## Problem: LinearAlgebra, Eigenvectors, MatrixExpon...

There must be an easy way to resolve this problem, I just haven't found it yet. > restart;with(LinearAlgebra); > A:=pp->eval(Matrix([[a1(p),0],[0,a2(p)]]),p=pp):A(p); [a1(p) 0 ] [ ] [ 0 a2(p)] > Eigenvectors(A(p)); Error, (in LinearAlgebra:-LA_Main:-Eigenvectors) expecting a Matrix of rationals, rational functions, algebraic numbers, or algebraic functions > Is there a way to make the LinearAlgebra routines treat a Matrix function just like a regular Matrix? thanks

## how to optimize a numerical function...

I have defined a function: ft(n,v)=Zeta(0,n+1,1-2*Pi*v*I)/Zeta(n+1) mag(n,v)=sqrt(ft(n,v)*conjugate(ft(n,v))) I want to find the points v at which mag(n,v)=0.5 (i.e. for n=2,3,4, etc.) Any of the so-called numerical solver techniques described in the help file with Maple simply return an expression containing the digamma function symbol (e.g. Psi) Any ideas? Thanks -Monty Wood

## Find the solution to a numerical function equation...

Find the solution to a numerical function equation? I have defined a function: f(n,v) = Zeta(0,n+1,1-2*Pi*v*I)/Zeta(n+1) mag(n,v) = sqrt(f(n,v)*conjugate(f(n,v)) For this funciton, n represents an integer, and v is real. Essentially, for different values of "n," I would like to find the numerical value of "v" at which mag(n,v) is equal to 0.5 Using various combinations of Optimize, fsolve, and NewtonsMethod, and interlacing evalf into the definitions, the program continues to give me a symbolic expression using the "Psi" symbol for the Digamma function. Is there a way to define the function strictly numerically so that the symbolic engine does not kick in?

## 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[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.)

## 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!