Integration with elliptic functions

[Waldek Hebisch]

I have now commited preliminary routine for integration in terms
of elliptic integrals. It only handles integrals of the
first and second kind (integrals of third kind are unhandled)
and among them onlu few classic form. Still, it can do
a lot of classic examples like:

(2) -> integrate(1/sqrt(4*x^3 - 3*x -2), x)

(2) weierstrassPInverse(3,2,x)
Type: Union(Expression(Integer),...)
(3) -> D(%, x)

1
(3) -----------------
+--------------+
| 3
\|4 x - 3 x - 2
Type: Expression(Integer)

Note that derivatives of our elliptic integrals contain specific
form of roots. It may happen that function that we want to
integrate contain different form of roots. Integrator transform
roots "moving" powers trough roots, but most our routines do not
do so. Due to this derivative of integral may contain different
roots than integrand and ATM normalize is not able to
simplify resulting difference to 0. For example:

(4) -> integrate(1/sqrt(x^3 + 2), x)

(4) 2 weierstrassPInverse(0,- 8,x)
Type: Union(Expression(Integer),...)
(5) -> D(%, x)

2
(5) -----------
+--------+
| 3
\|4 x + 8
Type: Expression(Integer)

There is factor 4 under root and normalize do not see that the
above is the same as the integrand.

--
Waldek Hebisch