Hello all!
I need to solve multivariate polynomial equations modulo a positive integer 'm', where 'm' is not prime. Which function would be best?
Also, how do I include constraints to the above set of equations? For instance, if I need to solve for 'x' and 'y' such that
f(x,y) = 0 mod m
g(x,y) = 0 mod m
f != g mod m
Any help would be great!!

How can I plot the following function?
x = cos(t) + 2*cos(2*t);
y = sin(t) + 2*sin(2*t);
To be clear this is one function.
Thank you in advance.

Hi,
I'm new to Maple 10 and have a quick question. I am generating a whole load of numbers which I am writing out to files using the ExportVector command. I want to run the worksheet many times and replace the numbers in the file names each time. I have 80 file names each time and wanted to do this via the Find/Replace command but it only seems to find text rather than command inputs. My worksheet looks like this:
> ExportVector("out_geg2.k015.e10_1n1.m", ans1a, target = Matlab, format = rectangular, transpose = false);
> ExportVector("out_geg4.k015.e10_1n1.m", ans2a, target = Matlab, format = rectangular, transpose = false);

hi, I have a big problem with my project. I need a help with solving and plotting three differential equations but I can´t do it. The project is about lotka-volterra system with three species, 2 predators and 1 prey with no competition between predators. Thanks for a help.
eqPrey := diff(X(t), t) = alpha1*X(t)*(1-X(t)/K) - beta1*X(t)*Y(t)-gamma*Y(t)*Z(t);
eqPred1 := diff(Y(t), t) = -alpha2*Y(t) + beta2*X(t)*Y(t);
eqPred2 := diff(Z(t), t) = -alpha3*Z(t) + beta3*Z(t)*Y(t);

Dear Sir/Madam:
I try the following maple commands:
> with(linalg):
> A:=matrix([[r1*X, (1-r1)*X],[1-r2,r2]]):
> eigsys:=eigenvectors(A);
> ES[1]:=eigsys[1][3];ES[2]:=eigsys[2][3];
> P:=augment(op(ES[1]),op(ES[2]));
> K:=map(simplify,evalm(inverse(P)&*A&*P));
> W:=map(simplify,evalm(P&*K&*inverse(P)));
> U:=map(expand, W);
> map(simplify,U);
Now, K and P are correct because P&*K&*inverse(P) = A.
But, when I use the following maple commands, I cannot get A^i with entries that are polynomials of r1 and r2 and X.
> V:=map(simplify, evalm(P&*(K^i)&*inverse(P)));
(Note: formula A^i = P*K^i* inverse of P is correct.)

can anyone help me start with how do I solve the equation sqrt(1 - y^2(t)) with initial value y(0)=0 and y(t) between -1 and 1 and t between -pi/2 and pi/2

Is it possible to mix geom3d and plot3d surfaces, and plot in the same plot? Ie, draw a sphere then overlay a spherical [r,theta,phi] plot.?
Cheers
Chris

I got this problem from my proffesor :
*Provide a MAPLE procedure which plots ANY curve C given by a pair
of Cartesian implicit equations { f(x,y)=0 & g(x,y)=0 }, without
plotting as well the two surfaces ( f=0 and respectively g=0 ),
which provide C by their intersection (just the curve C has to
appear as output). Do NOT attempt to parametrize the curve; use
the MAPLE plotting functions for Cartesian plots.
Example: C: { x^2+y^2+z^2-1=0 and z=0 } is a circle in the xOy
plane;
plot the circle, but not the sphere or the plane which provide C.
*

Hi everyone,
I am trying to solve an ode like this:
diff(y(x),x,x)=-(1+0.2*cos(x))*sinh(y(x))+0.3*cosh(y(x)),
the only boundary condition I want to impose is y(0)=y(2*Pi),Dy(0)=Dy(2*Pi). Anybody knows about it? Thanks!

hey :)
i have a set of equations on the form in the example below. i included my attempt at a solution which, as you might suspect, does not give me the answer on the form i want.
what i want is to solve this assuming that the coefficients for each term in the polynomial of u and v sould be equal.
eq1 := a1*u^2 + (a4 + 3 + 2*a6)*u*v + a3*v^2 + (a1 + a2 + a6)*u + a5*v + a6 = 5*u^2 + 7*v;
solve(eq1, {a1,a2,a3,a4,a5,a6});
this example would for example have the solutions:
a1 = 5
a2 = -5
a3 = 0
a4 = -3
a5 = 7
a6 = 0
but if you type the code ive written into maple, youll see thats not what i get at all :)

hi!
Could somebody tell me if Maple has the capability of solving Partial Differential Equations using the method of Separation of Variables.
Thanks,
Raj

Dear Sir/Madam:

I try to find a close form for A^k,

where k is an arbitrary interger and A is 2 by 2 matrix as the following:

A = ([[r1*X, (1-r1)*X],[1-r2,r2]]);

r1 and r2 are symbolic constants, X is a variable.

First, I run the following commands in maple:

A:=matrix([[r1*X, (1-r1)*X],[1-r2,r2]]);

Z3:=A^3;

simplify(evalm(Z3),symbolic);

I hope to simplyfy the entries of Z3 in the order of X, i.e.,

z11 = a0*X^3 + a1*X^2 + a2*X +a3;

z12 = ....... (the same as the above)

z21 = .......

z22 = .......

But I do not know how to do it.

I try to find a law for representations of the entries of A^k by looking at the cases k=3,4,....

restart; interface(version);
Classic Worksheet Interface, Maple 10.06, Windows, Oct 2 2006 Build ID 255401
expr:=hypergeom([1-I*a,1-I*b],[1],x);
convert(expr, hypergeom, "lower c");
expr := hypergeom([1 - a I, 1 - b I], [1], x)
0
Digits:=14:
subs(a=1, b=2, c=1, expr):
eval(%,x=2); evalf(%);
#Re(%%%); plot( %, x=-1..0.9); plot( %%, x=1.1 .. 3);
hypergeom([1 - I, 1 - 2 I], [1], 2)
0.010385802579659 + 0.068521539093061 I

I am calculating the standard deviation of an function with StandardDeviation command both symbolically and numerically and I get different result for the symbolic and numeric calculation. The result of the symbolic calculation is wrong.
Here is my problem:
restart;with(Statistics):
X := RandomVariable(Uniform(-Pi, Pi));
f:=1/abs(1-0.5*exp(-I*X));
StandardDeviation(f);
# It gives 0, which is wrong.
StandardDeviation(f, numeric);
Re(%);
Any idea?

I have a mechanics question with position given by
phi = omega t
theta = (1/2)Pi * (1+ (1/4)cos(4*omega*t))
r = b
This is to be solved in spherical coords. That's not the problem. I solved this just fine, but I would really like to plot this to see what it looks like! Checking the help pages in maple, it says plot3d expects a function r(theta,phi) (might be the other way around?). So, is there a way to plot my 3 parts, or, failing that, how do I turn that into r wrt phi and theta?
Cheers
Chris
PS. How do you post 2D math? I tried, but nothing really worked?