#7742: add a compose function to sage
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Reporter: was | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.6.1
Component: basic arithmetic | Keywords:
Author: Christopher Olah, Felix Lawrence | Upstream: N/A
Reviewer: Paul Zimmermann | Merged:
Work_issues: |
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Comment(by flawrence):
Replying to [comment:18 jrp]:
> Replying to [comment:17 jrp]:
> > At the moment the powers-of-two speed up isn't helping even in the
symbolic case, because the implementation is to return lambda x: f(g(x)).
If both inputs to compose are symbolic, then I think we want to just
return f(g(x)) instead.
>
> Given that symbolic functions have named variables, is this the correct
behavior?
>
>
> sage: f(x) = x+1
> sage: g(y) = y+1
> sage: compose(f,g)
> y + 2
> sage: compose(g,f)
> x + 2
I don't actually know anything about symbolic functions in Sage. As such,
all doctests and examples in the patch are for regular python functions
not symbolic functions. The compose functions in the patch use lambda
functions, which may or may not break symbolic functions.
With normal python functions (such as those in the doctest), the powers-
of-two provides a major speedup for large n over the other techniques I
tried, both for the function composition and for the evaluation of the
resulting function (benchmarked using "timeit"). In fact, without a
powers-of-two-type algorithm, the self_compose function regularly hit the
recursion limit and crashed for large n (above 500 or 1000). But I don't
know if anyone is interested in large n cases.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7742#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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