Re: Troubles with Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg70279] Re: Troubles with Integrate
- From: Peter Pein <petsie at dordos.net>
- Date: Wed, 11 Oct 2006 01:53:43 -0400 (EDT)
- References: <eg84hk$nir$1@smc.vnet.net>
Roman V. Kiseliov schrieb:
> If I try to do following calculation Mathematica 5.2.0.0 can't evaluate
> integrals.
>
> psi:= (-Pi^(-1))*((Sin[Pi*((t - 5/4)/3)]/(t - 5/4))*Cos[Pi*(t - 5/4)] +
> (Sin[Pi*(t + 1/4)]/(t + 1/4))*Cos[Pi*(t + 1/4)]) +
> (1/Pi)*((Sin[2*Pi*((t - 7/8)/3)]/(t - 7/8))*Sin[2*Pi*(t - 7/8)] -
> (Sin[2*Pi*((t - 1/8)/3)]/(t - 1/8))*Sin[2*Pi*(t - 1/8)]);
>
> Integrate[psi*psi, t]
> Integrate[psi*psi, {t, -inf, +inf}]
>
> If I try to interrupt calculation, Mathematica sometimes says
> 'Mathematica has detected a possible internal error. If possible, report
> the error to
> support at wolfram.com, quoting "Assertion 'interruptMenuType != 0' failed at
> KernelPackets.c:726", and describe in as much detail as possible what
> you were
> doing when the error occurred.'
>
> Note also that Integrate[psi, {t, -inf, +inf}] in Mathematica 4.2.0.0
> evaluates as 0
> but Mathematica 5.2.0.0 give value -1/2
>
> Roman V. Kiseliov
> Kursk State University
> Theor. Phys. Dept.
>
Hi Roman,
is it correct to have a factor 1/3 resp. 2/3 in the first sine of the
trig. products in term 1,3 and 4 but not in term2? I ask, because the
outcome would be significantly simpler:
In[10]:=
\[Psi] := -(((Sin[(1/3)*Pi*(t - 5/4)]*Cos[Pi*(t - 5/4)])/(t - 5/4) +
(Sin[(1/3)*Pi*(t + 1/4)]*Cos[Pi*(t + 1/4)])/(t + 1/4))/Pi) +
((Sin[(2/3)*Pi*(t - 7/8)]*Sin[2*Pi*(t - 7/8)])/(t - 7/8) -
(Sin[(2/3)*Pi*(t - 1/8)]*Sin[2*Pi*(t - 1/8)])/(t - 1/8))/Pi
In[11]:=
Timing[(Integrate[#1 /. t -> Cases[Factor[Denominator[#1]],
(c_.)*t + (a_) /; c =!= 0 :> x - a/c, Infinity, 1],
{x, -Infinity, Infinity}] & ) /@ Expand[\[Psi]^2]]
Out[11]=
{28.061999999999998*Second, {1}}
Greetings,
Peter