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73 lines
2.1 KiB
73 lines
2.1 KiB
from sympy.tensor import Indexed
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from sympy.core.containers import Tuple
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from sympy.core.symbol import Dummy
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from sympy.core.sympify import sympify
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from sympy.integrals.integrals import Integral
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class IndexedIntegral(Integral):
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"""
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Experimental class to test integration by indexed variables.
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Usage is analogue to ``Integral``, it simply adds awareness of
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integration over indices.
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Contraction of non-identical index symbols referring to the same
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``IndexedBase`` is not yet supported.
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Examples
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========
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>>> from sympy.sandbox.indexed_integrals import IndexedIntegral
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>>> from sympy import IndexedBase, symbols
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>>> A = IndexedBase('A')
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>>> i, j = symbols('i j', integer=True)
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>>> ii = IndexedIntegral(A[i], A[i])
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>>> ii
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Integral(_A[i], _A[i])
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>>> ii.doit()
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A[i]**2/2
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If the indices are different, indexed objects are considered to be
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different variables:
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>>> i2 = IndexedIntegral(A[j], A[i])
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>>> i2
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Integral(A[j], _A[i])
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>>> i2.doit()
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A[i]*A[j]
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"""
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def __new__(cls, function, *limits, **assumptions):
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repl, limits = IndexedIntegral._indexed_process_limits(limits)
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function = sympify(function)
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function = function.xreplace(repl)
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obj = Integral.__new__(cls, function, *limits, **assumptions)
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obj._indexed_repl = repl
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obj._indexed_reverse_repl = {val: key for key, val in repl.items()}
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return obj
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def doit(self):
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res = super().doit()
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return res.xreplace(self._indexed_reverse_repl)
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@staticmethod
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def _indexed_process_limits(limits):
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repl = {}
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newlimits = []
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for i in limits:
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if isinstance(i, (tuple, list, Tuple)):
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v = i[0]
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vrest = i[1:]
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else:
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v = i
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vrest = ()
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if isinstance(v, Indexed):
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if v not in repl:
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r = Dummy(str(v))
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repl[v] = r
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newlimits.append((r,)+vrest)
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else:
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newlimits.append(i)
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return repl, newlimits
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