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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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