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

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].

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
• 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=>...)
• 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)
• isPrime(Ideal,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
• normalCone(Ideal,RingElement,Strategy=>...) (missing documentation)
• normalCone(Ideal,Strategy=>...) (missing documentation)
• 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