#9706: New Version of orthogonal Polynomials
-------------------------------+--------------------------------------------
Reporter: maldun | Owner: burcin
Type: defect | Status: new
Priority: minor | Milestone:
Component: symbolics | Keywords: orthogonal polynomials, symbolics
Author: Stefan Reiterer | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-------------------------------+--------------------------------------------
Comment(by maldun):
Replying to [comment:5 fredrik.johansson]:
> > The complete versions for legendre_Q, gen_legendre_P, and
gen_legendre_Q will not be finished soon since the mpmath functions, don't
seem to work correctly...
>
> Care to elaborate?
Sorry for the late answer, I was on holidays.
In mpmath I have probs with the legenp and legenq functions. For some
inputs I get this error:
sage: mpmath.call(mpmath.legenp,5,1,2)
---------------------------------------------------------------------------
OverflowError Traceback (most recent call
last)
/home/maldun/prog/sage/ortho/<ipython console> in <module>()
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/sage/libs/mpmath/utils.so in sage.libs.mpmath.utils.call
(sage/libs/mpmath/utils.c:5021)()
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/functions/hypergeometric.pyc in legenp(ctx, n, m, z, type,
**kwargs)
1481 T = [1+z, 1-z], [g, -g], [], [1-m], [-n, n+1], [1-m],
0.5*(1-z)
1482 return (T,)
-> 1483 return ctx.hypercomb(h, [n,m], **kwargs)
1484 if type == 3:
1485 def h(n,m):
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/functions/hypergeometric.pyc in hypercomb(ctx, function,
params, discard_known_zeros, **kwargs)
125 [ctx.gamma(a) for a in alpha_s] + \
126 [ctx.rgamma(b) for b in beta_s] + \
--> 127 [ctx.power(w,c) for (w,c) in zip(w_s,c_s)])
128 if verbose:
129 print " Value:", v
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/ctx_base.pyc in power(ctx, x, y)
417 3.16470269330255923143453723949e+12978188
418 """
--> 419 return ctx.convert(x) ** ctx.convert(y)
420
421 def _zeta_int(ctx, n):
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/sage/libs/mpmath/ext_main.so in
sage.libs.mpmath.ext_main.mpnumber.__pow__
(sage/libs/mpmath/ext_main.c:13946)()
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/sage/libs/mpmath/ext_main.so in sage.libs.mpmath.ext_main.binop
(sage/libs/mpmath/ext_main.c:4588)()
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/libmp/libelefun.pyc in mpf_pow(s, t, prec, rnd)
340 # General formula: s**t = exp(t*log(s))
341 # TODO: handle rnd direction of the logarithm carefully
--> 342 c = mpf_log(s, prec+10, rnd)
343 return mpf_exp(mpf_mul(t, c), prec, rnd)
344
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/libmp/libelefun.pyc in mpf_log(x, prec, rnd)
725 # optimal between 1000 and 100,000 digits.
726 if wp <= LOG_TAYLOR_PREC:
--> 727 m = log_taylor_cached(lshift(man, wp-bc), wp)
728 if mag:
729 m += mag*ln2_fixed(wp)
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/libmp/libelefun.pyc in log_taylor_cached(x, prec)
643 else:
644 a = n << (cached_prec - LOG_TAYLOR_SHIFT)
--> 645 log_a = log_taylor(a, cached_prec, 8)
646 log_taylor_cache[n, cached_prec] = (a, log_a)
647 a >>= dprec
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/libmp/libelefun.pyc in log_taylor(x, prec, r)
607 """
608 for i in xrange(r):
--> 609 x = isqrt_fast(x<<prec)
610 one = MPZ_ONE << prec
611 v = ((x-one)<<prec)//(x+one)
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/libmp/libintmath.pyc in isqrt_fast_python(x)
240 y = (y + x//y) >> 1
241 return y
--> 242 bc = bitcount(x)
243 guard_bits = 10
244 x <<= 2*guard_bits
/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-
packages/mpmath/libmp/libintmath.pyc in python_bitcount(n)
78 if bc != 300:
79 return bc
---> 80 bc = int(math.log(n, 2)) - 4
81 return bc + bctable[n>>bc]
82
OverflowError: cannot convert float infinity to integer
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9706#comment:7>
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