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# randomPoints(...,Strategy=>...) -- values for the option Strategy when calling randomPoints

## Description

When calling randomPoints, set the strategy to one of these. BruteForce simply tries random points and sees if they are on the variety.

LinearIntersection intersects with an random linear space. Setting the DecompositionStrategy => MultiplicationTable or DecompositionStrategy=>Decompose will change how ideals corresponding to points are broken up into minimal primes which can have a substantial impact on speed. Otherwise, the function chooses which strategy it thinks will be better. See DecompositionStrategy.

Default performs a sequence of different strategies, with successively increasing complexity of the linear subspaces that are intersected.

## See also

- randomPoints -- a function to find random points in a variety.
- randomKRationalPoint -- pick a random K rational point on the scheme X defined by I
- projectionToHypersurface -- Generic projection to a hypersurface

## 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
- `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)
- `extendIdealByNonZeroMinor(...,Strategy=>...)`
- `findANonZeroMinor(...,Strategy=>...)`
- randomPoints(...,Strategy=>...) -- values for the option Strategy when calling randomPoints
- saturate(...,Strategy=>...) (missing documentation)
- `syz(...,Strategy=>...)` -- see syz(Matrix) -- compute the syzygy matrix

## Further information

- Default value: Default
- Function: randomPoints -- a function to find random points in a variety.
- Option key: Strategy -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomPoints.m2:1851:0.