Hi, Dan
I've tried the commercial software Mathematica. However it takes a long
time to integrate then I turn to Maxima. I just wonder why Maxima keep
asking these questions.
On Thu, Apr 15, 2010 at 8:20 AM, Dan Stanger <dan.stanger at ieee.org> wrote:
> The commercial macsyma was able to integrate this, and after some
> simplification produces this result:
> (((%pi)^4 * l^4)/(sqrt(t - 2 * s + r + 1) * sqrt(t + 2 * s - r + 1) *
> sqrt(3 * t - 2 * s - r - 1) * sqrt(3 * t + 2 * s + r - 1) * (t^2 + 2 * t -
> r^2 + 1)))
>
> It does not ask any questions involving any of the variables, either.
> Dan Stanger
>
> Lin Xie wrote:
>
>> Hi,
>> I'm new to Maxima and would like to calculate a full integration of
>> %e^(-(x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2-2*r*(x1*x2+x3*x4+x5*x6+x7*x8)-2*s*(x1*x3+x2*x4+x1*x5+x2*x6+x4*x8+x3*x7+x5*x7+x6*x8)-2*t*(x1*x4+x2*x3+x1*x6+x2*x5+x1*x7+x3*x5+x2*x8+x4*x6+x5*x8+x6*x7+x8*x3+x4*x7))/L).
>> Here the parameters L, r, s and t satisfy L>0, r^2+s^2+t^2+2*r*s*t<1,
>> r^2+s^2<1, r^2+t^2<1 and s^2+t^2<1. The first two
>> steps of the integration are just fine. However, I came across a problem
>> during carrying out the third integration step. It asks me if t^2+s^2-1 is
>> positive or negative! I couldn't figure out why it ask this stupid question.
>> Since
>> I know that the t^2+s^2-1 is negative, I just answer the question. But it
>> asks me another question about the positive or negative, because the
>> x1,x2,...,x8 are all variables and I could not define its sign. This
>> question almost
>> drives me mad.
>>
>> Here's the execution results:
>> (%i1)
>> assume(L>0,r^2<1,s^2<1,t^2<1,r^2+s^2+t^2+2*r*s*t<1,t^2+s^2<1,r^2+s^2<1,r^2+t^2<1);
>>
>> integrate(%e^(-(x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2-2*r*(x1*x2+x3*x4+x5*x6+x7*x8)-2*s*(x1*x3+x2*x4+x1*x5+x2*x6+x4*x8+x3*x7+x5*x7+x6*x8)-2*t*(x1*x4+x2*x3+x1*x6+x2*x5+x1*x7+x3*x5+x2*x8+x4*x6+x5*x8+x6*x7+x8*x3+x4*x7))/L),x8,minf,inf);
>> (%o1) [L>0,r^2<1,s^2<1,t^2<1,-t^2-2*r*s*t-s^2-r^2+1>0,-t^2-s^2+1>0]
>> (%o2) blablabla...
>>
>> (%i3) integrate(%o2,x1,minf,inf);
>> (%o3) blablabla...
>>
>> (%i4) integrate(%o3,x3,minf,inf);
>> Is t^2+s^2-1 positive,negative, or zero? negative;
>> Is s(t(2x7+4x6+4x4)+2x7+2rx2)+... positive, negative, or zero? <= Here's
>> the problem!
>>
>> Can anyone give me a help or some suggestions? Thanks!
>>
>> --
>> Lin Xie
>> Beijing National Center for Electron Microscopy
>> Department of Material Science and Engineering
>> Tsinghua University
>> Beijing, PR of China
>>
>>
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>>
>>
>
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--
Lin Xie
Beijing National Center for Electron Microscopy
Department of Material Science and Engineering
Tsinghua University
Beijing, PR of China