ActiveUser

475 Reputation

10 Badges

6 years, 346 days
i would also not like to ask, but if not ask, what should i do?

MaplePrimes Activity


These are replies submitted by ActiveUser

@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?

@Carl Love 

if both are the same basically after normalised , then which algorithm ‘s solution is the correct and standard in physics? Floating or fraction or integer? Is there only two algorithms? Or three?

it seems need to care whether algorithm using is consistent in whole operation.

@Carl Love 

when calculating eigenvector after use QR iteration  to calculate eigenvalues,

i use Rayleigh iterations, but eigenvector result is not equal to official function of eigenvector, where is wrong?

 

solve(sqrt(x^2 + x^2 + x^2) = 1, x);
yk := Matrix([[(1/3)*sqrt(3)],[(1/3)*sqrt(3)],[(1/3)*sqrt(3)]]):
evalf(sqrt(yk[1,1]*yk[1,1] + yk[2,1]*yk[2,1] + yk[3,1]*yk[3,1]));
v0 := Matrix([[(1/3)*sqrt(3)],[(1/3)*sqrt(3)],[(1/3)*sqrt(3)]]):

EigenVector2 := proc(e1,e2,e3)
u := e1:
vk := Matrix([[(1/3)*sqrt(3)],[(1/3)*sqrt(3)],[(1/3)*sqrt(3)]]):
for i from 1 to 3 do
yk := MatrixMatrixMultiply(MatrixInverse(M - u*Matrix([[1,0,0],[0,1,0],[0,0,1]])), vk);
vk := yk/sqrt(yk[1,1]*yk[1,1] + yk[2,1]*yk[2,1] + yk[3,1]*yk[3,1]);
Mvk := MatrixMatrixMultiply(M, vk);
u := (Mvk[1,1]*vk[1,1] + Mvk[2,1]*vk[2,1] + Mvk[3,1]*vk[3,1])/(vk[1,1]*vk[1,1] + vk[2,1]*vk[2,1] + vk[3,1]*vk[3,1]); #Rayleigh
od:
v1 := evalf(vk);

u := e2:
vk := Matrix([[(1/3)*sqrt(3)],[(1/3)*sqrt(3)],[(1/3)*sqrt(3)]]):
for i from 1 to 3 do
yk := MatrixMatrixMultiply(MatrixInverse(M - u*Matrix([[1,0,0],[0,1,0],[0,0,1]])), vk);
vk := yk/sqrt(yk[1,1]*yk[1,1] + yk[2,1]*yk[2,1] + yk[3,1]*yk[3,1]);
Mvk := MatrixMatrixMultiply(M, vk);
u := (Mvk[1,1]*vk[1,1] + Mvk[2,1]*vk[2,1] + Mvk[3,1]*vk[3,1])/(vk[1,1]*vk[1,1] + vk[2,1]*vk[2,1] + vk[3,1]*vk[3,1]);
od:
v2 := evalf(vk);

u := e3:
vk := Matrix([[(1/3)*sqrt(3)],[(1/3)*sqrt(3)],[(1/3)*sqrt(3)]]):
for i from 1 to 3 do
yk := MatrixMatrixMultiply(MatrixInverse(M - u*Matrix([[1,0,0],[0,1,0],[0,0,1]])), vk);
vk := yk/sqrt(yk[1,1]*yk[1,1] + yk[2,1]*yk[2,1] + yk[3,1]*yk[3,1]);
Mvk := MatrixMatrixMultiply(M, vk);
u := (Mvk[1,1]*vk[1,1] + Mvk[2,1]*vk[2,1] + Mvk[3,1]*vk[3,1])/(vk[1,1]*vk[1,1] + vk[2,1]*vk[2,1] + vk[3,1]*vk[3,1]);
od:
v3 := evalf(vk);
return [v1, v2, v3];
end proc:

uu := evalf(EigenValues2(M,7))[2];
EigenVector2(uu[1,1],uu[2,2],uu[3,3]); # uu are the eigenvalues

v, e := evalf(Eigenvectors(M));

@tomleslie 

i use QR iterations, 

 --- it can approximate decimal number of eigenvalues, but can not do exact fraction of maple official function do.

 --- QR iterations only return eigenvalues, how about eigenvectors? how do QR iterations do eigenvectors?

@Carl Love 

how to use GivensRotationMatrix in maple 2015?

i use matrix or vector , still return error


        A2 := GivensRotationMatrix(A1, 1, 2);
Error, (in LinearAlgebra:-GivensRotationMatrix) invalid input: LinearAlgebra:-GivensRotationMatrix expects its 1st argument, V, to be of type Vector() but received A1


        with(LinearAlgebra):

A := array(0 .. 2, 0 .. 2, [[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
A1 := convert(A, vector);
A := Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
A1 := convert(A, vector);

A2 := GivensRotationMatrix(A1, 1, 2);

@Carl Love 

 

with(Groebner):
sol := [{a*b = 1, c*d = 1, conjugate(a*c) - b*d = 0, a*d-b*c = sqrt(3)*I}, {}];
K := {(rhs(sol[1][1])-lhs(sol[1][1]))-x1,(rhs(sol[1][2])-lhs(sol[1][2]))-x2,(rhs(sol[1][3])-lhs(sol[1][3]))-x3,(rhs(sol[1][4])-lhs(sol[1][4]))-x4};
G := Basis(K, 'tord', degrevlex(x1,x2,x3,x4));
R1 := eliminate(G, {x1,x2,x3,x4}); # eliminate is the reverse of Basis
nops(G);
nops(K);
Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,x1,x2,x3,x4));
Ga := remove(has, Ga, [u1,u2,u3,u4,a]);

 

i tried this method , but it return [1] ,

is there method to find the rest ?

