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This repository was archived by the owner on Feb 1, 2023. It is now read-only.

Commitbf942ae

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Trac #34581: Implement substitution in InfinitePolynomialRing
Add the ability to substitute variables in `InfinitePolynomialRing`.{{{sage: R.<z> = InfinitePolynomialRing(QQ)sage: f = z[1] + z[1]*z[2]*z[3]sage: f.subs({z[1]:z[0]})---------------------------------------------------------------------------TypeError Traceback (most recent calllast)Input In [3], in <cell line: 1>()----> 1 f.subs({z[Integer(1)]:z[Integer(0)]})File ~/Applications/sage/src/sage/structure/element.pyx:830, insage.structure.element.Element.subs() 828 if str(gen) in kwds: 829 variables.append(kwds[str(gen)])--> 830 elif in_dict and gen in in_dict: 831 variables.append(in_dict[gen]) 832 else:TypeError: unhashable type: 'InfinitePolynomialGen'}}}URL:https://trac.sagemath.org/34581Reported by: tkarnTicket author(s): Trevor K. KarnReviewer(s): Tomer Bauer, Travis Scrimshaw
2 parents88fd702 +a56e345 commitbf942ae

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‎src/sage/rings/polynomial/infinite_polynomial_element.py‎

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@@ -58,6 +58,18 @@
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returns non-negative integers, then ``c^P`` means to apply ``P`` to
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the variable indices occurring in ``c``.
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If you want to substitute variables you can use the standard polynomial
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methods, such as
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:meth:`~sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial_sparse.subs`::
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sage: R.<x,y> = InfinitePolynomialRing(QQ)
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sage: f = x[1] + x[1]*x[2]*x[3]
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sage: f.subs({x[1]: x[0]})
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x_3*x_2*x_0 + x_0
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sage: g = x[0] + x[1] + y[0]
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sage: g.subs({x[0]: y[0]})
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x_1 + 2*y_0
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TESTS:
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We test whether coercion works, even in complicated cases in which
@@ -317,6 +329,10 @@ def __call__(self, *args, **kwargs):
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sage: a(x_1=x[100])
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x_100 + x_0
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sage: M = matrix([[1,1],[2,0]])
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sage: a(x_1=M)
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[x_0 + 1 1]
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[ 2 x_0]
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"""
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# Replace any InfinitePolynomials by their underlying polynomials
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ifhasattr(self._p,'variables'):
@@ -433,6 +449,88 @@ def __getattr__(self, s):
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exceptAttributeError:
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raiseAttributeError('%s has no attribute %s'% (self.__class__,s))
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defsubs(self,fixed=None,**kwargs):
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"""
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Substitute variables in ``self``.
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INPUT:
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- ``fixed`` -- (optional) ``dict`` with ``{variable:value}`` pairs
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- ``**kwargs`` -- named parameters
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OUTPUT:
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the resulting substitution
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EXAMPLES::
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sage: R.<x,y> = InfinitePolynomialRing(QQ)
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sage: f = x[1] + x[1]*x[2]*x[3]
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Passing ``fixed={x[1]: x[0]}``. Note that the keys may be given
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using the generators of the infinite polynomial ring
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or as a string::
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sage: f.subs({x[1]: x[0]})
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x_3*x_2*x_0 + x_0
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sage: f.subs({'x_1': x[0]})
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x_3*x_2*x_0 + x_0
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Passing the variables as names parameters::
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sage: f.subs(x_1=y[1])
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x_3*x_2*y_1 + y_1
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sage: f.subs(x_1=y[1], x_2=2)
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2*x_3*y_1 + y_1
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The substitution returns the original polynomial if you try
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to substitute a variable not present::
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sage: g = x[0] + x[1]
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sage: g.subs({y[0]: x[0]})
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x_1 + x_0
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The substitution can also handle matrices::
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sage: M = matrix([[1,0],[0,2]])
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sage: N = matrix([[0,3],[4,0]])
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sage: g = x[0]^2 + 3*x[1]
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sage: g.subs({'x_0': M})
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[3*x_1 + 1 0]
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[ 0 3*x_1 + 4]
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sage: g.subs({x[0]: M, x[1]: N})
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[ 1 9]
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[12 4]
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If you pass both ``fixed`` and ``kwargs``, any conflicts
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will defer to ``fixed``::
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sage: R.<x,y> = InfinitePolynomialRing(QQ)
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sage: f = x[0]
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sage: f.subs({x[0]:1})
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1
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sage: f.subs(x_0=5)
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5
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sage: f.subs({x[0]:1}, x_0=5)
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1
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TESTS::
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sage: g.subs(fixed=x[0], x_1=N)
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Traceback (most recent call last):
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...
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ValueError: fixed must be a dict
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"""
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iffixed:
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ifnotisinstance(fixed,dict):
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raiseValueError('fixed must be a dict')
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kwargs.update(fixed)
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try:
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returnself(**kwargs)
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exceptTypeError:
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str_kwargs= {str(k):vfork,vinkwargs.items()}
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returnself(**str_kwargs)
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defring(self):
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"""
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The ring which ``self`` belongs to.

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