** [bugs:#2615] Numeric evaluation of inverse Jacobi elliptic functions is wrong for some inputs**

**Status:** open

**Created:** Fri Jul 26, 2013 03:34 AM UTC by Eviatar Bach

**Last Updated:** Fri Jul 26, 2013 03:34 AM UTC

**Owner:** Raymond Toy

Numeric evaluation of inverse Jacobi elliptic functions is wrong for some inputs. For example,

(%i6) jacobi_dn(float(inverse_jacobi_dn(-2, 3)), 3); (%o6) 2.0000000000000004 - 2.4980018054066022e-16 %i

is clearly wrong; it should be -2, as you can see with the symbolic simplification:

(%i1) jacobi_dn(inverse_jacobi_dn(-2, 3), 3); (%o1) - 2

The reason for this problem is that `inverse_jacobi_dn`

is computed as `inverse_jacobi_dn(u, m)=elliptic_f(asin(sqrt((1 - u^2)/m)), m)`

. Since that function is even in `u`

, `inverse_jacobi_dn(-2, 3)=inverse_jacobi_dn(2, 3)`

, which is wrong. It should be computed in some other way.

Presumably this problem will also cause errors with some of the other inverse Jacobi functions, since I think some are defined in terms of `inverse_jacobi_dn`

for numeric evaluation.

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