topDegree -- top degree of a simplicial module

Usage:

topDegree C
Inputs:
- C, a Simplicial Module,
Outputs:
- d, an integer, an integer specifying the top degree to which the face/degeneracy maps of a simplicial module have been computed

Description

In this package, each simplicial module necessarily has a top degree which is a finite bound up to which Macaulay2 will compute the face and/or degeneracy maps. This function is mainly used in programming, to loop over all non-zero modules or maps in the simplicial module.

i1 : S = ZZ/101[a..c];

i2 : C = simplicialModule(freeResolution coker vars S, 8)

      1      4      10      20      35      56      84      120      165
o2 = S  <-- S  <-- S   <-- S   <-- S   <-- S   <-- S   <-- S    <-- S   <-- ...
                                                                     
     0      1      2       3       4       5       6       7        8

o2 : SimplicialModule

i3 : topDegree C

o3 = 8

i4 : C' = simplicialModule(freeResolution coker vars S, 6)

      1      4      10      20      35      56      84
o4 = S  <-- S  <-- S   <-- S   <-- S   <-- S   <-- S  <-- ...
                                                    
     0      1      2       3       4       5       6

o4 : SimplicialModule

i5 : assert(topDegree C' == 6)

Indices that are outside of the top degree automatically return the zero object.

i6 : C_-1

o6 = 0

o6 : S-module

i7 : C_9

o7 = 0

o7 : S-module

i8 : C'_7

o8 = 0

o8 : S-module

The function topDegree does no computation, and just accesses a cached value.

Ways to use topDegree:

topDegree(SimplicialModule)
topDegree(SimplicialModuleMap)

For the programmer

The object topDegree is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:406:0.

topDegree -- top degree of a simplicial module

Description

See also

Ways to use topDegree:

For the programmer