ExtDegreeLimit(ZZ,Module,Matrix,ZZ) -- Computes the map Ext^i(M, source f)_{<=d} -> Ext^i(M, target f)_{<=d} induced by f.

Synopsis

Usage:
g=ExtDegreeLimit(i,M,f,d)
Function: ExtDegreeLimit
Inputs:
- i, an integer
- M, a module
- f, a matrix
- d, an integer
Optional inputs:
- printTimings => ..., -- a Boolean value, default value false, whether to print timings of the key steps of the function.
Outputs:
- g, a matrix

Description

If M is an ideal, it is regarded as a module in the evident way.

i1 : kk = ZZ/10007;

i2 : R = kk[y_0..y_2];

i3 : betti (N1 = (prune coker random(R^{2:-2},R^{1:-3}))**R^{1:2})

            0 1
o3 = total: 2 1
         0: 2 1

o3 : BettiTally

i4 : betti (N2 = coker (presentation N1)^{0})

            0 1
o4 = total: 1 1
         0: 1 1

o4 : BettiTally

i5 : betti (M = (prune coker random(R^{1:-1,1:-2,1:-3},R^{3:-4}))**R^{1:0})

            0 1
o5 = total: 3 3
         1: 1 .
         2: 1 .
         3: 1 3

o5 : BettiTally

i6 : f = homomorphism((Hom(N1,N2))_{0});

o6 : Matrix

i7 : time ExtDegreeLimit(1,M,f,-4)
     -- used 0.0143339 seconds

o7 = {-4} | 1 0 0 0 0 0 |
     {-4} | 0 0 1 0 0 0 |
     {-4} | 0 0 0 0 1 0 |

o7 : Matrix