ActiveUser

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7 years, 173 days
i would also not like to ask, but if not ask, what should i do?

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@tomleslie 

I need 1 and 0 in all combination as described above

i expect larger , 10 one and 75 zero

@Mariusz Iwaniuk 

my application is quantum matrix

one of invariant value sometimes is not exactly 1.0 

i am thinking why invariant is not always invariant.

i searched that is caused by superposition 

but convolution of list and sum result is the same as distributive law

so, how to use convolution to make invariant always invariant?

@Mariusz Iwaniuk 

 

restart:
conv := proc(a, b)
c := []:
for k from 1 to nops(a)+nops(b)-1 do
 result := 0:
 for i from 1 to k do
  if k-i+1 <= nops(b) and i <= nops(a) then
  result := result + a[i]*b[k-i+1]:
  end if:
 od:
 c := [op(c), result]:
od:
return c:
end proc:
with(LinearAlgebra):
M := Matrix([[1,2,3],[4,5,6],[7,8,9]]):
X := Matrix([[x1],[x2],[x3]]);
MatrixMatrixMultiply(M,X);
something should be convsolve(conv(M, X) = a value);
row1 := conv([seq(M[1][a],a=1..nops(M[1]))], [seq(Transpose(X)[1][a],a=1..nops(Transpose(X)))]):
sum(row1[mm], mm=1..nops(row1));
row2 := conv([seq(M[2][a],a=1..nops(M[2]))], [seq(Transpose(X)[1][a],a=1..nops(Transpose(X)))]);
sum(row2[mm], mm=1..nops(row2));
row3 := conv([seq(M[3][a],a=1..nops(M[3]))], [seq(Transpose(X)[1][a],a=1..nops(Transpose(X)))]);
sum(row3[mm], mm=1..nops(row3));
solve([sum(row1[mm], mm=1..nops(row1)), sum(row2[mm], mm=1..nops(row2)), sum(row3[mm], mm=1..nops(row3))], [x1,x2,x3]);
 
 
i do not know the definition of convolution of matrix with x to form a system of equations
i guessed shown above
if above is correct, then does it mean that solve can also solve this system?
 
how to replace distributive rules with convolution in maple?
if this can not be done, can i do it when only not use bracket ( ) to do multiply?
 
is there any example to show only convolution is correct when distributive is wrong?
 

@tomleslie 

is there any one know maple 12 use which method to expand the size of display graph?

@tomleslie 

 

what is yr ?

is there an simple example using dualaxisplot 

vertical line is only x=1, x=2, x=3 etc for example around 12 lines 

because i collect these lines with

L := [op(L), 1]

L := [op(L), 2]

etc

@acer 

firstly I enabled maple security, then =0 not work then I disable security, it work but can not changed yesterday

after tried today, it work in window maple

i just curious why this command is applied globally but not session applied and it has affected after closed and open again

then I try again window discover =2 , display %1 = imaginary value before display matrix

then set =3 to solve this issue in maple 

I use =0 mainly for copying many matrix in window 

because =2 or =3 can not copy matrix

@stefanv 

but i really find invariant in 4x4

why is it pointless in more dimension?

there is no papers mention how to construct a general invariant matrix

and there is not only one kind of matrix invariant. Is there book teaching different kind of general module to find numerical invariant matrix?

@mmcdara 

i do not know the formula 

is there example code to show what happen?

If cube is not matrix

why do people solve cube game?

 

@Carl Love 

not physics this time, 

i am calculating combination of matrix 9 x 9 with 9 different elements, enumration to run all combinations

and also would like to know how the limit of maple , which size of matrix is the limit , such as 23^(23^2) combinations etc....

recently i write a function suitable for parallel computing, if one day run in amazon, how to massive install maple in amazon automatically and run script

is it manually copy script to 100 machines, and how to distributed computing this situation?

some people may guess 7 x 7 is the limit in x64 computer, but i do not believe, and would like to try

 

and also want to know whether there is technique to guess which range of combinations that have what i want to find, so that no need to run all

 

i just run , start from 30^(30^2) has zero ending

i guess limit is 29^(29^2)

@Carl Love 

is Schdinger equation correct?

