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These are replies submitted by ComputerUser


I have replied tom with code 

so not need to retype

You can run with a time series called close3 

then you will see most using fraction as input to eigenvectors are wrong 


previous reply from my question,

someone told me to use fraction, but i verify eigenvector result of fraction, it is incorrect


originally , start from float value , there is very little difference, not exactly 1.0 after verify then today i test it is exactly one.


is it a bug in maple 12 ?



can you explain why start from fraction and start from floating value, different?

i mean that one columns are all one , another one column is 0.57...,  

which start is the most accurate?


why fraction and float are near the same thing, but result has such big difference like totally different thing?


which should be used?



example is


c(t) has result


i edited your function for all elements in matrix, but not all cases considered, such as transpose or partly transpose

IsEquivalent:=proc(obj1::Matrix, obj2::Matrix, var::list)
local P, S;
uses combinat, LinearAlgebra;
S:=[seq(subs(zip(`=`,var,p),obj2), p=P)];
SS := choose(S,2);
result := false:
for i from 1 to nops(SS) do
if `or`(seq(Equal(obj1,s), s=SS[i])) then 
 result := true:
end if:
return result:
end proc:
elementss := proc(AA)
local elements1:
elements1 := [op(indets(AA))];
elements1 := [op(elements1), op(indets(AA,float))];
elements1 := [op(elements1),op(indets(AA,constant))];
return elements1:
end proc:
A1 := Matrix([[777,x,x],[77,7,7],[2,y,y]]);
B1 := Matrix([[777,y,y],[77,7,7],[2,x,x]]);
IsEquivalent(A1, B1, elementss(A1)); # correct
A1 := Matrix([[777,x,x],[77,7,7],[2,y,y]]);
B1 := Matrix([[777,y,y],[77,7,7],[2,x,y]]);
IsEquivalent(A1, B1, elementss(A1)); # correct

A1 := Matrix([[x,x,x],[77,7,7],[z,y,y]]);
B1 := Matrix([[z,y,y],[77,7,7],[x,x,x]]);
IsEquivalent(A1, B1, elementss(A1)); # incorrect

A1 := Matrix([[x,x,x],[77,7,7],[z,y,y]]);
B1 := Matrix([[z,y,y],[77,7,7],[x,x,y]]);
IsEquivalent(A1, B1, elementss(A1)); # correct

A1 := Matrix([[777,x,x],[77,7,7],[2,y,y]]);
B1 := Transpose(A1);
IsEquivalent(A1, B1, elementss(A1)); # incorrect

A1 := Matrix([[777,x,x],[77,7,7],[2,y,y]]);
B1 := Matrix([[777,x,2],[77,7,7],[x,y,y]]);
IsEquivalent(A1, B1, elementss(A1)); # incorrect

A1 := Matrix([[777,x,x],[77,7,7],[2,y,y]]);
B1 := Matrix([[777,77,2],[x,7,7],[x,y,y]]);
IsEquivalent(A1, B1, elementss(A1)); # incorrect


i got error when input a list having 3 elements x, y, z

it expects 2 arguments

how to edit the function for more than 2 elements?


is there any clues to write the extension?

what things need to consider?



in maple 12 , it return not true, can it change to run in maple 12?


second question is about two operations, such as symmetric flip and then rotate

for example:

IsEquivalent(Matrix([[777,x,x],[77,7,7],[2,y,y]]), Matrix([[777,y,y],[77,7,x],[2,7,x]]), [x,y]);


can this express in print or printf to show the operation it recognised ?

because expect to count how many same operations in series.

I have some understanding not clear is that

if there are two or three operations to achieve between two matrix , is it one equivalent can be considered as one operations for two or more operations?

@Joe Riel 

i mean self modifying maple code application

and need a database to record the change

it write maple code itself


Not use procedure 

and run directly , it can show animation now


do not know why i run in maple 2015 , no result.



i run your code in maple 12 and maple 2015 , no graph and animation was shown.


assume rotation matrix is (Matrix([[cos(t),sin(t)],[sin(t),cos(t)]])

how to animate a particle rotate around another particle?

how to plot the track of x and y coordinate with the change of t from -Pi to Pi?

would like to draw this track in 2D diagram but there are 3 variable?

how to set an initial point for x and y and then change t to see how x and y change in 2D coordinate?


i understand now,

by the way,

do you know how to predict a future matrix 

belong to which one of 3 matrix?

actually eigenvector has very small difference in 

Decimal value , can linear regression help to predict the exact eigenvector values?

i find book mention magnetron , neucleon these words, but I use Time series only to find Pauli equation. Is it the end after find Pauli equation ?

how to use Pauli equation for Time series?

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