#19416: Implement some generic category methods
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/generic_methods-19416|
f9b5da0e38fc793122ac2615df86efa3a590f3ad
Dependencies: | Stopgaps:
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Comment (by jhpalmieri):
I would prefer if the docstring for `is_commutative` said "Return
''whether'' self is a commutative algebra" (or "Return whether this
algebra is a commutative algebra").
Is it worth saving any time by removing `self.one()` from the basis before
doing the iteration? With the following change:
{{{
#!diff
diff --git a/src/sage/categories/finite_dimensional_algebras_with_basis.py
b/src/sage/categories/finite_dimensional_algebras_with_basis.py
index da1a870..8934e6c 100644
--- a/src/sage/categories/finite_dimensional_algebras_with_basis.py
+++ b/src/sage/categories/finite_dimensional_algebras_with_basis.py
@@ -951,7 +951,7 @@ class
FiniteDimensionalAlgebrasWithBasis(CategoryWithAxiom_over_base_ring):
@cached_method
def is_commutative(self):
"""
- Return if ``self`` is a commutative algebra.
+ Return whether ``self`` is a commutative algebra.
EXAMPLES::
@@ -963,6 +963,7 @@ class
FiniteDimensionalAlgebrasWithBasis(CategoryWithAxiom_over_base_ring):
True
"""
B = list(self.basis())
+ B.remove(self.one())
return all(b*bp == bp*b for i,b in enumerate(B) for bp in
B[i+1:])
class ElementMethods:
}}}
it appears to be faster to check commutativity for
`SymmetricGroupAlgebra(5, QQ)`. (I removed the `@cached_method` line
before testing.) It's even a little faster for commutative algebras: the
time spent removing the
--
Ticket URL: <http://trac.sagemath.org/ticket/19416#comment:2>
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