If gi : Ci →Dd+i, and hj : Dj →Ee+j, then the composition corresponds to fi := hd+i * gi : Ci →Ei+d+e. In particular, the degree of the composition f is the sum of the degrees of g and h.
i1 : R = ZZ/101[a..d] o1 = R o1 : PolynomialRing |
i2 : C = freeResolution coker vars R 1 4 6 4 1 o2 = R <-- R <-- R <-- R <-- R 0 1 2 3 4 o2 : Complex |
i3 : 3 * dd^C 1 4 o3 = 0 : R <------------------- R : 1 | 3a 3b 3c 3d | 4 6 1 : R <----------------------------------- R : 2 {1} | -3b -3c 0 -3d 0 0 | {1} | 3a 0 -3c 0 -3d 0 | {1} | 0 3a 3b 0 0 -3d | {1} | 0 0 0 3a 3b 3c | 6 4 2 : R <--------------------------- R : 3 {2} | 3c 3d 0 0 | {2} | -3b 0 3d 0 | {2} | 3a 0 0 3d | {2} | 0 -3b -3c 0 | {2} | 0 3a 0 -3c | {2} | 0 0 3a 3b | 4 1 3 : R <--------------- R : 4 {3} | -3d | {3} | 3c | {3} | -3b | {3} | 3a | o3 : ComplexMap |
i4 : 0 * dd^C o4 = 0 o4 : ComplexMap |
i5 : dd^C * dd^C o5 = 0 o5 : ComplexMap |