Hi Travis,
On 2017-03-31, Travis Scrimshaw <tsc...@ucdavis.edu> wrote:
> I agree that this is something that should be fixed (actually 0 is not
> recognized as being in a CFM, which is a bug IMO).
AFTER the fix from #22707?
> Well, we do have a number of CFM subclasses that explicitly have a total
> ordering of the indices (e.g., symmetric functions and partitions by lex
> order). However, I could see this being slower than as dicts for elements
> with a lot of terms when you have to, e.g., add two elements: you have to
> sort the two chains (which my interpretation of your description is a chain
> is a singlely linked list).
Yes, addition is a problem with elements that are implemented as sorted lists,
but currently even the addition of big path algebra elements is faster than
addition of the corresponding free algebra elements:
sage: R.<x,y,z> = FreeAlgebra(QQ)
sage: f = (x+y+z-1)^7
sage: g = (x-y+z+1)^7
sage: %timeit f+g
1 loop, best of 3: 155 ms per loop
sage: P = DiGraph({1:{1:['x','y','z']}}).path_semigroup().algebra(QQ)
sage: P.inject_variables()
Defining e_1, x, y, z
sage: f = (x+y+z-1)^7
sage: g = (x-y+z+1)^7
sage: %timeit f+g
1000 loops, best of 3: 1.35 ms per loop
Best regards,
Simon
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