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guys, is there any possibility to obtain field equations of einstein-hilbert action?

best regards

Hi there,
I have a set of differential equations whose solution, Jacobian matrix and its eigenvalues, direction field, phase portrait and nullclines, need to be computed.

Each of the equations has a varying parameter.

I know how to get the above for a single parameter value, but when I set a range of values for the parameters, Maple is not able to handle all cases as I would expect: solving the differential equation system:

eq1 := x*(1.6*(1-(1/100)*x)-phi*y)
eq2 := (x/(15+x)-0.3e-1*x-.4)*y+.6+theta
desys := [eq1, eq2];
vars := [x, y];
steadyStates := map2(eval, vars, [solve(desys)])

already yields an error:
Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {-600*y+(Array(1..2, {(1) = 8400, (2) = 15900})), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0})}

The equations are the following:
de1 := diff(x(t), t) = x(t)*(1.6*(1-(1/100)*x(t))-phi*y(t));
de2 := diff(y(t), t) = (x(t)/(15+x(t))-0.3e-1*x(t)-.4)*y(t)+.6+theta

the parameters being:
phi:=[0 0.5 1 1.5 2]
theta:=[5. 10.]

How can I handle the situation so that Maple computes each of the above for each combination of the parameters?

I would like to avoid using two for loops and having to store all results in increasingly bigger and complicated arrays.

The worksheet at issue is this:


Hello everyone.

I have a vector field in 2d-cartesian coordinates which I would like to convert to a "normal" function, that is f(x, y) where when you put x and y in, you get the magnitude of the vector at that point.

Example vector field:

This one is very hard to handle by hand which is why I want to use Maple for it.

I tried VectorCalculus[Norm] but it gave me this:

The question of how to do matrix operations over a finite field with p^k elements k>1 was raised in this forum in April 27 2010. I wonder if there has been any progress since then for recent versions of Maple.

I am expecially interested in finding the rank of a matrix over a field of order p^k, k > 1.


Hello, I have a problem in plotting the vector field of dx/dt=sinx/sint

It shows me an error:

Error, (in DEtools/dfieldplot) unable to evaluate function `sin(x)` in evalhf

Dunno how to fix it

Here is my code:

DE := [diff(x(t), t) = sin(x)(t)/sin(t)];
dfieldplot(DE, x(t), t = -2 .. 2, x = -1 .. 2, arrows = medium, title = 'Diff', color = DC);

Hi, I am trying to plot a solution curve on a vector field with an initial condition of y(0)=0 and I keep getting error messages. This is what I have so far:


with(DEtools); dfieldplot(diff(y(x), x) = x^2+y(x)^2-1, y(x), x = 0 .. 5, y = -1 .. 5, arrows = line, title = 'Slope*Field');


Thank you. 

I am working over F_p, where p is prime. When p = 2, the number of 2x2x2 arrays (aka hypermatrices or tensors) over this field is 2^(2*2*2) = 256. Of those 256 arrays, I only want the symmetric ones: that is, if x_{ijk} is the ijk-th element of the array X, then x_{ijk} = x_{ikj} = x_{jik} = x_{jki} = x_{kij} = x_{kji}. Is there a quick loop that does this? 

I have plotted a predator/prey system using the following code and would now like to plot the same with the initial value problem of y=200, x=1000, with the end result being a graph of that one trajectory, without the phase field.  How can I do this?  Thanks.

DEtools[DEplot] ([diff(x(t), t) = 2*x(t)*(1-0.1e-3*x(t))-0.1e-1*x(t)*y(t), diff(y(t), t) = -.5*y(t)+0.1e-3*x(t)*y(t)], [x(t), y(t)], t=0 .. 10, x = 0 .. 11500, y = 0 .. 200, [[x(0) = 1000, y(0) = 200...

For example, i have the field x*ex+y*ey. Is there a command for transforming it into the same field with polar coordinates and polar unit vectors?

How to draw slope field associated to differential equation: dy/dt = sin(ty) on Maple software?

It's possible to define a field in Maple 15 with 2 kinds of indices, say type spacetime μ,ν,ρ... and one of the type integer, i,j,k varying from 1 to n?


I would like to define a field like Aμi where:





and so on.  


Thank you Washington Inacio

Hi everybody,

How can i plot a vector field and an animated curve on the same plotting window ?



I want to write this down in the maple:

V is a vector field namely(in cartesian coordinates) V:=VectorField(<u(x,y,z),v(x,y,z),w(x,y,z)>)

Now I want to make a vector like this:


which if write into components will be:

u*(diff(u, x))+v*(diff(u, y))+w*(diff(u, z))

I am working with two multivariate functions A and B, with coefficients over a finite field. The x-degree of A is greater than or equal to B, which is greater than or equal to 1, and thus I want to find q and r such that:

A = q*B + r, where q, r are elements of K(y,z)[x], where K is my finite field. Obviously, I would like the x-degree of r to be less than that of B, and r not equal to 0.

My problem is this: the Rem and Quo commands, which will deal with my...


I am missing two options in the "fieldplot3d" command, which I am using in cylindrical coordinates: one is "style=contour" and the other is "axes=cylindrical" where apparently only the "axes=boxed" option as available.
Any ideas how I can get this?

Or can I show a polar plane at one end of the cylinder? like in the post:

this is my plot:


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