complex(ComplexMap) -- make a complex by specifying the differential

Description

Given a map $d$ of complexes having degree -1 and whose source and targets are equal, this method constructs the chain complex whose differential is $d$. This constructor does not verify that $d^2 = 0$.

 i1 : S = ZZ/101[x_1..x_4]; i2 : F = freeResolution coker vars S 1 4 6 4 1 o2 = S <-- S <-- S <-- S <-- S 0 1 2 3 4 o2 : Complex i3 : d = randomComplexMap(F, F, Cycle => true, InternalDegree => -1, Degree => -1) 1 o3 = -1 : 0 <----- S : 0 0 1 4 0 : S <---------------------- S : 1 | -29 30 -36 -24 | 4 6 1 : S <--------------------------------- S : 2 {1} | -30 36 0 24 0 0 | {1} | -29 0 36 0 24 0 | {1} | 0 -29 30 0 0 24 | {1} | 0 0 0 -29 30 -36 | 6 4 2 : S <--------------------------- S : 3 {2} | -36 -24 0 0 | {2} | -30 0 -24 0 | {2} | -29 0 0 -24 | {2} | 0 -30 36 0 | {2} | 0 -29 0 36 | {2} | 0 0 -29 30 | 4 1 3 : S <--------------- S : 4 {3} | 24 | {3} | -36 | {3} | -30 | {3} | -29 | o3 : ComplexMap i4 : d^2 o4 = 0 o4 : ComplexMap i5 : C = complex d 1 4 6 4 1 o5 = S <-- S <-- S <-- S <-- S 0 1 2 3 4 o5 : Complex i6 : assert isWellDefined C i7 : assert all(0..4, i -> dd^C_i == d_i)
 i8 : e = randomComplexMap(F, F, InternalDegree => -1, Degree => -1) 1 o8 = -1 : 0 <----- S : 0 0 1 4 0 : S <--------------------- S : 1 | 19 19 -10 -29 | 4 6 1 : S <----------------------------------- S : 2 {1} | -8 -38 34 -18 -28 16 | {1} | -22 -16 19 -13 -47 22 | {1} | -29 39 -47 -43 38 45 | {1} | -24 21 -39 -15 2 -34 | 6 4 2 : S <--------------------------- S : 3 {2} | -48 15 48 40 | {2} | -47 -23 36 11 | {2} | 47 39 35 46 | {2} | 19 43 11 -28 | {2} | -16 -17 -38 1 | {2} | 7 -11 33 -3 | 4 1 3 : S <--------------- S : 4 {3} | 22 | {3} | -47 | {3} | -23 | {3} | -7 | o8 : ComplexMap i9 : D = complex e 1 4 6 4 1 o9 = S <-- S <-- S <-- S <-- S 0 1 2 3 4 o9 : Complex i10 : debugLevel = 1 o10 = 1 i11 : assert not isWellDefined D -- expected maps in the differential to compose to zero -- differentials at indices (2, 1) fail this condition