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 -- [image: http://www.facebook.com/alasdair.mcandrew] <http://www.facebook.com/alasdair.mcandrew> [image: https://plus.google.com/+AlasdairMcAndrew/posts] <https://plus.google.com/+AlasdairMcAndrew/posts> [image: https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108] <https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108> [image: https://twitter.com/amca01] <https://twitter.com/amca01> [image: http://numbersandshapes.net] <http://numbersandshapes.net>
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