Arbitrary Precision Quadrature Functions Added to Ch.8 Maxima by Example

Let S be the intersection of the cylinders x^2 + z^2 < 1 and y^2 + z^2 < 4.  Let's compute volume(S)  using:

(i) numerical quadrature and Ted's code:

    (%i30) fpprec : 97$
    (%i32) v1 : apnint(4 * sqrt(1-x^2)*sqrt(4-x^2),x,-1,1,80,90);
    (%o32) 1.21603199053831874596552819283058651286634990891354275741019108734603734811168687842711453b1

(ii) hand calculation of the antiderivative (a Gauss hypergeometric) and numerical evaluation

  (%i33) v2 : nfloat(4*%pi * hypergeometric([-1/2,1/2],[2],1/4),[],80);
  (%o33) 1.2160319905383187459655281928305865128663499089135427574101910873460373481116869b1

And compare :)

   (%i34) v1-v2;
   (%o34) 3.090794501435045958046918478475175622067054689750797600513921211676626755520312554236263611465723b-79


--Barton