filtrationModule -- converts a filtered module to an R[t]-module

Synopsis

Usage:

filtrationModule(Q, L)
Inputs:
- Q, a ring, of the form R[t] for some coefficient ring R and variable t
- L, a list, of the form { M_0, M_1, ..., M_k } for some k > 0 with each M_i $\subseteq$ M_{i+1} an inclusion of R-modules
Outputs:
- a module, graded, with M_0 sitting in degree zero, and where t acts by inclusions

Description

i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing

i2 : X = R^1 / x^9

o2 = cokernel | x9 |

                            1
o2 : R-module, quotient of R

i3 : submods = apply(5,k->image map(X,,{{x^(8-2*k)}}))

o3 = {subquotient (| x8 |, | x9 |), subquotient (| x6 |, | x9 |), subquotient
     ------------------------------------------------------------------------
     (| x4 |, | x9 |), subquotient (| x2 |, | x9 |), subquotient (| 1 |, | x9
     ------------------------------------------------------------------------
     |)}

o3 : List

i4 : Q = R[t]

o4 = Q

o4 : PolynomialRing

i5 : filtrationModule(Q, submods)

o5 = subquotient ({0, 0} | x8 0  0  0  0 |, {0, 0} | x8t 0   0   0   x9 0  0  0  0  |)
                  {1, 0} | 0  x6 0  0  0 |  {1, 0} | -x8 x6t 0   0   0  x9 0  0  0  |
                  {2, 0} | 0  0  x4 0  0 |  {2, 0} | 0   -x6 x4t 0   0  0  x9 0  0  |
                  {3, 0} | 0  0  0  x2 0 |  {3, 0} | 0   0   -x4 x2t 0  0  0  x9 0  |
                  {4, 0} | 0  0  0  0  1 |  {4, 0} | 0   0   0   -x2 0  0  0  0  x9 |

                               5
o5 : Q-module, subquotient of Q

Caveat

The ring Q should be valid for expectSequenceRing. The list L should be valid for expectFiltrationList.

Ways to use `filtrationModule`:

filtrationModule(Ring,List)

For the programmer

The object filtrationModule is a method function.

filtrationModule -- converts a filtered module to an R[t]-module

Synopsis

Description

Caveat

See also

Ways to use filtrationModule:

For the programmer

Ways to use `filtrationModule`: