Items tagged with complex complex Tagged Items Feed

Hi all.

I try to get the real part from the complex expression. But it turns out to not be the simplest result:

A:=I*sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*exp(-I*k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b)

convert(exp(-I*k[0]*h), sin);

simplify(Re(A));

Maple results in:

Re(sin(k*Pi*(-x+h*cos(theta))/a)*sin(l*Pi*(-y+h*sin(theta))/b)*exp(-I*k[0]*h)*sin(k*Pi*x/a)*sin(l*Pi*y/b))

while the simplified result should be:

sin(k*Pi*(x-h*cos(theta))/a)*sin(l*Pi*(y-h*sin(theta))/b)*sin(k*Pi*x/a)*sin(l*Pi*y/b)*sin(k[0]*h)

 

I wander how to get the simplifyed result in maple. Thanks

Solve IVP with complex coef. with compplex varables numerically..

the sys. is x'=-iDelta1x(t)+y(t)+epsilon

y'=-iDelta2y(t)+x(t)z(t)

z'=-2(x*(t)y(t)+x(t)y*(t)), where * means complex conjugate 

I solve it as:

epsilon:=5:Delta1:=4:Delta2:=4:assume(z(t),real):

var:={x_R(t),y_R(t),z_R(t),x_I(t),y_I(t),z_I(t)}:
dsys :={diff(x(t),t)=-I*Delta1*x(t)+y(t)+epsilon, diff(y(t),t)=-I*Delta2*y(t)+x(t)*z(t), diff(z(t),t)=-2*(conjugate(x(t))*y(t)+conjugate(y(t))*x(t))}:
functions := indets(dsys, anyfunc(identical(t))):
redefinitions := map(f -> f = cat(op(0, f), _R)(t) + I*cat(op(0,f), _I)(t), functions):
newsys := map(evalc @ Re, redefinitions) union map(evalc @ Im, redefinitions):

incs := {x_R(0)=0, x_I(0)=0, y_R(0)=0, y_I(0)=0,z_R(0)=-1/2, z_I(0)=0}:
dsol1 :=dsolve({newsys,incs},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1):

but it seems there is not runing propebly

 

If we a complex number in Maple, like for example:

I*b+a+x+I*y+I^2*c

 

How can we make maple rewrite it like this?

a+x-c+I*(y+b)

 

I tried using the comands Re(%) and Im(%) but Re just gives the whole expression again and Im gives 0.

I have been having problems with using the BodePlot function with units:

 

R1 := 18.2*10^3*Unit('Omega');

R2 := 10^3*Unit('Omega');

C1 := 470*10^(-12)*Unit('F');

C2 := 4.7*10^(-9)*Unit('F');

# wo is in hertz

wo := 1/sqrt(R1*R2*C1*C2);

# Q is unitless

Q := wo*R1*R2*C2/(R1+R2)

 

with(DynamicSystems);

sys := TransferFunction(wo^2/(s^2+wo*s/Q+wo^2));

 

This is the error message I got:

Error, (in Units:-Standard:-+) the units `1` and `Hz` have incompatible dimensions

 

I think the problem is that the BodePlot function doesn't expect 'wo' to have units.  

So I tried to work around the issue by using the loglogplot but it doesn't seem to like 

complex function even when I used abs to find the magnitude (with or without units).

 

 Any workaround is appreciated.

I was just wondering if there is such thing as a technique for solving integrals using a PFD(partial fraction decomposition) if the denominator's rational roots are complex numbers???

Hi all,

I am stuck with the following problem:

convert(cos(alpha), exp); works fine for me.

Once I have the trigonometric functions in a matrix, it does not work any more:

In the latter line, A keeps the trigonometric functions. Why is this the case? Is there any way to force maple to keep the complex exponentials instead of trigonometric functions?

 

I am using LinearAlgebra and VectorCalculus.

