Bugs with GradedCommutativeAlgebra

[jhpalmieri]

Two bugs with GradedCommutativeAlgebra:

• GradedCommutativeAlgebra(QQ, 'x') does not work: it seems to not work with only one generator.

• As reported on ​ask.sagemath.org, homomorphisms don't work.

[tscrim]

The first problem is a bug in the construction of g_algebra:

sage: F.<x,y> = FreeAlgebra(QQ)
sage: F.g_algebra({})
Noncommutative Multivariate Polynomial Ring in x, y over Rational Field, nc-relations: {}
sage: F.<x> = FreeAlgebra(QQ, 1)
sage: F.g_algebra({})
// ** commutative ring with 1 variable
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
TypeError: Cannot convert sage.rings.polynomial.plural.NCPolynomialRing_plural to sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular

Looks like a special case with 1 variable is not handled properly on Sage's side, but I am not sure.

The second problem comes from this:

sage: E = GradedCommutativeAlgebra(QQ,'x,y')
sage: E.cover().domain()
Noncommutative Multivariate Polynomial Ring in x, y over Rational Field, nc-relations: {y*x: -x*y}
sage: _.hom([x,y])
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-32-d481fe5146fc> in <module>()
----> 1 _.hom([x,y])

/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/structure/parent_gens.pyx in sage.structure.parent_gens.ParentWithGens.hom (build/cythonized/sage/structure/parent_gens.c:3773)()
    286         """
    287         if self._element_constructor is not None:
--> 288             return parent.Parent.hom(self, im_gens, codomain, check)
    289         if isinstance(im_gens, parent.Parent):
    290             return self.Hom(im_gens).natural_map()

/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent.hom (build/cythonized/sage/structure/parent.c:12711)()
   1380            return self.Hom(codomain)(im_gens)
   1381        else:
-> 1382            return self.Hom(codomain)(im_gens, check=check)
   1383 
   1384     #################################################################################

/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/homset.pyc in __call__(self, im_gens, check)
    182             return self._coerce_impl(im_gens)
    183         else:
--> 184             return morphism.RingHomomorphism_im_gens(self, im_gens, check=check)
    185 
    186     def natural_map(self):

/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/morphism.pyx in sage.rings.morphism.RingHomomorphism_im_gens.__init__ (build/cythonized/sage/rings/morphism.c:8719)()
   1036             if len(im_gens) != parent.domain().ngens():
   1037                 raise ValueError("number of images must equal number of generators")
-> 1038             t = parent.domain()._is_valid_homomorphism_(parent.codomain(), im_gens)
   1039             if not t:
   1040                 raise ValueError("relations do not all (canonically) map to 0 under map determined by images of generators")

/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent._is_valid_homomorphism_ (build/cythonized/sage/structure/parent.c:11950)()
   1252        is raised.
   1253        """
-> 1254        raise NotImplementedError("Verification of correctness of homomorphisms from %s not yet implemented."%self)
   1255 
   1256     def Hom(self, codomain, category=None):

NotImplementedError: Verification of correctness of homomorphisms from Noncommutative Multivariate Polynomial Ring in x, y over Rational Field, nc-relations: {y*x: -x*y} not yet implemented.

So IMO that is not strictly a bug, but a missing feature.

[vdelecroix]

update milestone 8.3 -> 8.4

[jhpalmieri]

Here is a branch dealing with the singly generated case. I will move the morphism issue to a separate ticket.

---

New commits:

​79bb0c2

trac 25276: implement singly generated differental graded commutative algebras

[jhpalmieri]

See #26027 for morphisms.

[tscrim]

Can you also add an example for when the generator is even? Otherwise LGTM.

[git]

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

​2bf55eb

trac 25276: add one more example

[jhpalmieri]

Good idea.

[tscrim]

Thank you.