bug ih hom?

[Enrique Artal]

I am running sage in Fedora 33, x86_64 sage 9.3beta4 (though the bug appears also in ubuntu sage 9.1). This is a toy example:

K=GF(2)

V=K^2

B=V.basis()

B1=[vector(K,[i,j]) for i,j in [(1,0),(1,1)]] 

V1=V.subspace_with_basis(B1)

I considere a vector space V of dimension 2 over the field of two elements with two distinct bases. The following define linear maps using hom:

a=V.hom(B,V)

b=V.hom(B1,V)

c=V1.hom(B,V)

d=V1.hom(B1,V)

The output of [a==k for k in (a,b,c,d)] is [True, False, True, False] and as it should be the output all([a(v)==c(v) for v in V]) is False and the output of all([a(v)==d(v) for v in V]) is True.

It seems it checks the equality of the lists of images and not the equality of the maps (a and d are the identity and not b and c).

Best, Enrique.