 

Best Regards

Wassja

Hello,

first of all, this is my very fist question in this forum, so please excuse some formal mistakes I may make...

Using Maple 18.01 on Windows 7 64bit

To the topic: I want to calculate the eigenvalues of a complex matrix like this (just as an example):

M := Matrix(2, 2, {(1, 1) = a+2.5*I, (1, 2) = 1-I*a, (2, 1) = 4, (2, 2) = a})

When I try to calculate

Eigenvalues(M)

I get

Error, (in LinearAlgebra:-Eigenvalues) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values

Strange, because if I replace the "2.5" with just "2", so an integer instead of a float, I get results:

I don't understand this strange behavior, since Mathematica i.e. calculates everything just fine...:

Thanks in advance for any suggestions.

Hi guys,

I am trying to solve for the roots in a polynomial of infinite order. The idea is simply to approximate the infinite polynomial by a high order Taylor expansion, solve for the roots in this polynomial (both real and complex roots exists) and use these roots as initial guesses for finding the authentic roots of the infinite polynomial in this specific range.

I have tried to use the evalf(RootOf(PolyInfinite=0,x,Re + Im)), however the output from RootOf seems to converge to the same 2 or 3 roots almost independent of the initial guess. Is there specific options of this RootOf function that can stabilize the solution or another/better command to use?

On the other hand i could solve this by simply minimizing a least sqaure, however i have not found any optimization solver which supports solutions in the complex domain?

I sincerely hope that you are able to help me.

Kind regards

Lasse

 

 While calculating an integral including complex numbers, I have encountered with the output "undefined if a+ib>0". What does this mean?A complex number bigger than zero???

I notice that when I tried to factor the polynomial

x^3+x^2+2*x+1 I did not get the rational roots of the polynomial, then I tried using synthetic division to solve for the roots but I could not find a root. So I believe that the roots of the polynomial equation are complex numbers...

How could I use synthetic division to find the rational roots of this integral so that I could do a Partial Fraction Decomposition for the integral...

Hello everybody,

I want to find all of roots of the complex variables functions in two ways.

(1) find the value which can make the function equals 0

(2) find the real value and imaginary value which make real part and imaginary part of function equal 0

(I know answers of these two case is not equal completely.)

 

The function is a non-linear function, including sin, cos and Bessel function, such as:

 


And, I used Analytic and fsolve to do case (1) and (2), but failure. The follow result is how I tried to find the real value answer:

 

It seems that both of two commands can only find some of roots. 

How to find all of roots of these cases? The related .mw file is attached.

Cannot_find_all_of_roots.mw

 

Thanks a lot.

 

t := exp(2*(I*Pi*(1/11)))

u := t^10*a[10]+t^9*a[9]+t^8*a[8]+t^7*a[7]+t^6*a[6]+t^5*a[5]+t^4*a[4]+t^3*a[3]+t^2*a[2]+t*a[1]+a[0]

 

How can get maple to simplify expressions like u^3+u^2-1 so that the exponents are between 2*(I*Pi*(1/11)) and 1.

Essentially it keeps outputting things like exp(2*(I*Pi*(1/11)))^12 and not simplifying it as it is a root of unity

Ok so i have a matrix M filled with complex roots of unity. I want to execute the following code but it seems to be failing to do so correctly

t:=exp(2 Pi I/11);

m := (i, j) -> M[(i mod 11)+1, (j mod 11)+1] ;  

mu :=(i,j)->(add(add(add(a[k]*a[m]*a[n]*t^(m)*m((i+k-m),(j+n-m))),n=0..10),m=0..10),k=0..10));

 

Something is wrong with my indexing of the matrix . or when the mod procs.

Hello every one,

I had a 3 equations with 3 unknown (X,Y,Z, conjugate(Y),conjugate(Z))

this is the code:

solve( {ao*x + a1*y + conjugate(a1)*conjugate(y)+a2*z+conjugate(a2)*conjugate(z) = 0.5, conjugate(a1)*x + bo*y + conjugate(a2)*conjugate(y)+a1*z = 0, 10*x + 10*y/4 + 10*z = 10}, {x, y, z});

where the coefficients are complex numbers

Is thee any simple way to solve it

thanks

hi all.

