Opened 6 years ago

Closed 8 months ago

# Evaluation of Jacobi elliptic functions for non-real arguments depends on previously computed values

Reported by: Owned by: davidamadore major sage-8.9 numerical special function elliptic integral jacobi jakobkroeker, vklein Frédéric Chapoton Vincent Klein N/A 4dd9669 (Commits) 4dd9669aff58380d98e88b6ba06ced9ece823684

### Description

The following example shows that numerically evaluating sn(I,1/2) first fails ("cannot evaluate symbolic expression numerically") and then succeeds once the value sc(1,1/2) has been computed:

```sage: N(jacobi("sn", I, 1/2))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-1-e0000742d9d6> in <module>()
----> 1 N(jacobi("sn", I, Integer(1)/Integer(2)))

/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/misc/functional.pyc in numerical_approx(x, prec, digits)
1395             prec = int((digits+1) * LOG_TEN_TWO_PLUS_EPSILON) + 1
1396     try:
-> 1397         return x._numerical_approx(prec)
1398     except AttributeError:
1399         from sage.rings.complex_double import is_ComplexDoubleElement

/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._numerical_approx (sage/symbolic/expression.cpp:22615)()

TypeError: cannot evaluate symbolic expression numerically
sage: N(jacobi("sc", 1, 1/2))
1.34737147138542
sage: N(jacobi("sn", I, 1/2))
1.34737147138542*I
```

(in fact, evaluating sc with any arguments whatsoever seems to make the sn function work afterward).

### comment:1 Changed 6 years ago by vbraun_spam

• Milestone changed from sage-6.1 to sage-6.2

### comment:2 Changed 6 years ago by vbraun_spam

• Milestone changed from sage-6.2 to sage-6.3

### comment:3 Changed 6 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:4 Changed 3 years ago by jakobkroeker

seems fixed meanwhile, needs a test?

### comment:5 Changed 8 months ago by chapoton

• Branch set to u/chapoton/15334
• Commit set to 4dd9669aff58380d98e88b6ba06ced9ece823684
• Milestone changed from sage-6.4 to sage-8.9
• Status changed from new to needs_review

here is a doctest

New commits:

 ​4dd9669 `trac 15334 adding one doctest for Jacobi function`

### comment:6 Changed 8 months ago by chapoton

green bot, please review, easy one

### comment:7 Changed 8 months ago by chapoton

• Authors set to Frédéric Chapoton

### comment:8 Changed 8 months ago by vklein

• Reviewers set to Vincent Klein
• Status changed from needs_review to positive_review

Looks good to me.

### comment:9 Changed 8 months ago by chapoton

• Cc tscim removed

merci Vincent

### comment:10 Changed 8 months ago by vbraun

• Branch changed from u/chapoton/15334 to 4dd9669aff58380d98e88b6ba06ced9ece823684
• Resolution set to fixed
• Status changed from positive_review to closed
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