## 96 Reputation

15 years, 70 days

## Quaternions - Error?...

Maple

Hello!

I got the Quaternions package (version 2007) from MapleSoft:

www.maplesoft.com/applications/app_center_view.aspx

Now I type in the following statements:

## Solve parametric equations with restrict...

Maple
Hello! How can I solve a linear equation which depends on two parameters (a,b) for which the assumption a^2 + b^2 = 1 shall hold. This does not work by writing assume or assuming. The problem has the following form: tau := f(a,b) -> eigenvalues of a matrix U = U(a,b) M := U - tau*Id = M(tau,a,b) = M(a,b) find the kernel of M (eigenvectors of U) and simplify using a^2 + b^2 = 1. I do not want to write down the exact matrix and hope that this information is enough. If not, I will take some time to write it down. Greetings, yadaddy.

## Assumption not working with PDE...

Maple
Hello! I have the following PDE: PDE := { diff(alpha(u, v), u) = -I*exp(I*u)*beta(u, v), diff(alpha(u, v), v) = -I*exp(-I*v)*beta(u, v), diff(alpha(u, v), u) = I*exp(-I*u)*beta(u, v), diff(alpha(u, v), v) = -I*exp(I*v)*beta(u, v), diff(beta(u, v), u) = (1/8*(I*exp(-I*v)*alpha(u, v)+(2*I)*beta(u, v)+(2*I)*exp(-I*(v+u))*beta(u, v)))*(a-1)-(1/8*(-I*exp(-I*u)*alpha(u, v)-(2*I)*beta(u, v)+(2*I)*exp(-I*(v+u))*beta(u, v)))*b, diff(beta(u, v), v) = (1/8*(I*exp(-I*u)*alpha(u, v)+(2*I)*beta(u, v)-(2*I)*exp(-I*(v+u))*beta(u, v)))*(a-1)-(1/8*(I*exp(-I*v)*alpha(u, v)+(2*I)*beta(u, v)+(2*I)*exp(-I*(v+u))*beta(u, v)))*b,

## Find more solutions to a PDE...

Maple
Hello! I have a quasilinear first-order PDE system and Maple gives me only the trivial zero-solution after some seconds of computations. I know from theory that there are nontrivial solutions to the PDE, too. Can I get them somehow (from for example Maple)? This is the PDE: PDE := {diff(alpha(u, v), u) = -I*exp(I*u)*beta(u, v), diff(alpha(u, v), v) = -I*exp(-I*v)*beta(u, v), diff(alpha(u, v), u) = I*exp(-I*u)*beta(u, v), diff(beta(u, v), v) = 1/4*I*exp(I*u)*alpha(u, v)+1/2*I*exp(I*(v+u))*beta(u, v)+1/2*I*(beta)(u, v), diff(alpha(u, v), v) = -I*exp(I*v)*beta(u, v),

## PDSolve, Error: duplicated elements (ran...

Maple
Hello! I have some trouble with getting an explicit solution to a PDE: f=f(u,v) in IC^4 (IC=complex numbers) So i have a system of 8 equations, first order, integrable (i.e. solution exists by theory). I'm getting the following, when calling pdsolve(PDE, fcns), where PDE is the set of the PDEs and fcns are the 4 complex functions f[i], i=1,2,3,4: "Error, (in pdsolve/sys) duplicated elements (ranking)" What could it be? Thx, yadaddy.
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