Macsyma elliptic integrals



Richard Fateman wrote:
> Unless there is some other code not called by integrate,  only the 3rd of
> these examples is integrated. The others return the noun form.
> After ascertaining that neither a nor b is zero, the answer to item 3 comes
> out as the sum of 3 asinh..
>  
> 
> B^2*ASINH(2*ABS(B)*T/(ABS(A)*ABS(2*T+2*ABS(B)))
> 	   -2*A^2/(ABS(A)*ABS(2*T+2*ABS(B))))
>  /(2*SQRT(B^2+A^2)*ABS(B))
>  +B^2*ASINH(2*ABS(B)*T/(ABS(A)*ABS(2*T-2*ABS(B)))
> 	     +2*A^2/(ABS(A)*ABS(2*T-2*ABS(B))))
>   /(2*SQRT(B^2+A^2)*ABS(B))-ASINH(T/ABS(A))$
> 
> 

Hmm.  Oops.  I typed that wrong.  It should be

integrate(t^2/sqrt((t^2+a^2)*(t^2+b^2)),t)

the sqrt of a quartic.

So, Macsyma doesn't know how to do any elliptic integrals?

On a related note, does any have a reference on how to factor a real 
quartic into two quadratics?  I know I can do it by solving the quartic 
and then recombining the roots together to make the quadratic factors, 
but that seems expensive.

Ray