I have a tensor like
tensor([a,b,c])
where a, b, c lie in some CombinatorialFreeModule. Where (in Sage syntax) does this tensor lie? (I need to know, because I am writing a function using module_morphism, and it requires me to explicitly specify its codomain.)
Writing
type(tensor([a,b,c]))
doesn't help (it just gives generic trash).
The tensor should lie in tensor([a,b,c]).parent(), which should be the same as parent(tensor([a,b,c])).
sage: a = SteenrodAlgebra(2).an_element()
sage: M = CombinatorialFreeModule(GF(2), 's,t,u')
sage: s = M.basis()['s']
sage: T = tensor([a,s])
sage: parent(T)
mod 2 Steenrod algebra, milnor basis # Free module generated by s,t,u over Finite Field of size 2
sage: type(parent(T))
<class 'sage.combinat.free_module.CombinatorialFreeModule_Tensor_with_category'>
Well, I want something that I can use as a codomain for a map. I surely can't write "codomain=mod 2 Steenrod algebra, milnor basis" or "codomain=sage.combinat.free_module.CombinatorialFreeModule_Tensor_with_category".
Other than type, a good trick is to look at the top of the output from introspection:
sage: tensor?
Base Class: <class 'sage.categories.tensor.TensorProductFunctor'>
String Form: The tensor functorial construction
Namespace: Interactive
File: /Applications/sage/local/lib/python2.6/site-packages/sage/categories/tensor.py
Definition: tensor(self, args)
Docstring:
...
Two questionmarks, as in
sage: tensor??
will get you the source code too, or you can browse an html version, which is sometimes more helpful.
Asked: 2012-02-27 18:33:16 +0100
Seen: 1,012 times
Last updated: Feb 28 '12
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What does `parent(tensor([a,b,c]))` say?
It says, in my case, "The Malvenuto-Reutenauer Hopf algebra over <class 'sage.interfaces.r.r'=""> # The Malvenuto-Reutenauer Hopf algebra over <class 'sage.interfaces.r.r'="">". I wish it would just give me the damned type name...
?! Something's gone horribly wrong. That "R" isn't the R of the reals, it's the R of the statistical package.
It's supposed to be QQ (the rationals)... and I have no idea how the R package could have entered the picture. Here is the part of the code necessary to reproduce the mess: http://mit.edu/~darij/www/wtf.htm / http://mit.edu/~darij/www/wtf.sws
PS. I have taken the tensor of two rather than three elements to simplify the situation.