Description
A presentation of
M is a map
p so that
coker p is isomorphic to
M. The presentation obtained is expressed in terms of the given generators, i.e., the modules
cover M and
target p are identical. The isomorphism can be obtained as
map(M,coker p,1).
Since a module M may be described as a submodule or a subquotient module of a free module, some computation may be required to produce a presentation. See also
trim, or
minimalPresentation, which do a bit more work to try to eliminate redundant generators.
i1 : R = QQ[a,b,c];

i2 : I = ideal"a2b2,abc"
2 2
o2 = ideal (a  b , a*b*c)
o2 : Ideal of R

i3 : M = I/(I^2+a*I)
o3 = subquotient ( a2b2 abc ,  a42a2b2+b4 a3bcab3c a2b2c2 a3ab2 a2bc )
1
o3 : Rmodule, subquotient of R

i4 : presentation M
o4 = {2}  a b2 0 0 
{3}  0 0 a b2 
2 4
o4 : Matrix R < R
