Maple 12 Questions and Posts

These are Posts and Questions associated with the product, Maple 12
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

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

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?

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

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 = []), 

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

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

 

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?

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
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?

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

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

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?

I have an analytical equation with respect to time that is a Fourier series expansion of a specific function.  I would like MAPLE to generate a table of results against time.  I have always used MATLAB to handle numeric data.  How can I generate a data table in MAPLE.  I have never used the Spreadsheet tool in MAPLE.  Is that the way to go?  Is there some examples on how to do this?

My analytical function is attached:

untitled4.mw

I read from another posting that plottools:-getdata is the way to go, but I do not see that functionality in MAPLE 12?

when use cmaple and print command to show result in text file, it use multiple line to express

but not maple command

how to print the maple command instead of multiple line expression when use cmaple

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