#13720: Scale legendre_P to [a,b]
------------------------------------+---------------------------------------
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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Changes (by fwclarke):
* status: needs_review => needs_work
Comment:
* The code seems over-complicated to me. Replacing the last few lines
with
{{{
R = PolynomialRing(ZZ, 't')
f = R([(-1)^(n - k)*binomial(n, k)*binomial(n + k, k) for k in range(n
+ 1)])
return f((x - a)/(b - a))
}}}
is much simpler and is significantly faster. Moreover, this makes
expressions such as
{{{
legendre_P(4, Zmod(5), 3, 6)
}}}
evaluate correctly; at it stands the patch yields an
{{{
ArithmeticError: 0^0 is undefined.
}}}
* I don't see why `a` and `b` need to be real numbers. Actually they
could be polynomial variables, giving:
{{{
sage: R.<r,s,t> = QQ[]
sage: legendre_P(2, t, r, s)
6*((r - t)/(r - s) - 1)*(r - t)/(r - s) + 1
}}}
* I don't see the need to use `bool` in doctests such as
{{{
bool(legendre_P(0, x, 0, 1) == p0)
}}}
* It's not clear to me why back-quotes are used in some of the error
strings:
{{{
raise TypeError('`n` must be a natural number')
}}}
but
{{{
raise ValueError('n must be nonnegative')
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13720#comment:2>
Sage <http://www.sagemath.org>
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