[Axiom-developer] [#198 integrate(sin(x**2),x) is not handled ]

[kratt6]

Changes 
http://page.axiom-developer.org/zope/mathaction/198IntegrateSinX2XIsNotHandled/diff
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Although this does not really solve the original problem, I think I found a bug 
in 'INTPM'. Currently, there is an operation::

           pmComplexintegrate(f, x) ==
             (rc := splitConstant(f, x)).const ^= 1 =>
               (u := pmintegrate(rc.nconst, x)) case "failed" => "failed"
               rec := u::ANS
               [rc.const * rec.special, rc.const * rec.integrand]
             cse := (rec := matcherfei(f, x, true)).which
             cse = ERF  => [rec.coeff * erf(rec.exponent), 0]
             "failed"

It is pretty obvious that the third line should read::

               (u := pmComplexintegrate(rc.nconst, x)) case "failed" => "failed"

instead. If we perform this change, we get instead of
\begin{axiom}
complexIntegrate(-%i/2*e^(%i*x^2),x)
\end{axiom}

the correct answer, same for
\begin{axiom}
complexIntegrate(%i/2*e^(-%i*x^2),x)
\end{axiom}

For some reason, it still won't do 
\begin{axiom}
complexIntegrate(sin(x^2),x)
\end{axiom}

Curiously, the pattern matcher is not even invoked in this case... Even if we 
enter the integral as
\begin{axiom}
complexIntegrate(-%i/2*e^(%i*x^2)+%i/2*e^(-%i*x^2),x)
\end{axiom}
it fails, although in this case the pattern matcher is invoked. It would need 
to be invoked on each summand seperately, though.

Martin
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forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden