Maybe tensor indices should be identified as variables/wilds in unification ? Should A(i, j, -j) unify to A(a, b, -b)?
On Fri, Mar 28, 2014 at 5:38 AM, F. B. <[email protected]> wrote: > The second point concerns unification of tensor, there are some issues on > contracted indices, with some boilerplate > > from sympy.tensor.tensor import * > L = TensorIndexType('L') > i0, i1, i2 = tensor_indices('i0:3', L) > A = tensorhead('A', [L]*2, [[1]*2]) > > The arguments > > >>> A(i0, i1).args > (1, (A(L,L),), (i0, i1)) > > >>> A(i0, -i0).args > (1, (A(L,L),), (dummy_index_0, -dummy_index_0)) > > > > > That is, the third argument is the list of indices, and in the contracted > form the index i0 gets replaced by dummy_index_0, which makes unification > hard: > > >>> from sympy.unify import * > > >>> list(unify(A(i0, i1), A(i0, i2), {}, variables=[i2])) > [{i2: i1}] > >>> list(unify(A(i0, -i0), A(i1, -i1), {}, variables=[i1])) > [{}] > > > > The second unify expression does not return anything because the arguments > i0 and i1 have been substituted. A possible solution is to keep the > arguments of a TensMul as they have been created, and store the > dummy_index_0 inside the corresponding TIDS object. > > A possible implementation of TensorDerivative (by which I mean the > derivatives usually employed to get the equation of motions from the > Lagrangian in QFT) can simply rely on rewriterule contained in the unify > module. > > The ability to define new objects such as TensorDerivative, > PartialDerivative, CovariantDerivative is the primary reason why I want to > make the tensor expression objects just containers, and possible transfer > all index manipulation algorithms to either TIDS or a new object. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/0bcab04e-6d84-465e-8fa8-2592b28b8b3c%40googlegroups.com<https://groups.google.com/d/msgid/sympy/0bcab04e-6d84-465e-8fa8-2592b28b8b3c%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAJ8oX-E4QCqars8wyu1fnckpW1Xfaiyk3-FPmvpfX-Sy9KZiHw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
