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Axel Vogt

5821 Reputation

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20 years, 225 days
Munich, Bavaria, Germany
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These are replies submitted by Axel Vogt

theoretically or practically...

Axel Vogt 5821
November 13 2017

Correct, and I do have a citation at hand. Though it is enough that the very machine or program can not decide it ( = practically).

remark aside...

Axel Vogt 5821
November 12 2017

As vv pointed out: just use the more expensive setting for Testzero. Det is certainly not the right way.

If you want to report a bug: consider Rank. Maple says Rank(M) = 5, while it is 4 (numerically and symbolically).

Anyway: if b is undecidable to be zero or not (theoretically or practically) then the 1-dim matrix b will be returned as 1/b.

no bug...

Axel Vogt 5821
November 12 2017

No bug, as I said.

Your personal opinion may be different.

No bug...

Axel Vogt 5821
November 12 2017

This is not a bug.

Only the help should be more precise, something like "If A is recognized as singular matrix, an error message is returned."

Re: 64 vs 32 bit...

Axel Vogt 5821
October 29 2017

@vv yes, my setting is WIN 7 SP 1 64 Bit Intel, 32 Bit Maple on 64 Bit Windows

An error (2)...

Axel Vogt 5821
October 29 2017

Unfortunately I get the same error (I have has no ini-file that test), using your posted sheet in the application area), executing MultiIntPoly(1, rels, [x,y]) - the last example in that sheet.

Re: CAD...

Axel Vogt 5821
October 23 2017
0 0

@_Maxim_ , thank you.

Re: Don't know it...

Axel Vogt 5821
October 22 2017
0 0

@Markiyan Hirnyk 

It was a rhetorical question, yes.

But I think it is a bit "asymmetric" and not polite to demand "code comments" if the result of MMA is just cited and MMA neither exhibits its code nor comments on it.

@maxim: would you mind to explain it a bit?

lame way...

Axel Vogt 5821
October 22 2017
0 0

Either I reset the variable before the call or would use

x:=m;
m:='m'; # forget m
return x;

BTW...

Axel Vogt 5821
October 22 2017
0 0

How MMA computes it?

flawed (2)...

Axel Vogt 5821
October 15 2017
0 0

@ecterrab 

Plotting Re and Im shows that there is a problem for z < 0 as well, I would say (black = the line from convert):


 

> 

restart: interface(version);
MeijerG([[a], [b]],[[c], [d]],z):
Re(%), Im(%), convert(%, hypergeom):
eval(%, [a=1/2,d=1, b=2, c=1]);
plot([%], z=-4 .. 4, thickness=3, color=[red, blue, grey]);

`Classic Worksheet Interface, Maple 2017.2, Windows, Jul 19 2017, Build ID 1247392`

Re(MeijerG([[1/2], [2]], [[1], [1]], z)), Im(MeijerG([[1/2], [2]], [[1], [1]], z)), Pi^(1/2)*z/2

  
> 

MeijerG([[a], [b]],[[c], [d]],z):
eval(%, [a=1/2,d=1, b=2, c=1]); eval(%, z=-2);
evalf(%);

MeijerG([[1/2], [2]], [[1], [1]], z)

MeijerG([[1/2], [2]], [[1], [1]], -2)

-0.551653471779524e-16+0.915439115453814e-1*I

 (1)


 

Download tmp.mws

flawed...

Axel Vogt 5821
October 14 2017
0 0


 

> 

MeijerG([[a], [b]],[[c], [d]],z):
%=convert(%, hypergeom);
eval(%, [a=1/2,d=1]):
EQ:=eval(%, [b=2, c=1]);
[op(%)]: plot(%, color=[red, blue]);

MeijerG([[a], [b]], [[c], [d]], z) = GAMMA(1-a+c)*z^c*hypergeom([1-a+c, 1-b+c], [1-d+c], z)/(GAMMA(b-c)*GAMMA(1-d+c))

EQ := MeijerG([[1/2], [2]], [[1], [1]], z) = Pi^(1/2)*z/2

  
> 

 


 

Download tmp.mws

upload ?...

Axel Vogt 5821
October 12 2017
0 0

Yes, upload your very task.

bivariate normal...

Axel Vogt 5821
September 25 2017
0 0

I think that is essentially a bi-variate normal over 1 quadrant (formulae
are in Abramowitz & Stegun, with some minor typos if I remember). For the
following I have not cared too much about all cases for B and G.

P := (x,y)->(1/2)*exp(-(1/2)*(x^2+G*y^2-2*B*x*y)/(-B^2+G))/(Pi*sqrt(-B^2+G));

Int(Int(P(x,y),x=0..infinity),y=-infinity..0);
PDEtools:-dchange({x=-sqrt(G)*xx,y=yy},%,[xx,yy]): subs(xx=x,yy=y,%):
combine(%):
eval(%, B=-2*R*sqrt(G)/2);
factor(%);

Now compare with the integrand for the bivariate normal

Int(Int(exp(-(xi^2-2*rho*xi*eta+eta^2)/2/(1-rho^2))/2/Pi/sqrt(1-rho^2),
  eta = -infinity .. y),xi = -infinity .. x);
subs(x=0, y=0, %);
combine(%): factor(%);

# subs(rho=R, xi=x,eta=y, %);

provide code, not images...

Axel Vogt 5821
September 22 2017
0 0

Either provide the code as text or upload you worksheet using the "green arrow" which you have in the editor if you post.

And you may say what you get and what you expect to get

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