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will this difference in result from the same comma...

Asked by: LeeHoYeung 535
December 21 2017
0  2

with(LinearAlgebra):
test1 := Matrix([[1,-1],[-1,1]]);
for i from 1 to 20 do
print(Eigenvectors(test1)[2]);
od:

i run the same command 20 times, but sometimes left has negative 1 , sometimes right has negative 1

why position is like random , is my maple has virus?

the result are not consistent, i am learning quantum computation, will this influence the quantum computation and result?

i am doing up and down and change to a differential equation, Pauli equation

It seems only one Pauli equation

i find 3*3 matrix 

has 3 different kinds of matrix

one is row 1 and row 2

second is row 1 and row 3

Third is row 2 and 3

column 1 is constant 

Is there any one has the same experience to predict these 3 kind of matrix, and know what I mentioned?

 

fsolve versus RootFinding...

Asked by: tsunamiBTP 292
rootfinding fsolve
December 15 2017
1  7

I executed finding the roots of the derivative of a series expansion containing 500 terms.  I did it 2 ways.  The 1st using fsolve & the 2nd using RootFinding.  The fsolve took over 20 minutes to find a single root within a specified range while the RootFinding took less than 60 seconds to find all roots within a larger range.  I do not know of the inner mechanisms of either command, but why is this the case?  Why would the algorithms differ?  My results are in the link below.

fsolve_vs_RootFinding.mw

how to collect value from a matrix like factor mat...

Asked by: LeeHoYeung 535
matrix collect factor
December 13 2017
0  8
Matrix([[xx3[1,2],xx3[1,3]],[xx3[2,2],xx3[2,3]]])
Matrix(2, 2, {(1, 1) = (1/6)*sqrt(3)+(1/2)*I, (1, 2) = (1/6)*sqrt(3)-(1/2)*I, (2, 1) = (1/6)*sqrt(3)-(1/2)*I, (2, 2) = (1/6)*sqrt(3)+(1/2)*I})
expect output be
but these example are wrong
((1/6)*sqrt(3)+(1/2)*I)*Matrix([[1,-I].[-I,1]])
but these example are wrong
MatrixMatrixMultiply(Matrix([[(1/6)*sqrt(3),(1/2)],[(1/6)*sqrt(3),(1/2)]]),Matrix([[1,-I],[1,I]]));
concept like this output

simplify command expresses results by unconvention...

Asked by: tsunamiBTP 292
sum simplify special-function
December 12 2017
0  1

Below is MAPLE code to simplify a series.  MAPLE expresses the result in terms of functions which many people are not familiar with.  Is there a way to express the answer in terms of more conventional functions expecially if N is a positive integer?


 

Cn := ((-I)*(1/2))*(2*(I*Pi*n*tau-(2*I)*Pi*n)*cos(Pi*n*tau/T)-T*(2*I)*sin(Pi*n*tau/T)+(4*I)*Pi*n)/(Pi^2*n^2); S4 := a[0]+sum(Cn*sin(2*Pi*n*x/T), n = 1 .. k); a[0] := 0; T := 4; tau := 2; Cn; S5 := unapply(S4, k, x); T := simplify(S5(N, x))

convert(T, StandardFunctions);

(-polylog(2, exp(-((1/2)*I)*Pi*(x-1)))*N^2-exp(-((1/2)*I)*Pi*N*(x+1))*LerchPhi(exp(-((1/2)*I)*(x+1)*Pi), 2, N)*N^2+polylog(2, exp(((1/2)*I)*(x+1)*Pi))*N^2+exp(-((1/2)*I)*Pi*N*(x-1))*LerchPhi(exp(-((1/2)*I)*Pi*(x-1)), 2, N)*N^2+polylog(2, exp(-((1/2)*I)*(x+1)*Pi))*N^2-exp(((1/2)*I)*Pi*N*(x+1))*LerchPhi(exp(((1/2)*I)*(x+1)*Pi), 2, N)*N^2-polylog(2, exp(((1/2)*I)*Pi*(x-1)))*N^2+exp(((1/2)*I)*Pi*N*(x-1))*LerchPhi(exp(((1/2)*I)*Pi*(x-1)), 2, N)*N^2+exp(((1/2)*I)*Pi*N*(x+1))-exp(((1/2)*I)*Pi*N*(x-1))+exp(-((1/2)*I)*Pi*N*(x+1))-exp(-((1/2)*I)*Pi*N*(x-1))-I*exp(-((1/2)*I)*x*Pi*N)*LerchPhi(exp(-((1/2)*I)*x*Pi), 1, N)*N^2*Pi-I*ln(1-exp(-((1/2)*I)*x*Pi))*N^2*Pi+I*exp(((1/2)*I)*x*Pi*N)*LerchPhi(exp(((1/2)*I)*x*Pi), 1, N)*N^2*Pi+I*ln(1-exp(((1/2)*I)*x*Pi))*N^2*Pi-I*exp(((1/2)*I)*x*Pi*N)*N*Pi+I*exp(-((1/2)*I)*x*Pi*N)*N*Pi)/(N^2*Pi^2)

 (1)

``


 

Download simplify.mw

fsolve interval resolution...

