Numerical libraries? (And starting HyperDoc from TeXmacs?)

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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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<div dir=3D"ltr"><div><div><div><div>The other day I was trying to do a num=
erical integral: (1-cos(x))/x^2 between 0 and pi/2.=C2=A0 It took me quite =
a while to get Axiom/FriCAS to handle this directly, as the trapezoidal rul=
e and Romberg integration require the value of the integrand at the end poi=
nts.=C2=A0 I ended up using<br><br>romberg(x+-&gt;if x=3D0 then 1/2 else (1=
-cos(x))/x^2,0,1,0.1,0.1,8,10)<br><br></div><div>and then later discovering=
<br><br>rombergo(x+-&gt;(1-cos(x))/x^2,0,1,0.1,0.1,8,10)<br></div><div><br>=
</div>which took me a long time, first to find the functions, and then work=
 out how to use them.=C2=A0 Can open-source numerical libraries (such as Ne=
tlib&#39;s BLAS, LAPACK, QUADPACK) be linked with Axiom/FriCAS?<br><br></di=
v><div>Also note that the documentation for romberg(o) is tucked away in it=
s SPAD file; I couldn&#39;t find it using HyperDoc, because when I start a =
session in TeXmacs, it doesn&#39;t start HyperDoc; I have to start HyperDoc=
 as a separate process with `)hd`, and so it&#39;s not connected to the run=
ning session.=C2=A0 My Session menu includes &quot;FriCAS&quot; but not &qu=
ot;Axiom&quot;; however on my system there are only tm_axiom files.=C2=A0 S=
o I don&#39;t know how TeXmacs is doing what it does.=C2=A0 (By the way, I =
compiled both FriCAS and TeXmacs from source.)<br></div><div><br></div>Back=
 to numerical integration, has anybody ever written more up-to-date numeric=
al routines, such as Clenshaw-Curtis, or Gauss-Kronrod (which is used in QU=
ADPACK) for use with Axiom/FriCAS?<br><br></div>Thanks,<br></div>Alasdair<b=
r clear=3D"all"><div><div><div><div><div><br>-- <br><div class=3D"gmail_sig=
nature"><div dir=3D"ltr"><a href=3D"http://www.facebook.com/alasdair.mcandr=
ew" target=3D"_blank"><img alt=3D"http://www.facebook.com/alasdair.mcandrew=
" src=3D"https://dl.dropboxusercontent.com/u/2796170/facebook.png"></a> <a =
href=3D"https://plus.google.com/+AlasdairMcAndrew/posts" target=3D"_blank">=
<img alt=3D"https://plus.google.com/+AlasdairMcAndrew/posts" src=3D"https:/=
/dl.dropboxusercontent.com/u/2796170/f-gplus_256-48.png"></a> <a href=3D"ht=
tps://www.linkedin.com/pub/alasdair-mcandrew/a/178/108" target=3D"_blank"><=
img alt=3D"https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108" src=3D=
"https://dl.dropboxusercontent.com/u/2796170/linkedin.png"></a> <a href=3D"=
https://twitter.com/amca01" target=3D"_blank"><img alt=3D"https://twitter.c=
om/amca01" src=3D"https://dl.dropboxusercontent.com/u/2796170/twitter.png">=
</a> <a href=3D"http://numbersandshapes.net" target=3D"_blank"><img alt=3D"=
http://numbersandshapes.net" src=3D"https://dl.dropboxusercontent.com/u/279=
6170/wordpress.png"></a><br></div></div>
</div></div></div></div></div></div>

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