minors(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms

Synopsis

• Usage:

  minors(M, Strategy => s)

• Inputs:
  • M, a matrix
  • s, a symbol, either Bareiss or Cofactor
• Consequences:

  • If s is Bareiss, then the Bareiss algorithm is used; if s is Cofactor, then cofactor expansion is used.

Description

The ring of M determines the default strategy. If the ring is a polynomial ring or a field (as identified by isField) then the Bareiss algorithm is used. If the ring is a quotient ring (which has not been declared a field by toField), then the Cofactor algorithm is used.

Further information

• Default value: null
• Function: minors -- ideal generated by minors
• Option key: Strategy -- an optional argument

Caveat

The Bareiss algorithm returns a ring element that may differ from the actual determinant by a zero divisor in the ring. Thus, an incorrect answer may be computed if the ring contains zero divisors.

See also

• determinant -- determinant of a matrix
• exteriorPower -- exterior power

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
• "associatedPrimes(...,Strategy=>...)" -- see associatedPrimes -- find associated primes
• "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
• determinant(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "dual(MonomialIdeal,List,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
• "dual(MonomialIdeal,RingElement,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
• dual(MonomialIdeal,Strategy=>...)
• exteriorPower(...,Strategy=>...) -- choose between Bareiss and Cofactor 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)
• "hooks(...,Strategy=>...)" -- see hooks -- list hooks attached to a key
• "idealizer(...,Strategy=>...)" -- see idealizer -- compute Hom(I,I) as a quotient ring
• integralClosure(...,Strategy=>...) -- control the algorithm used
• "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
• "intersectInP(...,Strategy=>...)" -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• "isPrimary(...,Strategy=>...)" -- see isPrimary -- determine whether a submodule is primary
• "isPrime(Ideal,Strategy=>...)" -- see isPrime(Ideal) -- whether an ideal is prime
• LLL(...,Strategy=>...) -- choose among different algorithms
• "localize(...,Strategy=>...)" -- see localize -- localize an ideal at a prime ideal
• "match(...,Strategy=>...)" -- see match -- regular expression matching
• "decompose(Ideal,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "minimalPrimes(...,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
• minors(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "primaryComponent(...,Strategy=>...)" -- see primaryComponent -- find a primary component corresponding to an associated prime
• pushForward(...,Strategy=>...) (missing documentation)
• quotient(...,Strategy=>...)
• "radical(...,Strategy=>...)" -- see radical -- the radical of an ideal
• "radicalContainment(...,Strategy=>...)" -- see radicalContainment -- whether an element is contained in the radical of an ideal
• "analyticSpread(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "distinguished(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "isLinearType(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "isReduction(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "minimalReduction(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "multiplicity(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "normalCone(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "reesAlgebra(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "specialFiber(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "specialFiberIdeal(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "regSeqInIdeal(...,Strategy=>...)" -- see regSeqInIdeal -- a regular sequence contained in an ideal
• resolution(...,Strategy=>...)
• saturate(...,Strategy=>...)
• "primaryDecomposition(...,Strategy=>...)" -- see strategies for computing primary decomposition
• "syz(...,Strategy=>...)" -- see syz(Matrix) -- compute the syzygy matrix
• "tangentCone(...,Strategy=>...)" -- see tangentCone(Ideal)