Such a morphism takes advantage of the universality of tensors for multilinear functions.
I'd like to define a morphism that acts on the order 2 term below, for example, by
-e4*p1 # p2*p3*ph1*ph2 |---> -3*p2*p3*ph1*ph2
I.E. it maps the tensor product of two exterior algebras into an exterior algebra, specified by two mappings f1, f2 on exterior algebra basis products (* is how Sage inputs and prints exterior product, and # is how it prints tensor product):
map_wanted(f1, f2): (e1*e2*... # e3*e4*...) |---> f1(e1*e2*...)*f2(e3*e4*...)
Here,
f1: (e4*p1) |---> 3 and f2 is the identity map
Also, to do this, how would I define the f1 and f2? I can specify a table of
exterior *s of the finitely many generator elements and the image I want, where
I illustrated f1 by one table entry.
Here is a full example of the context:
type(typterm)
<class 'sage.algebras.clifford_algebra.ExteriorAlgebra_with_category.element_class'>
typterm
-e4*p1*p2*p3*ph1*ph2
typterm.parent().gens()
(e1, e2, e3, e4, eh1, eh2, eh3, eh4, p1, p2, p3, ph1, ph2, ph3)
cop = typterm.coproduct()
copterm = cop.terms()[3]
type(copterm)
<class 'sage.combinat.free_module.CombinatorialFreeModule_Tensor_with_category.element_class'>
tensors=copterm.parent()
tensors
The exterior algebra of rank 14 over Rational Field # The exterior algebra of rank 14 over Rational Field
copterm
-e4*p1 # p2*p3*ph1*ph2
Here, f1: (e4*p1) |---> 3, and f2 is the identity map so I'd like
-e4*p1 # p2*p3*ph1*ph2 |---> -3*p2*p3*ph1*ph2
Thanks!