I have wrore the following program for optimization with bernstein and block pulse hybrid functions.

the program have some errors which i can't understand.

Bernestien1.mws

restart:

alias(C=binomial):
with(LinearAlgebra):
macro(LA= LinearAlgebra):


HybrFunc:=proc(N, M,  tj)               # N=Number of subintervals,  M=Number of functions in subintervals
 
local B, n, m;

global b;

for n from 1 to N do
for m from 0 to M-1 do

B := (i,m,t) -> C(m,i)*(1-t)^(m-i)*t^i:

b[n,m]:=unapply(piecewise(t>=(n-1)*tj/N and t<n*tj/N, B(m,2,N*t-(n-1)*tj), 0), t):
 od:od:


Array(1..N, 0..M-1, (n,m)->b[n,m](t)):

#convert(%,vector);
end proc:

HybrFunc(3, 3, 1);




                                       # End Of Definition
 
g2(t):=t;            #*exp(t-1):                      # Any other function can be replaced here
    

g1(t):=add(add(c[n,m]*b[n,m](t), m=0..2), n=1..3);
Optimization[Minimize](sqrt(int((g2(t)-g1(t))^2, t=0.. 1)));
assign(op(%[2]));
plot([g2(t),g1(t)], t=0..1, 0..5, color=[blue,red],thickness=[1,3],discont, scaling=constrained);

Array(1 .. 3, 0 .. 2, {(1, 0) = piecewise(0 <= t and t < 1/3, (1-3*t)^2, 0), (1, 1) = piecewise(0 <= t and t < 1/3, (6*(1-3*t))*t, 0), (1, 2) = piecewise(0 <= t and t < 1/3, 9*t^2, 0), (2, 0) = piecewise(1/3 <= t and t < 2/3, (2-3*t)^2, 0), (2, 1) = piecewise(1/3 <= t and t < 2/3, (2*(2-3*t))*(3*t-1), 0), (2, 2) = piecewise(1/3 <= t and t < 2/3, (3*t-1)^2, 0), (3, 0) = piecewise(2/3 <= t and t < 1, (3-3*t)^2, 0), (3, 1) = piecewise(2/3 <= t and t < 1, (2*(3-3*t))*(3*t-2), 0), (3, 2) = piecewise(2/3 <= t and t < 1, (3*t-2)^2, 0)}, datatype = anything, storage = rectangular, order = Fortran_order)

g2(t) := t

"g1(t):=c[1,0] ({[[(1-3 t)^2,0<=t and t<1/3],[0,otherwise]])+c[1,1] ({[[6 (1-3 t) t,0<=t and t<1/3],[0,otherwise]])+c[1,2] ({[[9 t^2,0<=t and t<1/3],[0,otherwise]])+c[2,0] ({[[(2-3 t)^2,1/3<=t and t<2/3],[0,otherwise]])+c[2,1] ({[[2 (2-3 t) (3 t-1),1/3<=t and t<2/3],[0,otherwise]])+c[2,2] ({[[(3 t-1)^2,1/3<=t and t<2/3],[0,otherwise]])+c[3,0] ({[[(3-3 t)^2,2/3<=t and t<1],[0,otherwise]])+c[3,1] ({[[2 (3-3 t) (3 t-2),2/3<=t and t<1],[0,otherwise]])+c[3,2] ({[[(3 t-2)^2,2/3<=t and t<1],[0,otherwise]])"

Error, (in Optimization:-NLPSolve) complex value encountered

Error, invalid left hand side in assignment

(1)



Download Bernestien1.mws

 I'll be so grateful if any one can help me.

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

1 2 3 4 5 6 7 Last Page 1 of 26