy=>...)` -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
- quotient'(...,Strategy=>...) (missing documentation)
- quotient(...,Strategy=>...) (missing documentation)
- saturate(...,Strategy=>...) (missing documentation)
- `syz(...,Strategy=>...)` -- see syz(Matrix) -- compute the syzygy matrix

## Further information

- Default value: Standard
- Function: groebnerWalk -- convert a Groebner basis
- Option key: Strategy -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GroebnerWalk.m2:507:0.