Opened 3 years ago
Last modified 2 years ago
#22467 needs_work defect
simplify_hypergeometric bug
Reported by: | rws | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-7.6 |
Component: | calculus | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
The result of expansion of a 2F1
expression using simplify_hypergeometric
differs from computing the numeric directly:
sage: hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1)) hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1)) sage: _.n() 1.04296605906833 sage: hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1)) hypergeometric((1/5, 4/5), (6/5,), 1/10*sqrt(5)*(sqrt(5) - 1)) sage: _.simplify_hypergeometric() 0
Inside maxima:
maxima: hgfred([1/5, 4/5], [6/5], 1/10*sqrt(5)*(sqrt(5) - 1)); ((1-(sqrt(5)-1)/(2*sqrt(5)))^(1/10)*assoc_legendre_p(-4/5,-1/5,1-(sqrt(5)-1)/sqrt(5))*gamma(1/5))/(5*((sqrt(5)-1)/(2*sqrt(5)))^(1/10))
Change History (11)
comment:1 Changed 3 years ago by
- Milestone changed from sage-7.6 to sage-duplicate/invalid/wontfix
- Status changed from new to needs_review
comment:2 Changed 3 years ago by
- Status changed from needs_review to positive_review
comment:3 Changed 3 years ago by
- Description modified (diff)
- Milestone changed from sage-duplicate/invalid/wontfix to sage-7.6
- Status changed from positive_review to needs_work
- Summary changed from hypergeometric 2F1 bug to simplify_hypergeometric bug
Hijacking ticket to prevent waste. Quite a similar error, this time for real.
comment:4 Changed 3 years ago by
- Description modified (diff)
comment:5 Changed 2 years ago by
- Description modified (diff)
comment:6 Changed 2 years ago by
This is an issue in conversion from maxima:
sage: maxima('((1-(sqrt(5)-1)/(2*sqrt(5)))^(1/10)*assoc_legendre_p(-4/5,-1/5,1-( ....: sqrt(5)-1)/sqrt(5))*gamma(1/5))/(5*((sqrt(5)-1)/(2*sqrt(5)))^(1/10))') ((1-(sqrt(5)-1)/(2*sqrt(5)))^(1/10)*assoc_legendre_p(-4/5,-1/5,1-(sqrt(5)-1)/sqrt(5))*gamma(1/5))/(5*((sqrt(5)-1)/(2*sqrt(5)))^(1/10)) sage: bla=_ sage: bla.sage() 0
comment:7 Changed 2 years ago by
Probably boils down to
sage: maxima('assoc_legendre_p(-4/5,-1/5,1)') assoc_legendre_p(-4/5,-1/5,1) sage: _.sage() 0
which in turn comes from
sage: gen_legendre_P(-4/5,-1/5,x) 0
comment:8 Changed 2 years ago by
mpmath returns 0.000000000000000
with
import mpmath from sage.libs.mpmath.all import call as mpcall mpcall(mpmath.legenp, -0.8, -0.2, 1)
and Wolfram Alpha agrees with it but also agrees with the nonzero value for the 2F1 expression so the simplification by Maxima seems wrong.
On another note there is this in Func_assoc_legendre_P._eval_special_values(self,n,m,x)
:
if m > n: return ZZ(0)
However in Wikipedia that if |m|>l then P_{l}^{m}=0, so the code seems wrong (missing the abs).
comment:9 Changed 2 years ago by
Confirmation from arb:
sage: CBF(1/10*sqrt(5)*(sqrt(5) - 1)).hypergeometric([1/5,4/5],[6/5]) [1.0429660590683 +/- 5.27e-14] sage: CBF(1).legendre_P(-4/5,-1/5) 0
comment:10 Changed 2 years ago by
Maybe because Legendre polynomials can be extended to rational parameters either by 0 or by hypergeometric functions. What we see looks like a clash of extensions, no ?
comment:11 Changed 2 years ago by
No, the relevant extension is http://dlmf.nist.gov/14.3.E6 and it holds for x > 1 but the 2F1 argument here is 0.276 which makes x around 0.447, i.e. < 1. Agree?
User error. Assumptions given earlier interferred with
simplify_hypergemetric
.