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- """ Functions to support rewriting of SymPy expressions """
- from sympy.core.expr import Expr
- from sympy.assumptions import ask
- from sympy.strategies.tools import subs
- from sympy.unify.usympy import rebuild, unify
- def rewriterule(source, target, variables=(), condition=None, assume=None):
- """ Rewrite rule.
- Transform expressions that match source into expressions that match target
- treating all ``variables`` as wilds.
- Examples
- ========
- >>> from sympy.abc import w, x, y, z
- >>> from sympy.unify.rewrite import rewriterule
- >>> from sympy import default_sort_key
- >>> rl = rewriterule(x + y, x**y, [x, y])
- >>> sorted(rl(z + 3), key=default_sort_key)
- [3**z, z**3]
- Use ``condition`` to specify additional requirements. Inputs are taken in
- the same order as is found in variables.
- >>> rl = rewriterule(x + y, x**y, [x, y], lambda x, y: x.is_integer)
- >>> list(rl(z + 3))
- [3**z]
- Use ``assume`` to specify additional requirements using new assumptions.
- >>> from sympy.assumptions import Q
- >>> rl = rewriterule(x + y, x**y, [x, y], assume=Q.integer(x))
- >>> list(rl(z + 3))
- [3**z]
- Assumptions for the local context are provided at rule runtime
- >>> list(rl(w + z, Q.integer(z)))
- [z**w]
- """
- def rewrite_rl(expr, assumptions=True):
- for match in unify(source, expr, {}, variables=variables):
- if (condition and
- not condition(*[match.get(var, var) for var in variables])):
- continue
- if (assume and not ask(assume.xreplace(match), assumptions)):
- continue
- expr2 = subs(match)(target)
- if isinstance(expr2, Expr):
- expr2 = rebuild(expr2)
- yield expr2
- return rewrite_rl
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