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

How can I breal kong code lines in "Code Edit Region" like "..." in Matlab?

How can one use maple to linearized nonlinear ODE of this type Linearize.mw

with maple.

Best regards.

Hi,

  Suppose I have the following code

***

f[1]:=x1^2+x2;
f[2]:=-x2^3+x1-2;

solve({f[1], f[2]}, {x1, x2}):
a,b:= eval([x1, x2], %[1])[]:
a, b;

***

It could work and give me "1 and -1". 

I would like to have a general subroutine, solving f[1]...f[n]. I cannot input  "solve({f[1], f[2],....,f[n]}, {x1, x2}):" just like that. Is ther any way to use "solve" or similar module to handle arbitary number of variables?

I am trying to use solve to determine 5 unknowns from 12 equations each with seperate data points); however, maple requires you to have equal number equations and variables. Is there any way around this?

There are two ways of expressing the solution to a cubic equation, one of them uses cos and arccos [1]. How do I / is there a way to ask Maple to get this form?

More generally, can Maple be instructucted to solve equations using trig identities?

[1] http://en.wikibooks.org/wiki/Trigonometry/The_solution_of_cubic_equations

I am fitting polynomial differential equations to data, and I came across some troubling behavior. I have sets of coordinates in x, y, z, and values w at these coordinates. The x,y,z coordinates and the data at these coordinates are concatenations of three subsets of data each, and depending on the order of the concatenation, I get different polynomials from the stats fit command. The difference is not trivial -- it makes a huge differentce in the stability of the differential equations. I have written a demonstration worksheet to show this problem.

John Starrett

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.

Hey

I have a excel spreadsheet with a number of data points which I want to plot in Maple.  I have imported the data and I did manage to produce a point plot, but how can I exclude some of the data points when I plot the point plot?
I would, for example, like to exclude the negative values and only plot the data which is greater than zero.

Thanks

I am relatively inexperienced with Maple and would like to either be pointed in the right direction or shown a similar example to my problem for reference.

My problem is I need to write a programme using the below equations

d^2x/dt^2=ax+by

d^2y/dt^2=cx+by

I then have to use the below values to show my programme works

a=b=c=d=1

x(0)=1

Dx(0)=0

y(0)=0

Dy(0)=1

After proving it works I have to apply it to a mass spring system using realistic parameters. Using visual and analytical ways to show findings.

md^2x/dt^2=-kx-k(x-y)

md^2y/dt^2=-k(y-x)-ky

when x and y are the displacement from the equilibrium. Initially the masses are displaced from their equilibrium posistions and released so that

x(0)=a, y(0)=b, Dy(0)=Dx(0)=0

then repeat with different smaller calculations

Any help would be much appreciated

Thanks

When I write in maple the following:

x*(x+y)

What do I need to write to make maple make the operation that will evaluate the expression and show the following?

x^2+x*y

simplify(%) or evaluate(%) only shows it the same way it was inputted to start with.

Hi,

  I have the following code for using "PolynomialSystem" solve equations of polynomial

*********

with(SolveTools):

f:=PolynomialSystem({x+y-3, x^2+y^2-5}, {x, y}):

print(x,y);
print(f);
f[1];f[2];
a:=f[1][1];b:=f[1][2];
print(a,b);
c:=-evalf(a);d:=-evalf(b);

****************

The output is

***

x, y
{x = 2, y = 1}, {x = 1, y = 2}
{x = 2, y = 1}
{x = 1, y = 2}
x = 2
y = 1
x = 2, y = 1
-x = -2.
-y = -1.

***

From what I have seen, I cannot subtract the values of x and y as 2 and 1. Is there any way that I can get the values of solutions of variables, namely I can assign a variable "a" as 2, and the other variable "b" as 1?

Thank you very much!

How can one deduce values of f(eta), diff(f(eta),eta) and diff(f(eta),eta$2) from values of f1,f2,f3,f4,.. in the results of the finite difference here Trial.mw . I need the outcome for f and its 1st and 2nd derivatives as listed above. Please help.

How do I compute the Lyapunov exponents for Lorenz system