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Trac #31032: some raw string for pdf doc building in sage-on-gentoo
BAck in sage 9.1 we had issues with building pdf docs because of missing raw strings. Some issues that were also happening in vanilla sage have been fixed and merged but sage-on-gentoo continued to carry a few extra ones. This ticket is to merge those leftovers. URL: https://trac.sagemath.org/31032 Reported by: fbissey Ticket author(s): François Bissey Reviewer(s): Frédéric Chapoton
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src/sage/categories/pushout.py

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class InfinitePolynomialFunctor(ConstructionFunctor):
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"""
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r"""
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A Construction Functor for Infinite Polynomial Rings (see :mod:`~sage.rings.polynomial.infinite_polynomial_ring`).
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AUTHOR:
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...
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CoercionException: Incompatible term orders lex, degrevlex
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In an infinite polynomial ring with generator `a_\\ast`, the variable `a_3` will always be greater
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In an infinite polynomial ring with generator `a_\ast`, the variable `a_3` will always be greater
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than the variable `a_1`. Hence, the orders are incompatible in the next example as well::
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sage: A.construction()[0]*PolynomialRing(QQ,names=['x','y','a_1','a_3'], order='lex').construction()[0]
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Another requirement is that after merging the order of the remaining variables must be unique.
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This is not the case in the following example, since it is not clear whether the variables `x,y`
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should be greater or smaller than the variables `b_\\ast`::
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should be greater or smaller than the variables `b_\ast`::
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sage: A.construction()[0]*PolynomialRing(QQ,names=['a_3','a_1','x','y'], order='lex').construction()[0]
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Traceback (most recent call last):
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sage: X.<w,x,y> = InfinitePolynomialRing(ZZ)
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sage: Y.<x,y,z> = InfinitePolynomialRing(QQ)
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`X` and `Y` have an overlapping generators `x_\\ast, y_\\ast`. Since the default lexicographic order is
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`X` and `Y` have an overlapping generators `x_\ast, y_\ast`. Since the default lexicographic order is
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used in both rings, it gives rise to isomorphic sub-monoids in both `X` and `Y`. They are merged in the
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pushout, which also yields a common parent for doing arithmetic::
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src/sage/rings/polynomial/infinite_polynomial_element.py

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## Further methods
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def stretch(self, k):
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"""
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r"""
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Stretch ``self`` by a given factor.
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INPUT:
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OUTPUT:
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Replace `v_n` with `v_{n\\cdot k}` for all generators `v_\\ast` occurring in self.
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Replace `v_n` with `v_{n\cdot k}` for all generators `v_\ast` occurring in self.
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EXAMPLES::
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src/sage/rings/polynomial/infinite_polynomial_ring.py

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"""
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r"""
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Infinite Polynomial Rings
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By Infinite Polynomial Rings, we mean polynomial rings in a countably
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- Simon King <[email protected]>
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- Mike Hansen <[email protected]>
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An Infinite Polynomial Ring has finitely many generators `x_\\ast,
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y_\\ast,...` and infinitely many variables of the form `x_0, x_1, x_2,
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An Infinite Polynomial Ring has finitely many generators `x_\ast,
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y_\ast,...` and infinitely many variables of the form `x_0, x_1, x_2,
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..., y_0, y_1, y_2,...,...`. We refer to the natural number `n` as
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the *index* of the variable `x_n`.
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## The sparse implementation
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class InfinitePolynomialRing_sparse(CommutativeRing):
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"""
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r"""
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Sparse implementation of Infinite Polynomial Rings.
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An Infinite Polynomial Ring with generators `x_\\ast, y_\\ast,
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An Infinite Polynomial Ring with generators `x_\ast, y_\ast,
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...` over a field `F` is a free commutative `F`-algebra generated
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by `x_0, x_1, x_2, ..., y_0, y_1, y_2, ..., ...` and is equipped
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with a permutation action on the generators, namely `x_n^P =

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