Inconsistent behaviour of == for modules

[pzinn]

As part of trying to fix https://github.com/Macaulay2/M2/issues/1273, I encountered the following bug (or at least, inconsistent behaviour):

i1 : R=QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : M=ideal(x,y)/ideal(x^2,y)

o2 = subquotient (| x y |, | x2 y |)

                               1
o2 : R-module, subquotient of R

i3 : trim M

o3 = subquotient (| x |, | y x2 |)

                               1
o3 : R-module, subquotient of R

i4 : trim M == M

o4 = true

i5 : M'=ideal x/ideal(x^2,x*y)

o5 = subquotient (| x |, | x2 xy |)

                               1
o5 : R-module, subquotient of R

i6 : M==M'

o6 = false

i7 : trim M==M' -- should definitely be true

o7 = false

Note that all these modules are equal. If anything, one could argue that M and trim M are not exactly the same since the generators are different, so the modules are isomorphic but technically not equal; but M2 doesn't seem to care about that. However, it does notice that the relations of M and M' are different -- even though that makes no difference (in particular, trim M and M' are strictly equal). The corresponding code is tagged as "temporary"...

[pzinn]

OK I think I understand the logic. I implicitly assumed that when writing M/N we really meant $M/(N\cap M)$, whereas after checking the doc, I see that it's $(M+N)/N$ instead. then the answers as given are correct. closing.

[mahrud]

Playing with @d-torrance's PRs, I think this is a bug though:

R = QQ[x,y,z,w];
M = (comodule monomialCurveIdeal(R, {1,2,3}))^3;
m = map(M, , {{z^2}, {y*z}, {y^2}})
v1 = vector m
v2 = m_0
v1 === v2      -- false!
v1 ==  v2      -- false!! (should definitely call reduce)
v1 - v2 == 0_M -- false!!! (also v1 - v2 == 0 should work)

While:

peek v2 == peek v1 -- true XD

I think it's because of this:

i65 : source matrix v1

       1
o65 = R

o65 : R-module, free, degrees {2}

i66 : source matrix v2

       1
o66 = R

o66 : R-module, free

i67 : degree v1, degree v2

o67 = ({2}, {2})

o67 : Sequence

i68 : degree matrix v1, degree matrix v2

o68 = ({0}, {2})

o68 : Sequence

Somehow the vectors are the same, but the internal matrix representations have different degrees, which I think should be irrelevant (or rather, the internal matrix degree of vectors should be always set to zero).

[pzinn]

agreed. unrelated to my (now closed) issue though :-P