Solve multivariate polynomial equations...

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!!

Plotting parametric function...

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.

Replace exporting file names...

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);

Differential equations...

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);

How do I simplify the matrix?...

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:=eigsys;ES:=eigsys; > P:=augment(op(ES),op(ES)); > 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.)

Need help starting...

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

Mixing geom3D objects and plot3d surfaces?...

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

Problem...

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.

How to solve ODE numerically with periodic boundar...

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!

how do i identify coefficients in maple...

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 :)

Separation of variables...

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

How can I get the general form for A^k? where A =(...

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,....

Bug in convert/hypergeom?

by: Maple
```restart; interface(version);

Classic Worksheet Interface, Maple 10.06, Windows, Oct 2 2006 Build ID 255401

expr:=hypergeom([1-I*a,1-I*b],,x);
convert(expr, hypergeom, "lower c");

expr := hypergeom([1 - a I, 1 - b I], , 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], , 2)

0.010385802579659 + 0.068521539093061 I
```