Asked by: tsunamiBTP 292
December 12 2017
0  13

When attempting to numerically solve for a function using fsolv it is possible that the function has multiple roots.  So to focus on a particular region you specify a range such as:

xmax := fsolve(S, x = 0 .. 1/2)

Is it possible fsolve may not resolve the solution due to the fact that delta x is not small enough or does fsolve autonomously adjust delta x in order to find the solution?  If not, how do you manually dictate the delta x for the interval specified?

value & evalf syntax issues?...

Asked by: tsunamiBTP 292
syntax value evalf
December 10 2017
0  2

Below is a link to my worksheet.  I am attempting to evaluate a Fourier series for a particular number of terms & at a specific location xmax.  As far as I can tell xmax is assessed correctly.  Howver, when I go to evaluate the Fourier series for x = xmax using either the 'value' or 'evalf' command they do on seem to recognize that x = xmax.

So I am guessing I must have some syntax problem.  Can anyone show me what I have wrong?

command_syntax.mw

how to print matrix like command in text file with...

Asked by: LeeHoYeung 535
matrix
December 09 2017
0  2

interface(prettyprint=0):
interface(screenwidth=500):
with(LinearAlgebra):

expect 

Matrix([[a1,a2,3],[5,6,7],[9,10,12]])

but

it print datatype = anything,storage = rectangular,order = Fortran_order,shape  and (2,1) etc

Matrix(3,3,{(2, 1) = 1, (3, 1) = 1, (3, 2) = 1},datatype = anything,storage = rectangular,order = Fortran_order,shape = []), 

Creating a symmetric sequence using the Heaviside ...

Asked by: tsunamiBTP 292
symmetric heaviside
September 24 2017
0  4

The MAPLE worksheet associated with the link below attempts to generate a sequence of signals to be symmetric about t=0.  It worked for the 1st plot, but not for the 3rd plot.  I believe the problem resides with the Heaviside function.  I need to somehow create a function that is the mirror image of the Heaviside function.  Does anyone know how to do that?

untitled4.mw

Trouble with evalf() in generating a matrix...

Asked by: tsunamiBTP 292
matrix syntax sum
September 18 2017
0  4

The link below has my code for generating 2 matrices.  The 1st one does not generate flfoating point numerical data; whereas, the 2nd one does.  What is wrong with the 1st case?  I am attempting to single out one harmonic which works in the 2nd case.  Also, is there a way I can generate a spectrum of S2(k= 1 to 100, t= 0 to 1)?

?untitled6.mw

 

how to find p and q in this case...

Asked by: LeeHoYeung 535
series
September 17 2017
0  1

1.
tanh(1-x) = sum(p(ii)*x^q(ii), ii=0..infinity) or product(p*x^q(ii), ii=0..infinity) ?
2.
tanh(1-x)*1/(1-x) = sum(p(ii)*x^q(ii), ii=0..infinity) or product(p*x^q(ii), ii=0..infinity) ?
3.
tanh(x) = sum(p(ii)*x^q(ii), ii=0..infinity) or product(p*x^q(ii), ii=0..infinity) ?

Remark: it may not be possible to use diff to find p(ii)

update

series(tanh(1-x), x=0);
with(OrthogonalSeries):
Coefficients(series(1/(1-x), x=0));
coeffs(series(tanh(1-x), x=0));
coeffs(series(tanh(1-x), x=0),x);
Error, invalid arguments to coeffs;
 
and is it possible to find q(ii) only if assume p(ii) all are one?

how to plot this?...

