# ComplexMap _ ZZ -- access individual matrices in a complex map

## Synopsis

• Operator: _
• Usage:
f_i
• Inputs:
• f, ,
• i, an integer, the homological index
• Outputs:
• , the i-th map

## Description

A complex map $f : C \to D$ of degree $d$ is a sequence of maps $f_i : C_i \to D_{i+d}$. This method allows one to access the individual $f_i$.

 i1 : S = ZZ/101[a..c]; i2 : C = freeResolution coker matrix{{a^2, b^2, c^2}} 1 3 3 1 o2 = S <-- S <-- S <-- S 0 1 2 3 o2 : Complex i3 : D = freeResolution coker vars S 1 3 3 1 o3 = S <-- S <-- S <-- S 0 1 2 3 o3 : Complex i4 : f = randomComplexMap(D, C) 1 1 o4 = 0 : S <---------- S : 0 | 24 | 3 3 1 : S <-------------------------------------------------- S : 1 {1} | -36a-30b-29c -29a-24b-38c -39a-18b-13c | {1} | 19a+19b-10c -16a+39b+21c -43a-15b-28c | {1} | -29a-8b-22c 34a+19b-47c -47a+38b+2c | 3 3 2 : S <------------------------------------------------------------------------------------------------------ S : 2 {2} | 16a2+22ab-34b2+45ac-48bc-47c2 35a2+11ab+33b2-38ac+40bc+11c2 -37a2-13ab+30b2-10ac-18bc+39c2 | {2} | 47a2+19ab+7b2-16ac+15bc-23c2 46a2-28ab-3b2+ac+22bc-47c2 27a2-22ab-9b2+32ac-32bc-20c2 | {2} | 39a2+43ab-11b2-17ac+48bc+36c2 -23a2-7ab+29b2+2ac-47bc+15c2 24a2-30ab-15b2-48ac+39bc | 1 1 3 : S <------------------------------------------------------------------- S : 3 {3} | 33a3-49a2b-19ab2+44b3-33a2c+17abc-39b2c-20ac2+36bc2+9c3 | o4 : ComplexMap i5 : f_2 o5 = {2} | 16a2+22ab-34b2+45ac-48bc-47c2 35a2+11ab+33b2-38ac+40bc+11c2 {2} | 47a2+19ab+7b2-16ac+15bc-23c2 46a2-28ab-3b2+ac+22bc-47c2 {2} | 39a2+43ab-11b2-17ac+48bc+36c2 -23a2-7ab+29b2+2ac-47bc+15c2 ------------------------------------------------------------------------ -37a2-13ab+30b2-10ac-18bc+39c2 | 27a2-22ab-9b2+32ac-32bc-20c2 | 24a2-30ab-15b2-48ac+39bc | 3 3 o5 : Matrix S <--- S i6 : f_0 o6 = | 24 | 1 1 o6 : Matrix S <--- S

Indices that are outside of the concentration are automatically zero.

 i7 : concentration f o7 = (0, 3) o7 : Sequence i8 : f_-1 o8 = 0 o8 : Matrix 0 <--- 0 i9 : f_3 o9 = {3} | 33a3-49a2b-19ab2+44b3-33a2c+17abc-39b2c-20ac2+36bc2+9c3 | 1 1 o9 : Matrix S <--- S i10 : f_4 o10 = 0 o10 : Matrix 0 <--- 0