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

Description

This is an optional argument for the schurResolution routine. It specifies an upper bound for the degrees of the generators of the syzygy modules in the equivariant resolution of an equivariant module M to be computed by the routine. If a DegreeLimit is not specified, then it is assumed to be equal to the maximal degree in which the module M is specified as a representation.

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

Decreasing DegreeLimit truncates the output to syzygies of total degree at most the specified value, while the representations themselves are unchanged:

i7 : S = schurRing(QQ,s,3);

i8 : rep = s_{2};

i9 : M = {1_S,s_{2},s_{4},s_{6},s_{8},s_{10},s_{12}};

i10 : schurResolution(rep,M)

o10 = {{(0, s  )}, {(2, s   )}, {(3, s     )}, {(4, s     )}}
             ()          2,2          3,2,1          3,3,2

o10 : List

i11 : schurResolution(rep,M,DegreeLimit => 3)

o11 = {{(0, s  )}, {(2, s   )}, {(3, s     )}}
             ()          2,2          3,2,1

o11 : List

Functions with optional argument named DegreeLimit:

compose(Module,Module,Module,DegreeLimit=>...) -- see compose -- composition as a pairing on Hom-modules
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
minimalBetti(...,DegreeLimit=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
normalCone(Ideal,DegreeLimit=>...) (missing documentation)
normalCone(Ideal,RingElement,DegreeLimit=>...) (missing documentation)
pushForward(...,DegreeLimit=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
quotient(...,DegreeLimit=>...) (missing documentation)
saturate(...,DegreeLimit=>...) (missing documentation)
schurResolution(...,DegreeLimit=>...) -- Specifies the maximal degree of syzygies to be computed
syz(...,DegreeLimit=>...) -- see syz(Matrix) -- compute the syzygy matrix

Further information

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

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SchurRings.m2:6619:0.

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

Description

See also

Functions with optional argument named DegreeLimit:

Further information