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ZZdFactorization _ ZZ -- access individual object in a ZZ/d-graded factorization

Description

ZZ/d-graded factorizations can be either homologically or cohomologically graded. Subscripts refer to homological indices, and superscripts refer to cohomological indices.

In this package homological indices are used by default. We always have the equation $C^i = C_{-i}$.

i1 : S = ZZ/101[x_1..x_3]

o1 = S

o1 : PolynomialRing
 
i2 : C = koszulMF({x_1,x_2,x_3}, x_1^2+x_2^2+x_3^2)

      4      4      4
o2 = S  <-- S  <-- S
                    
     0      1      0

o2 : ZZdFactorization
 
i3 : C_2

      4
o3 = S

o3 : S-module, free
 
i4 : C^(-2)

      4
o4 = S

o4 : S-module, free
 
i5 : C_2 == C^(-2)

o5 = true

Indices that are outside of the period are taken modulo the period.

i6 : C_-7

      4
o6 = S

o6 : S-module, free

See also

Ways to use this method:

The source of this document is in MatrixFactorizations/MatrixFactorizationsDOC.m2:820:0.