coordinates for SubquoModuleElem

[JohnAAbbott]

I had expected coordinates to work the same on a SubquoModuleElem as on FreeMod elem; instead it gives an unexpected result. Are my expectations incorrect?

S, (x, y, z) = graded_polynomial_ring(QQ, ["x", "y", "z"], [1 0 1; 0 1 1]); # hard to read

GG = grading_group(S); ### apparently not the same as free_abelian_group(2);
FM_grad = graded_free_module(S, GG.([[1, 2], [-1, 3]]));
(ee1,ee2) = gens(FM_grad);

SS,_ = sub(FM_grad, [(x^2+y^2)*ee1 + (x*y+y*z+z*x)*ee2,  (x*y+y*z+z*x)*ee1 + (x^2+y^2)*ee2] );

LM = leading_module(SS); 
GLM = gens(LM);
GLM[1]
coordinates(GLM[1])    # unexpected result
coordinates(x^2*ee1)  # what I expected

[JohnAAbbott]

One solution/work-around would be to "lift" the SubquoModuleElem to a FreeModElem. But how?
Since there is no quotient here, lifting could be automatic.... or not?

[wdecker]

But everything is correct. You are confusing what the coordinates are. Just check the docu in both cases. you may also enter coordinates(x^2*GLM[1])

…

Am 05.05.2023 um 14:42 schrieb JohnAAbbott ***@***.***>: I had expected coordinates to work the same on a SubquoModuleElem as on FreeMod elem; instead it gives an unexpected result. Are my expectations incorrect? S, (x, y, z) = graded_polynomial_ring(QQ, ["x", "y", "z"], [1 0 1; 0 1 1]); # hard to read GG = grading_group(S); ### apparently not the same as free_abelian_group(2); FM_grad = graded_free_module(S, GG.([[1, 2], [-1, 3]])); (ee1,ee2) = gens(FM_grad); SS,_ = sub(FM_grad, [(x^2+y^2)*ee1 + (x*y+y*z+z*x)*ee2, (x*y+y*z+z*x)*ee1 + (x^2+y^2)*ee2] ); LM = leading_module(SS); GLM = gens(LM); GLM[1] coordinates(GLM[1]) # unexpected result coordinates(x^2*ee1) # what I expected — Reply to this email directly, view it on GitHub <#2346>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AASSXEUTLDNTDQOPYPRXLJDXETYUXANCNFSM6AAAAAAXXCEXNI>. You are receiving this because you are subscribed to this thread.

[JohnAAbbott]

Ouch! That was a subtlety I'd overlooked.

[JohnAAbbott]

I'd like to suggest that the manual make it clear that an element of a
submodule is not considered (by Oscar) to be an element of the ambient
free module; the change of point of view is achieved by the function
ambient_representative.

I wonder whether the function/method coordinates which operates on an
element of a submodule should have a name different from coordinates
which operates on an element of a free module. Personally I had
expected coordinates always to give the representation in terms of the
generators of the free module -- right now I cannot even find the manual
entries for coordinates as applied to elements of (sub-)modules.

Here is an example:

S, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
FM = free_module(S, 2);
(ee1,ee2) = gens(FM);

SubM,_ = sub(FM, [(x^2+y^2)*ee1 + (x*y+y*z+z*x)*ee2,
                  (x*y+y*z+z*x)*ee1 + (x^2+y^2)*ee2] );

LM = leading_module(SubM);

GLM = gens(LM);
GLM[1]
v = x^2*ee1  # looks the same, but is not!
coordinates(GLM[1])    # different results
coordinates(x^2*ee1)   # different results

[JohnAAbbott]

Let me clarify: I cannot find the manual description of coordinates in the web-version of the Oscar manual. In a Julia/Oscar session the ? operator does find a description (among many others).