coker is a synonym for cokernel.
The generators of the cokernel are provided by the generators of the target of f. In other words, cover target f and cover cokernel f are equal.
An argument f that is a RingElement is interpreted as a one by one matrix.
i1 : R = ZZ[a..d]; |
i2 : M = cokernel matrix{{2*a-b,3*c-5*d,a^2-b-3}} o2 = cokernel | 2a-b 3c-5d a2-b-3 | 1 o2 : R-module, quotient of R |
i3 : f = map(a*M, M, a^3+a^2*b) o3 = {1} | a+10b+18 | o3 : Matrix |
i4 : (target f,source f) o4 = (subquotient (| a |, | 2a-b 3c-5d a2-b-3 |), cokernel | 2a-b 3c-5d ------------------------------------------------------------------------ a2-b-3 |) o4 : Sequence |
i5 : N = cokernel f o5 = subquotient (| a |, | a2+10ab+18a 2a-b 3c-5d a2-b-3 |) 1 o5 : R-module, subquotient of R |
i6 : minimalPresentation N o6 = cokernel {1} | 81 27d 3c-5d 3b-18 a+b-9 9d2 bd-6d b2-b-30 3d3 d4 | 1 o6 : R-module, quotient of R |