Asked by: LeeHoYeung 535
plot
September 17 2017
0  7

ode1a := diff(y1(t), t) = round(rhs(odeparm1[1][1]))*y1(t)+round(rhs(odeparm1[1][2]))*y2(t)+round(rhs(odeparm1[1][3]))*y3(t);
ode2a := diff(y2(t), t) = round(rhs(odeparm1[1][4]))*y1(t)+round(rhs(odeparm1[1][5]))*y2(t)+round(rhs(odeparm1[1][6]))*y3(t);
ode3a := diff(y3(t), t) = round(rhs(odeparm1[1][7]))*y1(t)+round(rhs(odeparm1[1][8]))*y2(t)+round(rhs(odeparm1[1][9]))*y3(t);
try
ode1a := diff(y1(t), t) = rhs(odeparm1[1][1])*y1(t)+rhs(odeparm1[1][2])*y2(t)+rhs(odeparm1[1][3])*y3(t);
ode2a := diff(y2(t), t) = rhs(odeparm1[1][4])*y1(t)+rhs(odeparm1[1][5])*y2(t)+rhs(odeparm1[1][6])*y3(t);
ode3a := diff(y3(t), t) = rhs(odeparm1[1][7])*y1(t)+rhs(odeparm1[1][8])*y2(t)+rhs(odeparm1[1][9])*y3(t);
sys := DiffEquation([ode1a, ode2a, ode3a], inputvariable = [y1(t)], outputvariable = [y2(t), y3(t)]);
sysz := ToDiscrete(sys, ts); in_t := Sine(1, 1, 0, 0);
sol := Simulate(sys, [in_t]);
try
p1 := plots[odeplot](sol, [[t, y2(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 1 2", i)
catch:
print("error draw at ", i)
end try;
try
p1 := plots[odeplot](sol, [[t, y3(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 1 3", i)
catch:
print("error draw at ", i)
end try
catch: print("error at ", i);
print(lastexception);
print(ode1a);
print(ode2a);
print(ode3a);
end try;
try
ode1a := diff(y1(t), t) = rhs(odeparm1[1][1])*y1(t)+rhs(odeparm1[1][2])*y2(t)+rhs(odeparm1[1][3])*y3(t);
ode2a := diff(y2(t), t) = rhs(odeparm1[1][4])*y1(t)+rhs(odeparm1[1][5])*y2(t)+rhs(odeparm1[1][6])*y3(t);
ode3a := diff(y3(t), t) = rhs(odeparm1[1][7])*y1(t)+rhs(odeparm1[1][8])*y2(t)+rhs(odeparm1[1][9])*y3(t);
sys := DiffEquation([ode1a, ode2a, ode3a], inputvariable = [y2(t)], outputvariable = [y1(t), y3(t)]);
sysz := ToDiscrete(sys, ts);
in_t := Sine(1, 1, 0, 0);
sol := Simulate(sys, [in_t]);
try
p1 := plots[odeplot](sol, [[t, y1(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 2 1", i)
catch:
print("error draw at ", i)
end try;
try
p1 := plots[odeplot](sol, [[t, y3(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 2 3", i)
catch:
print("error draw at ", i)
end try
catch:
print("error at ", i);
print(lastexception);
print(ode1a);
print(ode2a);
print(ode3a)
end try;
try
ode1a := diff(y1(t), t) = rhs(odeparm1[1][1])*y1(t)+rhs(odeparm1[1][2])*y2(t)+rhs(odeparm1[1][3])*y3(t);
ode2a := diff(y2(t), t) = rhs(odeparm1[1][4])*y1(t)+rhs(odeparm1[1][5])*y2(t)+rhs(odeparm1[1][6])*y3(t);
ode3a := diff(y3(t), t) = rhs(odeparm1[1][7])*y1(t)+rhs(odeparm1[1][8])*y2(t)+rhs(odeparm1[1][9])*y3(t);
sys := DiffEquation([ode1a, ode2a, ode3a], inputvariable = [y3(t)], outputvariable = [y1(t), y2(t)]);
sysz := ToDiscrete(sys, ts);
in_t := Sine(1, 1, 0, 0);
sol := Simulate(sys, [in_t]);
try
p1 := plots[odeplot](sol, [[t, y1(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 3 1", i)
catch:
print("error draw at ", i)
end try;
try
p1 := plots[odeplot](sol, [[t, y2(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 3 2", i)
catch:
print("error draw at ", i)
end try
catch:
print("error at ", i);
print(lastexception);
print(ode1a);
print(ode2a);
print(ode3a)
end try

diff(y1(t), t) = 1.052936200*10^5*y1(t)+70106.19000*y2(t)+35169.00000*y3(t)
diff(y2(t), t) = 70106.19000*y1(t)+71031.61000*y2(t)+35511.00000*y3(t)
diff(y3(t), t) = 35169.00000*y1(t)+35511.00000*y2(t)+36100.00000*y3(t)
"the DEs contain functions with undefined values (probably caused by a discontinuity in the input that was differentiated). As a result, the numerical solution cannot be calculated. The DE system is: %1\"",[(&DifferentialD;)/(&DifferentialD;t) y1(t)=1.052936200 10^5 y1(t)+70106.19000 y2(t)+35169.00000 ({[[0,t<0],[sin(t),otherwise]]),(&DifferentialD;)/(&DifferentialD;t) y2(t)=70106.19000 y1(t)+71031.61000 y2(t)+35511.00000 ({[[0,t<0],[sin(t),otherwise]]),{[[0,t<0],[undefined,t=0],[cos(t),0<t]]=35169.00000 y1(t)+35511.00000 y2(t)+36100.00000 ({[[0,t<0],[sin(t),otherwise]]),y2(0)=0,y1(0)=0]
 
it has error when plot

unable to evaluate the function to numeric values ...

