next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Macaulay2Doc :: chainComplex(List)

chainComplex(List) -- make a chain complex

Synopsis

Description

The maps f1, f2, ... must be defined over the same base ring, and they must form a complex: the target of f(i+1) is the source of fi.

The following example illustrates how chainComplex adjusts the degrees of the modules involved to ensure that sources and targets of the differentials correspond exactly.

i1 : R = ZZ/101[x,y]

o1 = R

o1 : PolynomialRing
i2 : C = chainComplex{matrix{{x,y}},matrix{{x*y},{-x^2}}}

      1      2      1
o2 = R  <-- R  <-- R
                    
     0      1      2

o2 : ChainComplex
We check that that this is a complex:
i3 : C.dd^2 == 0

o3 = true
The homology of this complex:
i4 : HH C

o4 = 0 : cokernel | x y |                     

     1 : subquotient ({1} | -y |, {1} | xy  |)
                      {1} | x  |  {1} | -x2 |

     2 : image 0                              

o4 : GradedModule

See also