nonzeroMax -- computes the homological position of the last non-zero module in a ChainComplex

Synopsis

Usage:

nonzeroMin C

nonzeroMax C
Inputs:
- C, a chain complex,
Outputs:
- an integer,

Description

The function max applied to a chain complex returns the largest position of a defined term in a chain complex, which very well might be the zero module. The function nonzeroMax returns the largest positions of a non-zero module.

i1 : S=ZZ/101[x,y]/ideal(x*y)

o1 = S

o1 : QuotientRing

i2 : C=chainComplex(matrix{{x}},matrix{{y}}**S^{ -1},matrix{{x}}**S^{ -2})[1]

      1      1      1      1
o2 = S  <-- S  <-- S  <-- S
                           
     -1     0      1      2

o2 : ChainComplex

i3 : isChainComplex C

o3 = true

i4 : C'=prependZeroMap appendZeroMap C

             1      1      1      1
o4 = 0  <-- S  <-- S  <-- S  <-- S  <-- 0
                                         
     -2     -1     0      1      2      3

o4 : ChainComplex

i5 : min C', nonzeroMin C'

o5 = (-2, -1)

o5 : Sequence

i6 : max C', nonzeroMax C'

o6 = (3, 2)

o6 : Sequence

Ways to use nonzeroMax :

nonzeroMax(ChainComplex)

For the programmer

The object nonzeroMax is a method function.