@Carl Love 

how to correctly use eliminate for this example?

i tried eliminate but it return another set of a,b,c,d

isn't it to use input set and output set or/and the rest properties ?

m5 := eliminate([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, Jesus2[1,1]=a, Jesus2[1,2]=b, Jesus2[2,1]=c, Jesus2[2,2]=d],[a,b,c,d]);
m5 := eliminate([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, Jesus2[1,1]=a, Jesus2[1,2]=b, Jesus2[2,1]=c, Jesus2[2,2]=d,a*b = 1, c*d = 1, conjugate(a*c)-b*d = 0],[a,b,c,d]);

 

m5 := [{a = -(1/2)*(3439+(1145*I)*sqrt(3))/(1+(1146*I)*sqrt(3)), b = -(1/2)*(-3439+(1145*I)*sqrt(3))/(-1+(1146*I)*sqrt(3)), c = -(1/2)*(-3942243+(1311025*I)*sqrt(3))/(-2292+(1313317*I)*sqrt(3)), d = -(1/2)*(3942243+(1311025*I)*sqrt(3))/(2292+(1313317*I)*sqrt(3))}, {AA[1, 1], AA[1, 2], AA[2, 1], AA[2, 2]}]

@Carl Love 

i try sylvester solve(jesus7, jesus7, matrix([[0,0],[0,0]]) in maple 2015

but it return 0 matrix , why can not solve ?

but it actually has solution.

 

@Carl Love 

i have tried eliminiate but no solution return

m5 := solve([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, a= Jesus2[1,1], b=Jesus2[1,2], c=Jesus2[2,1], d=Jesus2[2,2], a*b = 1, c*d = 1, conjugate(a*c)-b*d = 0,a*d-b*c=sqrt(3)*I],[a,b,c,d]);

Original question is how to solve a, b, c and d for below equations:

Both known Matrix and solution Matrix Properties

Matrix([[a,b],[c,d]]);
a*b = 1
c*d = 1

conjugate(a*c)-b*d = 0
Determinant(Matrix([[a,b],[c,d]])) = sqrt(3)*I
a*d-b*c = sqrt(3)*I

How to solve system AA when known Jesus7 to find Jesus2 which is Matrix([[a,b],[c,d]]) ?


Jesus7 := Matrix(2, 2, {(1, 1) = (1296309/5)*(22243/5+((7358/5)*I)*sqrt(3))/((-384813/10+((33701837/10)*I)*sqrt(3))*(-2277/10+((13/10)*I)*sqrt(3))), (1, 2) = (1296309/5)*(22243/5-((7358/5)*I)*sqrt(3))/((-384813/10-((33701837/10)*I)*sqrt(3))*(-2277/10-((13/10)*I)*sqrt(3))), (2, 1) = -(1/5)*(-25372581+(8329256*I)*sqrt(3))/(-384813/10+((33701837/10)*I)*sqrt(3)), (2, 2) = -(1/5)*(-25372581-(8329256*I)*sqrt(3))/(-384813/10-((33701837/10)*I)*sqrt(3))});

AA := simplify(MatrixMatrixMultiply(Matrix([[a,b],[c,d]]),Jesus7)- MatrixMatrixMultiply(Jesus7,Matrix([[a,b],[c,d]]))):

I am using different properties and even full properties , still can not find the solution equal to exact solution, but number of equations had already been more than number of variables? where is incorrect?

m5 := solve([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, a*b = 1, c*d = 1, conjugate(a*c)-b*d = 0,a*d-b*c=sqrt(3)*I],[a,b,c,d]);

m5 := solve([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, a*b = 1, c*d = 1, a*d-b*c=sqrt(3)*I],[a,b,c,d]);

m5 := solve([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, a*b = 1, c*d = 1, conjugate(a*c)-b*d = 0],[a,b,c,d]);

m5 := solve([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, a*b = 1, c*d = 1],[a,b,c,d]);

Solution: Matrix([[a,b],[c,d]]) should be
Jesus2 := [[1313319/2 (3439+1145 I sqrt(3))/((-2292+1313317 I sqrt(3)) (-1146+I sqrt(3))),1313319/2 (3439-1145 I sqrt(3))/((-2292-1313317 I sqrt(3)) (-1146-I sqrt(3)))],[-1/2 (-3942243+1311025 I sqrt(3))/(-2292+1313317 I sqrt(3)),-1/2 (-3942243-1311025 I sqrt(3))/(-2292-1313317 I sqrt(3))]];

 

i find this combination of equations has solution

m5 := solve([AA[1,1]=0,AA[1,2]=0,AA[2,1]=0,AA[2,2]=0, a*b = 1, c*d = 1, a*d-b*c=sqrt(3)*I],[a,b,c,d]);

but the solution is not Jesus2, i did not know what inside in solve function, it is like somewhere has evalf it and then change back to fraction, may be my guess is incorrect.

 

2 3 4 5 6 7 8 Last Page 4 of 42