schurResolution(...,DegreeLimit=>...) -- Specifies the maximal degree of syzygies to be computed

Description

i1 : A = schurRing(a,3,GroupActing => "Sn");

i2 : B = schurRing(A,b,2);

i3 : rep = (a_3 + a_{2,1}) * b_1

o3 = (a  + a   )b
       3    2,1  1

o3 : B

i4 : d = dim rep

o4 = 6

i5 : M = {a_3 * 1_B};

i6 : sR = schurResolution(rep,M,DegreeLimit => d)

o6 = {{(0, a b  )}, {(1, (a  + a   )b )}, {(2, (a    + a     )b  + (2a  +
            3 ()           3    2,1  1           2,1    1,1,1  2      3  
     ------------------------------------------------------------------------
     2a   )b   )}, {(3, a     b  + (a  + 3a    + a     )b   )}, {(4, (a    +
       2,1  1,1          1,1,1 3     3     2,1    1,1,1  2,1           2,1  
     ------------------------------------------------------------------------
     a     )b    + (2a  + 2a   )b   )}, {(5, (a  + a   )b   )}, {(6,
      1,1,1  3,1      3     2,1  2,2           3    2,1  3,2        
     ------------------------------------------------------------------------
     a b   )}}
      3 3,3

o6 : List

Further information

• Default value: 0
• Function: schurResolution -- Compute an ``approximate'' equivariant resolution of a module.
• Option key: DegreeLimit -- an optional argument

See also

• schurResolution(...,SyzygyLimit=>...) -- Specifies the number of syzygy modules to be computed

Functions with optional argument named DegreeLimit:

• adjoint(...,DegreeLimit=>...) (missing documentation)
• compose(Module,Module,Module,DegreeLimit=>...) -- see compose -- composition as a pairing on Hom-modules
• dual(ChainComplex,DegreeLimit=>...) (missing documentation)
• dual(Matrix,DegreeLimit=>...) (missing documentation)
• dual(SheafMap,DegreeLimit=>...) (missing documentation)
• End(...,DegreeLimit=>...) -- see End -- module of endomorphisms
• gb(...,DegreeLimit=>...) -- see gb -- compute a Gröbner basis
• Hom(...,DegreeLimit=>...) -- see Hom -- module of homomorphisms
• homomorphism'(...,DegreeLimit=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
• intersectInP(...,DegreeLimit=>...) -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• minimalBetti(...,DegreeLimit=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• pushForward(...,DegreeLimit=>...) -- see pushForward(RingMap,Module)
• quotient(...,DegreeLimit=>...)
• saturate(...,DegreeLimit=>...) -- see quotient(...,DegreeLimit=>...)
• analyticSpread(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• associatedGradedRing(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• distinguished(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• isLinearType(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• isReduction(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• minimalReduction(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• multiplicity(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• normalCone(Ideal,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• normalCone(Ideal,RingElement,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• reesAlgebra(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• specialFiber(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• specialFiberIdeal(...,DegreeLimit=>...) -- see reesIdeal(...,DegreeLimit=>...) -- Bound the degrees considered in the saturation step. Defaults to infinity
• resolution(...,DegreeLimit=>...) -- compute only up to this degree
• schurResolution(...,DegreeLimit=>...) -- Specifies the maximal degree of syzygies to be computed
• sheafHom(...,DegreeLimit=>...) (missing documentation)
• syz(...,DegreeLimit=>...) -- see syz(Matrix) -- compute the syzygy matrix