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MaplePrimes Activity

These are replies submitted by MrYouMath

@Kitonum Sorry, for my epic fail :D. Your code works like a charm! Thank you for your help.

@Kitonum Could you maybe share your Worksheet? I copied your code and I get an error when I try to run LyapunovEq(<1,2;3,4>); and LyapunovEq(Matrix(3, symbol = a));



LyapunovEq := proc(A::Matrix)
 local n, P, Id, eqn;
 uses LinearAlgebra:
 n := op([1,1],A);
 P := Matrix(n, symobl = p);
 Id := Matrix(n, shape=identity);
 eqn := Transpose(A).P+P.A =~ -Id;
 solve({seq(seq(eqn[i,j], j=1..n), i=1..n)}, indets(P));
end proc;


@Kitonum Thank you a lot for your answer :). If I need to change this for a n by n problem, then I will need to change it the following way

solve({seq(seq(eqn[i,j], j=1..n), i=1..n)}, {p__11,p__12,...p__1n,p__12,...,p__2n,...,p__1n,....,p__nn});

am I right?

@Preben Alsholm Thank you for your answer, that was what I was looking for!

@tomleslie Thank you, that was what I was looking for :). You know by any chance how to rewrite it in Matrix form?

@Carl Love +1 for your answer. It works like a charm, but the answer of John Fredsted 1570 works also like a charm. And I seleced him as the accepted answer because his answer was first. As your answer is also correct I would like to accept both answers, but the forum does only allow one answer. Hope you don't mind :).

@Carl Love +1 for taking your time and answering my question, but that was not what I was looking for.

@tomleslie Thank you! That makes sense, I was thinking to complicated.

@Preben Alsholm Great thank you, but how can I expand this for two general vectors v =(v1,v2,v3) and v=(0,v2,v3)? See also my comment on Carl Loves answer.

@Carl Love Thank you alot for your effort, but I need something which also works with variables.

I have gotten alot of vectors form my analysis. I want to reduce them such that I am only left with the most general forms.

E.G. I have the vectors b_1=(0,0,a_3,0),b_2=(a_1,a_2,0,0),b_3=(a_1,a_2,a_3,0) and b_4=(0,0,0,a_4). I want to loop through the elements and delte all the elements that are a special case of another vector. So comparison of b_1 and b_2 should give false, b_1 and b_3 should give true (hence b_1 is a special case of b_3), so I would delete b_1, b_2 and b_3 should give true so I would delete b_2, b_3 and b_4 gives false and b_4 and b_3 gives false. So I would be left with only b_3 and b_4. I have up to 4000 such vectors and I want to reduce them programatically. 

Perelman was disappointed by the mathematical community. He also thinks that the proof is not the result of one single mathematician but rather a result which was generated by many mathematicians.

I find it very interessting that western media do not report about him, while his story is very amazing and interessting. But there is a very well made russian documentary on youtube with english subtitles that is really worth watching (

I don't think we will be able to fully understand the behaviour of a genius like Perelman and it is very sad for mathematics to loose such a great mind.

@Carl Love: That is exactly what I was looking for. Thank you alot.

@Carl Love Hi, thank you alot for your answer but I don't have the Iterator package. Maple tells me 'Error, 'Iterator' does not evaluate to a module'.

@Mariusz Iwaniuk Thank you alot for your help :). Could you upload your mathematica worksheet?

@vv +1 Thank you for your post. But I need to find the symmetries of such types of PDEs.

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