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