makeRes -- creates a resolution starting from three matrices

Synopsis

Usage:

makeRes(d1,d2,d3)
Inputs:
- d1, a matrix, of the differential in degree 1
- d2, a matrix, of the differential in degree 2
- d3, a matrix, of the differential in degree 3
Outputs:
- a chain complex, the resolution with differentials d1, d2, d3.

Description

Creates a resolution of length 3 that has the given three matrices as differentials.

i1 : Q = QQ[x,y,z];

i2 : d1=matrix{{-x^2,z^2-x*y,-y^2,-x*z,-y*z}}

o2 = | -x2 -xy+z2 -y2 -xz -yz |

             1      5
o2 : Matrix Q  <-- Q

i3 : d2=matrix{{0,0,z,0,-y},{0,0,0,-y,x},{-z,0,0,x,0},{0,y,-x,0,z},{y,-x,0,-z,0}}

o3 = | 0  0  z  0  -y |
     | 0  0  0  -y x  |
     | -z 0  0  x  0  |
     | 0  y  -x 0  z  |
     | y  -x 0  -z 0  |

             5      5
o3 : Matrix Q  <-- Q

i4 : d3=transpose d1

o4 = {-2} | -x2    |
     {-2} | -xy+z2 |
     {-2} | -y2    |
     {-2} | -xz    |
     {-2} | -yz    |

             5      1
o4 : Matrix Q  <-- Q

i5 : makeRes(d1,d2,d3)

      1      5      5      1
o5 = Q  <-- Q  <-- Q  <-- Q  <-- 0
                                  
     0      1      2      3      4

o5 : ChainComplex

For the programmer

The object makeRes is a function closure.