#13720: Scale legendre_P to [a,b]
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Reporter: mjo | Owner: burcin
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.6
Component: symbolics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Michael Orlitzky | Merged in:
Dependencies: | Stopgaps:
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Comment (by mjo):
Replying to [comment:5 fwclarke]:
> Why force them to be symbolic? Better, surely, to allow anything that
will evaluate and let coercion handle it.
[[BR]]
I removed the RR check, so you can actually pass in anything you want now.
I'm not convinced this isn't a foot-gun, but it's still a clear
improvement over what we have now so I'm happy with it.
[[BR]]
> This is what results from using `^` rather than `**` in python.
[[BR]]
Ah, yes, I should have caught that, sorry.
[[BR]]
> I'm sorry my proposed code had only been testing in Sage, and therefore
was being prepared. This dealt with, my version does pass all the
doctests, is faster when if the variable is a polynomial generator, and
the error
> {{{
> sage: legendre_P(4, Zmod(5)(1), 3, 6)
> ...
> ArithmeticError: 0^0 is undefined.
> }}}
> is eliminated. Apologies for mistyping this before.
>
[[BR]]
I believe this is another bug, elsewhere. I've set out to fix it and am
trapped in a rabbit hole at the moment, about four bugs from here. Once
that's sorted out, I'll do some experiments.
[[BR]]
[[BR]]
> > The `bool()` casts do have to stay, otherwise the tests just don't
work.
>
> Another way of doing this is to introduce a polynomial variable. Thus
> {{{
> sage: R.<x> = QQ[]
> sage: legendre_P(1, x) == x
> True
> }}}
> I know very little about the symbolic side of Sage, but I do find things
like
> {{{
> sage: SR(1) == SR(1)
> 1 == 1
> }}}
> very strange, and confusing when compared with
> {{{
> sage: 1 == 1
> True
> }}}
[[BR]]
You'll get no argument from me there. I do prefer to test with the default
symbol `x` though just because that's what most people will use.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13720#comment:6>
Sage <http://www.sagemath.org>
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