Error when defining differentials over GCA's with relations.

[miguelmarco]

The following code

sage: A.<a,b,x,u> = GradedCommutativeAlgebra(QQ,degrees=(2,2,3,3))
sage: A = A.quotient(A.ideal([a*u,b*u,x*u]))
sage: A.cdg_algebra({a:u,x:a*b})

Produces an error

...

File ~/sage/src/sage/algebras/commutative_dga.py:253, in Differential.__init__(self, A, im_gens)
    251 for i in A.gens():
    252     if not self(self(i)).is_zero():
--> 253         raise ValueError("The given dictionary does not determine a valid differential")

ValueError: The given dictionary does not determine a valid differential

which is wrong, because the differential is valid in the quotient algebra.

It seems that the computations for the differential are done in the free algebra instead of the quotient one.

CC: @tscrim @jhpalmieri

Component: algebra

Author: Miguel Marco

Branch/Commit: 8ba265b

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34818

[miguelmarco]

Branch: u/mmarco/error_when_defining_differentials_over_gca_s_with_relations_

[miguelmarco]

Commit: fe84785

[miguelmarco]

New commits:

fe84785

Check for ideal preservation without creating an auxiliary algebra with non-valid differential

[tscrim]

comment:3

A few minor things:

-Check that #34818 is solved::
+Check that :trac:`34818` is solved::

         if isinstance(im_gens, (list, tuple)):
-           im_gens = {A.gen(i): x for i, x in enumerate(im_gens)}
-
-        im_gens = {A(a): A(im_gens[a]) for a in im_gens}
+           im_gens = {A.gen(i): A(x) for i, x in enumerate(im_gens)}
+        else:
+            im_gens = {A(a): A(im_gens[a]) for a in im_gens}

         def image_monomial(exponent):
             i = 0
             cexp = list(exponent)
             while i < len(cexp):
-                if cexp[i] == 0:
+                if not cexp[i]:
                     i +=1
                     continue
                 a = A.gen(i)
                 try:
                     da = im_gens[a]
                 except KeyError:
                     da = A.zero()
                 cexp[i] -= 1
-                b = prod([A.gen(j)**cexp[j] for j in range(len(cexp))])
+                b = prod(A.gen(j) ** cexp[j] for j in range(len(cexp)))
                 db = image_monomial(cexp)
-                im =  da * b + (-1)**A._degrees[i]*a*db
-                return(A(im))
+                im =  da * b + (-1)**A._degrees[i] * a * db
+                return A(im)
             return A.zero()
 
         for g in I.gens():
             d = g.dict()
-            res = A(sum([d[ex]*image_monomial(ex) for ex in d]))
+            res = A.sum(d[ex] * image_monomial(ex) for ex in d)
             if not res.is_zero():
-                raise ValueError("The differential does not preserve the ideal")
+                raise ValueError("the differential does not preserve the ideal")

Note that this last change might change a few error messages, but this is to follow a Python convention.

[miguelmarco]

comment:4

Your changes look good. Can you push them?

[tscrim]

Changed commit from fe84785 to 9fde881

[tscrim]

Changed branch from u/mmarco/error_when_defining_differentials_over_gca_s_with_relations_ to u/tscrim/differential_gca_relations-34818

[tscrim]

comment:5

Done. I also took the liberty of making all of the error messages in the file follow the Python convention (to help prevent any inconsistencies).

---

New commits:

9fde881

Some small reviewer changes.

[tscrim]

Reviewer: Travis Scrimshaw

[miguelmarco]

comment:6

Great!

It can be set to positive review if nobody objects.

[fchapoton]

comment:7

pyflakes plugin says

+src/sage/algebras/commutative_dga.py:203:13 local variable 'squares' is assigned to but never used

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a8600ba

Removing the squares ideal.

[sagetrac-git]

Changed commit from 9fde881 to a8600ba

[tscrim]

comment:9

Fixed.

[sagetrac-git]

Changed commit from a8600ba to 2bf730c

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2bf730c

Merge branch 'develop' into u/tscrim/differential_gca_relations-34818

[sagetrac-git]

Changed commit from 2bf730c to 8ba265b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8ba265b

Addressing pyflakes.

[tscrim]

comment:12

Green bot modulo the pyflakes unused variable I just removed.

[tscrim]

comment:13

Morally green bot.

[miguelmarco]

comment:14

Positive review then?

[tscrim]

comment:15

Assuming Frédéric has no further ones, I think so.

[vbraun]

Changed branch from u/tscrim/differential_gca_relations-34818 to 8ba265b