adding the ring of quantum-valued polynomials #38952
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| INPUT: | ||
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| - ``R`` -- commutative ring |
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I think it would be good to have q be included as an argument, subsequently it would be a part of the ground ring. Now you can have an option like if the input is :
- Only
R, then appendqas currently implemented. - Both
(R, q), then doq = R(q). - Just
qand getR = q.parent().
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Hmm, I would rather not allow a custom q. The ring R is not there to provide q, in my mind. I have added a sentence about that in the doc.
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You don’t expect anyone to want to specialize q? It also feels slightly off mathematically to not have q in the base ring, but perhaps that is just from my experience with Hecke algebras and quantum groups...
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I am not sure. For my own usage, I have a base ring of coefficients, almost always QQ, and the variable q on top of that. For this algebra of quantum-valued polynomials, I can see no interest to have q a complex number. Of course, one can evaluate to polynomials and then evaluate q if one will.
| j = ZZ(n2) | ||
| if j < i: | ||
| j, i = i, j | ||
| q = self.base_ring().gen() |
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Rather than getting this every time, I think it would be better to store self._q = self.base_ring().gen() in the __init__.
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The new attribute "_q" is not inherited by the Bases. So I have made a method ".q" there. If you have a better way, please tell me.
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Either have an ABC for the basis or just have both of them provide it.
Nevertheless, having a method q() is a good idea.
This is a q-analogue of the ring of integer-valued polynomials. The elements are polynomials in x such that their evaluation at every q-integer is a polynomial in q.
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