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isVirtual(...,Strategy=>...) -- changes strategy from computing homology to computing minors of boundary maps

Description

If Strategy is set to Determinantal, isVirtual will check whether the given chain complex is a virtual resolution by checking the depth of the saturation of the ideals of maximal rank from the boundary maps. See Theorem 1.3 of [Loper, arXiv:1904.05994].

See also

Functions with optional argument named Strategy:

  • addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
  • annihilator(...,Strategy=>...) -- see annihilator -- the annihilator ideal
  • basis(...,Strategy=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
  • canonicalBundle(...,Strategy=>...) -- see canonicalBundle -- the canonical bundle of a projective variety
  • coarseMultigradedRegularity(...,Strategy=>...) -- see coarseMultigradedRegularity -- A truncation that has linear resolution
  • 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
  • cotangentSheaf(...,Strategy=>...) -- see cotangentSheaf -- cotangent sheaf of a projective variety
  • 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=>...)
  • dual(SheafMap,Strategy=>...) (missing documentation)
  • End(...,Strategy=>...) -- see End -- module of endomorphisms
  • exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
  • gb(...,Strategy=>...) -- see gb -- compute a Gröbner basis
  • gcdLLL(...,Strategy=>...) (missing documentation)
  • GF(...,Strategy=>...) -- see GF -- make a finite field
  • groebnerBasis(...,Strategy=>...) -- see groebnerBasis -- Gröbner basis, as a matrix
  • hermite(...,Strategy=>...) (missing documentation)
  • 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
  • idealSheaf(...,Strategy=>...) (missing documentation)
  • 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
  • isIsomorphic(...,Strategy=>...) -- see isIsomorphic -- probabilistic test for isomorphism of modules
  • isomorphism(...,Strategy=>...) (missing documentation)
  • isVirtual(...,Strategy=>...) -- changes strategy from computing homology to computing minors of boundary maps
  • LLL(...,Strategy=>...) -- choose among different algorithms
  • makeSimplicial(...,Strategy=>...) -- see makeSimplicial(NormalToricVariety) -- make a birational simplicial toric variety
  • makeSmooth(...,Strategy=>...) -- see makeSmooth(NormalToricVariety) -- make a birational smooth toric variety
  • match(...,Strategy=>...) -- see match -- regular expression matching
  • minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
  • multigradedRegularity(...,Strategy=>...) -- see multigradedRegularity -- computes the minimal elements of the multigraded regularity of a module over a multigraded ring
  • parallelApply(...,Strategy=>...) -- see parallelApply -- apply a function to each element in parallel
  • pseudoInverse(...,Strategy=>...) (missing documentation)
  • pushForward(...,Strategy=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
  • quotient'(...,Strategy=>...) (missing documentation)
  • quotient(...,Strategy=>...)
  • resolution(...,Strategy=>...)
  • saturate(...,Strategy=>...)
  • sheafHom(...,Strategy=>...) -- see sheafHom -- sheaf Hom
  • SVDComplex(...,Strategy=>...) -- see SVDComplex -- Compute the SVD decomposition of a chainComplex over RR
  • SVDHomology(...,Strategy=>...) -- see SVDHomology -- Estimate the homology of a chainComplex over RR with the SVD decomposition
  • syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix
  • tangentSheaf(...,Strategy=>...) -- see tangentSheaf -- tangent sheaf of a projective variety

Further information

  • Default value: null
  • Function: isVirtual -- checks whether a chain complex is a virtual resolution
  • Option key: Strategy -- an optional argument

The source of this document is in VirtualResolutions/doc.m2:143:0.