I/h is a very big number

and

where is Planck h coming from?

It seems can not Ket which show error 

@Carl Love 

my old book example use this,

i forget whether linear algebra in maple 12 have matrixexponential or not

Go to main topic , how to solve the ket

is it matrix or complex number?

should I really have a physics optic lab in order to understand this?

every time i read this still can not get it

some word such polarisation seems really need a optic lab 

Can Time series data play similar things?

where is initial state and how to find ket initial state?

@Carl Love 

_EnvAllSolutions := true;
solve(z^n - z = 0, z);
exp(-(2*I)*Pi*_Z1/(n-1)), 0;
 

there is _Z1, 

is there any things need to assume?

@tomleslie 

i tried and comment below, there is blank graph and error occur

 

M:=Matrix([[19,5,12+x/10],[12,7,21+x/10],[5,12,19+x/10]]);
e,v:=Eigenvectors(M):
colors:=[red,green,blue]:
display(Array(1..3, [seq( plot(e[j], x=-50..50, color=colors[j]), j=1..3)]));
display(Array(1..3,[ seq( spacecurve( v[..,j], x=-50..50, color=colors[j]), j=1..3)])); # blank graph?

restart:
with(LinearAlgebra):
with(plots):
randomize():
M:=Matrix([[19,5,12+x/10],[12,7,21+x/10],[5,12,19+x/10]]);
e,v:=Eigenvectors(M):
colors:=[red,green,blue]:
display(Array(1..3, [seq( complexplot(evalc(e[j]), x=-50..50, color=colors[j]), j=1..3)]));
display(Array(1..3,[ seq( spacecurve( Re(v[..,j]), x=-50..50, color=colors[j]), j=1..3)]));
display(Array(1..3,[ seq( spacecurve( Im(v[..,j]), x=-50..50, color=colors[j]), j=1..3)])); # Error

Error, invalid input: `simpl/Im` expects its 1st argument, x, to be of type {boolean, algebraic}, but received Vector(3, {(1) = (1/100)*(1900*x^2+22500*x+75000+70*x^3+(1500*I)*3^(1/2)*x+(15000*I)*3^(1/2)+x^4+3000*(-(1/20)*x-3/2+((1/20)*I)*3^(1/2)*x+((1/2)*I)*3^(1/2))*x+100*(-(1/20)*x-3/2+((1/20)*I)*3^(1/2)*x+((1/2)*I)*3^(1/2))*x^2)/(((-(1/20)*x-3/2+((1/20)*I)*3^(1/2)*x+((1/2)*I)*3^(1/2))*x^2+40*(-(1/20)*x-3/2+((1/20)*I)*3^(1/2)*x+((1/2)*I)*3^(1/2))*x+25*x-150+(25*I)*3^(1/2)*x+(250*I)*3^(1/2)+x^2)*(-(1/20)*x-3/2+((1/20)*I)*3^(1/2)*x+((1/2)*I)*3^(1/2))), (2) = -(1/10)*(-50*x^2-850*x-4500-x^3+(50*I)*3^(1/2)*x+(500*I)*3^(1/2))/((-(1/20)*x-3/2+((...

@Carl Love 

i had learnt in secondary school

and read books about it but I forget and lazy to find.

i think I can find it again

but my book use elimination to do

however this method is not maple use

i tried this many years ago. 

I just use QR algorithm to do, but discover that it can not output small integer fraction complex number.

is there any book shown the derive of QR from real number to complex number?

 

@Carl Love 

i use  3 x 3 or 4 x 4 matrix

but do not know whether diagonal is also symmetric , is there any function to check whether symmetric?

i just compare eigenvectors 

by observe perturbation to how it change when input change

i remember physics package had also a eigenvector function ? Is it?

should I use physics package ?

do you know physics package use integer, fraction or float , which is standard or accurate?

i would go home to compare physics package with linear algebra package to see which numeric are they match

if the most accurate come from floating number, how do beautiful fraction come from? Which algorithm can output beautiful and small integer complex eigenvectors?

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