Asked by: LeeHoYeung 535
plot
September 12 2017
0  6
ygraph1 := -.736312023696564122*exp(2.26140104440167664*10^5*tt)-.591826613918776445*exp(28994.5376895644186*tt)+.328002839648234568*o*exp(13767.7178702679158*tt);
ygraph2 := -.591859486202007235*exp(2.26140104440167664*10^5*tt)+.328381376616263988*exp(28994.5376895644186*tt)-.736116852194203974*o*exp(13767.7178702679158*tt);
ygraph3 := -.327943520064913564*exp(2.26140104440167664*10^5*tt)+.736143281263262450*exp(28994.5376895644186*tt)+.592069351595225779*o*exp(13767.7178702679158*tt);
FunctionAdvisor(branch_points, ygraph1);
plot(ygraph1, tt=-5..5);
plot(ygraph2, tt=-5..5);
plot(ygraph3, tt=-5..5);
Warning, unable to evaluate the function to numeric values in the region;
 
how to plot this system?

invalid input: PDEtools/NumerDenom...

Asked by: LeeHoYeung 535
dsolve
September 12 2017
0  2

ode1a := diff(a(t), t) = 1.342398800*10^5*a(t)+round(89591.20000)*b(t)+round(44647.44000)*c(t);
ode2a := diff(b(t), t) = round(89591.20000)*a(t)+round(89803.24000)*b(t)+round(44901.60000)*c(t);
ode3a := diff(c(t), t) = round(44647.44000)*a(t)+round(44901.60000)*b(t)+round(44859.24000)*c(t);
sol := dsolve([ode1a=exp(t), ode2a=exp(t), ode3a=exp(t)], [a(t),b(t),c(t)]);

Error, (in dsolve) invalid input: `PDEtools/NumerDenom` expects its 1st argument, ee, to be of type algebraic, but received diff(a(t), t) = (3355997/25)*a(t)+89591*b(t)+44647*c(t)

 

initially i guess the error come from decimal number coefficient

but after round it, still have error

how to apply ricci flow?...

Asked by: LeeHoYeung 535
differential-equations eigenvalues
September 12 2017
0  0

ode1a := diff(y1(tt), tt) = 1.342398800*10^5*y1(tt)+89591.20000*y2(tt)+44647.44000*y3(tt);
ode2a := diff(y2(tt), tt) = 89591.20000*y1(tt)+89803.24000*y2(tt)+44901.60000*y3(tt);
ode3a := diff(y3(tt), tt) = 44647.44000*y1(tt)+44901.60000*y2(tt)+44859.24000*y3(tt);

would like to find the origin eigenstate before it collapse to eigenvalues

how to apply ricci flow in this situation?

i find help file , and can not find some relationship between this application and inputs of ricci related function

which functions in maple can help to find origin of eigenstate

how to deplot this case?...

Asked by: LeeHoYeung 535
plot
September 12 2017
0  3
ode1a := diff(y1(tt), tt) = 1.342398800*10^5*y1(tt)+89591.20000*y2(tt)+44647.44000*y3(tt);
ode2a := diff(y2(tt), tt) = 89591.20000*y1(tt)+89803.24000*y2(tt)+44901.60000*y3(tt);
ode3a := diff(y3(tt), tt) = 44647.44000*y1(tt)+44901.60000*y2(tt)+44859.24000*y3(tt);
 
DEplot3d({ode1a,ode2a,ode3a}, {y1(tt), y2(tt), y3(tt)}, tt=0..10,[[y1(0) = 0, y2(0) = 0, y3(0) = 0]],scene=[tt,y1(tt),y2(tt)]);
DEplot3d({ode1a,ode2a,ode3a}, {y1(tt), y2(tt), y3(tt)}, tt=0..10,[[y1(0) = 0, y2(0) = 0, y3(0) = 0]],scene=[tt,y1(tt),y3(tt)]);
DEplot3d({ode1a,ode2a,ode3a}, {y1(tt), y2(tt), y3(tt)}, tt=0..10,[[y1(0) = 0, y2(0) = 0, y3(0) = 0]],scene=[tt,y2(tt),y3(tt)]);
 
can it plot 3 functions ?
and why it return a straight line 3d graph
 
is there some interesting graph from this system?
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