forgetDegeneracy(SimplicialModule) -- forget the data of degeneracy maps of a simplicial object

Function: forgetDegeneracy
Usage:

forgetDegeneracy(S)
Inputs:
- S, a Simplicial Module, A simplicial module whose degeneracy maps are to be forgotten.
Outputs:
- a Simplicial Module, The simplicial module S, but with no degeneracy maps stored.

Description

This function removes the data of degeneracy maps from a simplicial module `S`. It is useful when the user wants to ignore degeneracy maps for the purpose of speeding up computations or simplifying the simplicial object.

i1 : Q = ZZ/101[a..d]

o1 = Q

o1 : PolynomialRing

i2 : K = koszulComplex vars Q

      1      4      6      4      1
o2 = Q  <-- Q  <-- Q  <-- Q  <-- Q
                                  
     0      1      2      3      4

o2 : Complex

i3 : S = simplicialModule(K, 6, Degeneracy => true)

      1      5      15      35      70      126      210
o3 = Q  <-- Q  <-- Q   <-- Q   <-- Q   <-- Q    <-- Q   <-- ...
                                                     
     0      1      2       3       4       5        6

o3 : SimplicialModule

i4 : elapsedTime S**S
 -- .452996s elapsed

      1      25      225      1225      4900      15876      44100
o4 = Q  <-- Q   <-- Q    <-- Q     <-- Q     <-- Q      <-- Q     <-- ...
                                                             
     0      1       2        3         4         5          6

o4 : SimplicialModule

i5 : fS = forgetDegeneracy S

      1      5      15      35      70      126      210
o5 = Q  <-- Q  <-- Q   <-- Q   <-- Q   <-- Q    <-- Q   <-- ...
                                                     
     0      1      2       3       4       5        6

o5 : SimplicialModule

i6 : elapsedTime fS**fS --faster when degeneracy is ignored
 -- .369881s elapsed

      1      25      225      1225      4900      15876      44100
o6 = Q  <-- Q   <-- Q    <-- Q     <-- Q     <-- Q      <-- Q     <-- ...
                                                             
     0      1       2        3         4         5          6

o6 : SimplicialModule

The change in speed becomes much more noticeable as ranks get larger.

Ways to use this method:

forgetDegeneracy(SimplicialModule) -- forget the data of degeneracy maps of a simplicial object

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:3346:0.

forgetDegeneracy(SimplicialModule) -- forget the data of degeneracy maps of a simplicial object

Description

See also

Ways to use this method: