Description
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];
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i2 : M = cokernel matrix{{2*a-b,3*c-5*d,a^2-b-3}}
o2 = cokernel | 2a-b 3c-5d a2-b-3 |
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o2 : R-module, quotient of R
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If
f is a matrix, and the target of
f is a submodule, the resulting module will be a
subquotient module.
i3 : f = map(a*M, M, a^3+a^2*b)
o3 = {1} | a+10b+18 |
o3 : Matrix
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i4 : (target f,source f)
o4 = (subquotient (| a |, | 2a-b 3c-5d a2-b-3 |), cokernel | 2a-b 3c-5d
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a2-b-3 |)
o4 : Sequence
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i5 : N = cokernel f
o5 = subquotient (| a |, | a2+10ab+18a 2a-b 3c-5d a2-b-3 |)
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o5 : R-module, subquotient of R
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i6 : minimalPresentation N
o6 = cokernel | 81 27d 3c-5d 3b-18 a+b-9 9d2 bd-6d b2-b-30 3d3 d4 |
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o6 : R-module, quotient of R
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