Add an infinite weyl algebra class #40263
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Documentation preview for this PR (built with commit 5f260c8; changes) is ready! 🎉 |
src/sage/algebras/weyl_algebra.py
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| elif isinstance(R, InfinitePolynomialRing_dense): | ||
| return InfiniteDifferentialWeylAlgebra(R, names) |
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| elif isinstance(R, InfinitePolynomialRing_dense): | |
| return InfiniteDifferentialWeylAlgebra(R, names) | |
| elif isinstance(R, InfinitePolynomialRing_dense) and names is None: | |
| return InfiniteDifferentialWeylAlgebra(R.base_ring(), R.variable_names()) |
What if the base ring for a finitely generated Weyl algebra is an infinite polynomial ring? (Add a test checking this works as expected.)
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This seems to work as expected (added some tests to make sure both infinite over finite and finite over infinite work as expected.
One issue I noticed is that the InfinitePolynomialRing class collapses things down, so it would be tricky to define an infinite weyl algebra over and infinite polynomial ring. For instance, here it forgets that R is the base ring.
sage: R.<x> = InfinitePolynomialRing(QQ)
sage: R2.<y> = InfinitePolynomialRing(R)
sage: R2.base_ring()
Rational Field
src/sage/algebras/weyl_algebra.py
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| if isinstance(R, InfinitePolynomialRing_dense): | ||
| names = R.variable_names() | ||
| if len(names) > 1: | ||
| raise NotImplementedError("only one set of variables supported") | ||
| R = R.base_ring() | ||
| elif names is None: | ||
| names = ('x',) |
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| if isinstance(R, InfinitePolynomialRing_dense): | |
| names = R.variable_names() | |
| if len(names) > 1: | |
| raise NotImplementedError("only one set of variables supported") | |
| R = R.base_ring() | |
| elif names is None: | |
| names = ('x',) | |
| if isinstance(R, InfinitePolynomialRing_dense) and names is None: | |
| names = R.variable_names() | |
| if len(names) > 1: | |
| raise NotImplementedError("only one set of variables supported") | |
| R = R.base_ring() |
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removing this causes an error when you construct via
sage: W = DifferentialWeylAlgebra(QQ, n=oo)
I moved the check to the differential weyl classcall to handle this case.
src/sage/algebras/weyl_algebra.py
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| """ | ||
| An element of an infinitely generated differential Weyl algebra. | ||
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| TESTS:: |
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| TESTS:: | |
| EXAMPLES:: |
src/sage/algebras/weyl_algebra.py
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| for _ in range(p): | ||
| next = [] | ||
| for m, c in cur: | ||
| diff = dict(m[1].dict()) |
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| diff = dict(m[1].dict()) | |
| diff = m[1].dict() |
The extra dict call should not be necessary.
src/sage/algebras/weyl_algebra.py
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| We can construct an Infinite Weyl algebra by using the ``n=oo`` parameter in | ||
| the constructor for DifferentialWeylAlgebra:: |
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| We can construct an Infinite Weyl algebra by using the ``n=oo`` parameter in | |
| the constructor for DifferentialWeylAlgebra:: | |
| We construct an infinite Weyl algebra by using the ``n=oo`` in | |
| :class:`DifferentialWeylAlgebra`:: |
src/sage/algebras/weyl_algebra.py
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| Due to a bug in ``InfinitePolynomialRing`` (see :issue:`36788`) trying to define the infinite Weyl | ||
| algebra of an infinite polynomial ring with coefficients in another infinite | ||
| polynomial ring will result in unexpected behavior:: | ||
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| sage: R.<x> = InfinitePolynomialRing(QQ) | ||
| sage: R2.<y> = InfinitePolynomialRing(R) | ||
| sage: W = DifferentialWeylAlgebra(R2); W # known bug | ||
| Differential Weyl algebra in countably many variables z over Infinite | ||
| polynomial ring in x over Rational Field | ||
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| Due to a bug in ``InfinitePolynomialRing`` (see :issue:`36788`) trying to define the infinite Weyl | |
| algebra of an infinite polynomial ring with coefficients in another infinite | |
| polynomial ring will result in unexpected behavior:: | |
| sage: R.<x> = InfinitePolynomialRing(QQ) | |
| sage: R2.<y> = InfinitePolynomialRing(R) | |
| sage: W = DifferentialWeylAlgebra(R2); W # known bug | |
| Differential Weyl algebra in countably many variables z over Infinite | |
| polynomial ring in x over Rational Field | |
| Due to a bug in ``InfinitePolynomialRing`` (:issue:`36788`) trying to define the infinite Weyl | |
| algebra of an infinite polynomial ring with coefficients in another infinite | |
| polynomial ring will result in unexpected behavior:: | |
| sage: R.<x> = InfinitePolynomialRing(QQ) | |
| sage: R2.<y> = InfinitePolynomialRing(R) | |
| sage: W = DifferentialWeylAlgebra(R2); W # known bug | |
| Differential Weyl algebra in countably many variables z over Infinite | |
| polynomial ring in x over Rational Field | |
src/sage/algebras/weyl_algebra.py
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| sage: W = DifferentialWeylAlgebra(R); W | ||
| Differential Weyl algebra in countably many variables x over Rational Field | ||
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| .. WARNING: |
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| .. WARNING: | |
| .. WARNING:: |
src/sage/algebras/weyl_algebra.py
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| OUTPUT: A nonnegative integer | ||
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| EXAMPLE:: |
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| EXAMPLE:: | |
| EXAMPLES:: |
We generally make it plural, even if there is only 1 test/example.
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should be good to go now! |
sagemathgh-40263: Add an infinite weyl algebra class <!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes sagemath#12345". --> This PR adds a class ``InfiniteDifferentialWeylAlgebra``, the infinite analog of the currently existing ``DifferentialWeylAlgebra`` class. It is an algebra generated by two countable families of symbols x_i, dx_i subject to the relations [x_i, x_j] = [dx_i, dx_j] = 0 and [x_i, dx_j] = \delta_{i, j} Part of sagemath#40241 cc: @tscrim ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#40263 Reported by: Joe McDonough Reviewer(s): Joe McDonough, Travis Scrimshaw
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Fails with the same error as the CI |
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@vbraun I'm a bit confused by the cause of this error. Somehow importing Also cc'ing @tscrim in case he needs to re positive review the PR. edit: it seems like one of the CI tests is now failing on a doctest for singular, but I'm not sure how to go about diagnosing why. |
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Now it is passing all of the builds. |
This PR adds a class
InfiniteDifferentialWeylAlgebra, the infinite analog of the currently existingDifferentialWeylAlgebraclass. It is an algebra generated by two countable families of symbols x_i, dx_i subject to the relations [x_i, x_j] = [dx_i, dx_j] = 0 and [x_i, dx_j] = \delta_{i, j}Part of #40241
cc: @tscrim
📝 Checklist
⌛ Dependencies