Do you want to do a G+ hangout about this? Looks like there are couple options to go about this, it might be the fastest to brainstorm this face to face.
Ondrej On Fri, Mar 28, 2014 at 8:29 AM, Matthew Rocklin <[email protected]> wrote: > 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. >> >> 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. -- 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/CADDwiVC2dOYvobCDcjMBySQx8TS-j7peBsxk2NmqKBrMWqRBQQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
