[Axiom-mail] Numerical libraries? (And starting HyperDoc from TeXmacs?)

[Alasdair McAndrew]

The other day I was trying to do a numerical integral: (1-cos(x))/x^2 between 0 and pi/2.  It took me quite a while to get Axiom/FriCAS to handle this directly, as the trapezoidal rule and Romberg integration require the value of the integrand at the end points.  I ended up using

romberg(x+->if x=0 then 1/2 else (1-cos(x))/x^2,0,1,0.1,0.1,8,10)

and then later discovering

rombergo(x+->(1-cos(x))/x^2,0,1,0.1,0.1,8,10)

which took me a long time, first to find the functions, and then work out how to use them.  Can open-source numerical libraries (such as Netlib's BLAS, LAPACK, QUADPACK) be linked with Axiom/FriCAS?

Also note that the documentation for romberg(o) is tucked away in its SPAD file; I couldn't find it using HyperDoc, because when I start a session in TeXmacs, it doesn't start HyperDoc; I have to start HyperDoc as a separate process with `)hd`, and so it's not connected to the running session.  My Session menu includes "FriCAS" but not "Axiom"; however on my system there are only tm_axiom files.  So I don't know how TeXmacs is doing what it does.  (By the way, I compiled both FriCAS and TeXmacs from source.)

Back to numerical integration, has anybody ever written more up-to-date numerical routines, such as Clenshaw-Curtis, or Gauss-Kronrod (which is used in QUADPACK) for use with Axiom/FriCAS?

Thanks,

Alasdair

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