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These are questions asked by John2020

Hi, I have a problem with tensor calculus. Please guide me.

I have two Tensors B[mu, nu] and A[~mu, ~nu].

Furthermore, I have two mixed tensors as U[~1, mu, nu] and U[~2,mu,nu]

rho, mu, and nu can run from 1 to 2. Hence, A, B, and both Us are 2*2 matrices.

Note that there was only one U, but since it is a mixed tensor, hence I have separated it into two tensors for making it easy.

Now I want to compute the following summation:

U[~rho,mu,nu] U[~alpha,beta,gamma] B[rho,alpha] A[~mu,~beta] A[~nu,~gamma].

Maple must give a number for rho, mu, nu, alpha, beta, and gamma (which can take 1 and 2) and compute "all" possible summations. Since the result will be just "a number", hence I could not use TensorArray.

How can I do it and get a result?

The forms of all tensors are in the attached maple file:



I have two coupled algebraic equations (not differential equations; but only simple algebraic equations; call them "equ1" and "equ2") in which there are three parameters: "x", "y", and "z".

I want to use "fsolve" (Numerical solve) for solving them and then plotting. But since there are three parameters and two equations hence one of the parameters must be given. I want to give a range for "z", for example [2..9], and step size, for example "0.5", such that maple first puts "2" in both equations and solve them numerically and get the values of "x" and "y" and then record them, and then set the value "2.5" for "z" and again repeat the above cycle until the value "z=9". Finally plot both "x" and "y" in terms of "z".

How do I write this?

Thanks in advance

How can I  get the "phase portrait including vector fields" and several trajectories of the following dynamical system in the polar coordinates (Note that the system is also in polar coordinate)??



I have a problem, please help me to solve it.

I am trying to extract coefficients of some polynomial expressions but I receive Error.

For example:


>Setup(mathematicalnotation = true)

>S := a*(x^2)+b*x+c*(1/(x-h)):

>Coefficients(S, x, 1)

>Error, (in Physics:-Coefficients) unable to compute coeff.

**** Note that if instead of the term (1/(x-h)) we have (1/x), then we get the true result. The error occurs only when we have some extra things in the denominator namely "-h".


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