## Using fieldplot for function over a domain...

Dears,  I have a questian about the fieldplot.

I use the following

with(plots):

fieldplot([x^2+y^2, 3*sin(x)-y^2], x = -1 .. 1, y = -1 .. 1, arrows = SLIM, color = x) ;

The domain is bounded from x = -1 .. 1, y = -1 .. 1.

Now, I want to use the same order to plot this function over a pentagon definde as

with(plots):

Q11R := plottools[polygon]([[0, -1], [3/4, -1], [1, 0], [3/4, 1], [0, 1]], style = line, thickness = 3);

plots[display](Q11R, size = [.3, .5]).

I hope that I can find help.

Amr

## Solving Matrix ODEs numerically with Variable Coe...

I have a coupled pair of anharmonic oscillators and need to calculate the stability matrix and find the lyaupanov exponent for how the nearby trajectories diverge. In particular, I have the Hamiltonian

H = (p1^2+p2^2 + q1^4+q2^4 + 12*q1^2*q2^2 )/2

and I need to compute the matrix M given by

dM/dt = J*Hess*M

where J := Matrix(4,4,[0,0,1,0,  0,0,0,1,  -1,0,0,0,  0,-1,0,0]), and the Hessian takes the form:

Matrix(4,4, [6*q1_12(t)^2 + 12*Q2_12(t)^2, 2*12*Q1_12(t)*Q2_12(t),0,0,   2*12*Q1_12(t)*Q2_12(t), 6*Q2_12(t)^2 + 12*q1_12(t)^2,0,0,    0,0,1,0,    0,0,0,1])

The solver finds the trajectories of p1,p2,q1,q2 fine, but I don't seem to find a way to incorporate their solutions as inputs to reevaluate the Hessian at each time step. I read through https://www.maplesoft.com/support/help/Maple/view.aspx?path=DEtools%2fmatrixDE and the dsolve since I'm trying to do this numerically.

I thought I could get around this just by resolving the trajectories, but it's spitting out an error that arrays must be initialized with lists.

The actual code is here: AMO_HW4.mw

Sorry, I still need to clean it up a bit. Any help would be appreciated. I need to calculate M(t), then calculate the matrix norm and find the exponent.

## array with parallelogram...

How do i plot

in one plot with this paraellogram (it has to come out of the center of it)

## Strange Evaluation of Explore in Collapsed Sectio...

test_sections.mw

Hi, I'm getting some unusual behaviour between the Explore() command / graphs and collapsed sections, as exemplified in the attached (linked) worksheet.  I'm trying to develop some worksheets with several sections where some of the sections have an explore() graph in them.  To keep things simple, I'd like some sections to be collapsed with the graphs hidden (and remain collapsed: View - Section - Autoexpanding - Uncheck) when the worksheet is evaluated.  In the attached, the section remains collapsed, so does the normal graph, but the explore "graph" gets published outside the collapsed section and when there is other information on the worksheet, the explore window appears almost randomly.

So is there any way to ensure the explore graph remains inside the collapsed section?

Sorry for the slightly longwinded explanation :-)

Thanks,

## Newbie that can't even maximize a quadratic needs ...

So I needed a CAS, and I spent a couple of months trying to get a basic understanding of SymPy and various applications starting with "M". We have Maple version 2016.

My "prototype problem" can be solved by hand, and is a system of quadratic Bellman equations, for i=1,2.  I'll return to it below, as I am obviously too clumsy to get even the second-to-simplest max/min working.  Oh, and I can't even insert Maple Math here in the forum, it does not like maximize or minimize.

Let's start easy. I enter
maximize((b-x)x,x)
which works as I expect. Then already at
maximize((abs(b)-x)x,x>=0)
I am stuck. Please, sweet Maple, you know that the answer is the same as before, don't you? (In the meantime I have tried to feed it maximize((b-x)x,x=0..1)... )

I was hoping my "proper" problem should be doable. What I really need is a sequence of quadratic optimization problems, where I have a vector x maximizing b'x-x'Ax subject to linear constraints, so it should not be too hard.  The "prototype problem" I needed for starters, is a system where for i=1,2 I have

v_i(0,y)=0 and inductively v_i(t+1,y)=max{x_i*(b_i-x_1-x_2)+ r_i v_i(t,y-x)}

where b_i and r_i are constants, x=(x_1,x_2), y=(y_1,y_2), and everything is nonnegative - including, the choice variables x_i must be between 0 and min{y_i, b_i-x_1-x_2}. And I want to plot both functions and the x with time as a slider, but ... I don't think I'll ever get that far?

Sorry for whining. (I know why I dropped out of computer science.)

## How to plot the roots of two complex polynomials i...

This is my first post here, and any help is really appreciated.

I have two complex polynomials

f(w)= w^8+w^6+4*w^4+w^2+1 , and

g(w)= w^16+2*w^14+9*w^12-2*w^10+44*w^8-2*w^6+9*w^4+2*w^2+1 .

I want to plot the roots of f in blue, roots of g in red and a unit circle in black at the same picture.

## Solid between planes in Maple?...

Good day, I have an assignment in which I'm required to plot the solid that results from the cone (x^2+y^2-z^2=0), limited by the planes z=0 and x+2z=3. So far I've been trying to use plot3d and implicitplot3d, to no avail: the parametric expression from plot3d returns something quite different from the intented, and implicitplot3d won't allow the use of variable parameters.

Any ideas on how to solve this?

## acximetric tolerance...

Hi everyone.    How i can introduce an acximetric tolerance?. For example +10/-5. Thanks!

## How can only unconditional solutions be obtained f...

This solve command produces both unconditional and conditional solutions.

Is there a way to have it only output unconditional solutions, or, failing that, is there a way to select the unconditional solutions from its output?

solve({2*x+y+z = 3, x^2+y^2+z^2 = 3}, [x, y, z], real, parametric)

## difficulty solving equations over reals...

I would like to solve {x^2+y^2+z^2 = 3, x+y+z = 3} over the reals. Clearly x=1,y=1,z=1 is a solution.

Maple seems to have a hard time with this. I have tried using with(RealDomain) and various commands.

The last solution  is getting closer to the real number answer if i substitute z = 1, but then i get the strange answer { 1=1, x=1,y=1}

I tried using wolfram and it showed me the correct answer.

Rest assured, I am a strong maple fan. I sometimes use wolfram for quick and dirty solutions.

Also is there a way to turn off "with(RealDomain)", switch back to the default domain, without using 'restart'.

## How to display an unevaluated cross product like R...

I am using the LinearAlgebra package to do dynamics between a rotating Cartesian coordinate system and a fixed Cartesian coordinate system. The VectorCalculus package is not what I need.

Since I can't seem to get my test worksheet to paste into this post, I will manually enter an "approximation" to it. I assume that the notation [x, y, z] represents a column vector. I also assume that x represents the cross product operator from the operator pallete.

I just want to get any one of the three ways of doing a vector cross product (see below) to simply display in math notation as R x V. What I get from the three methods below for an unevaluated cross product is "ugly".

Any help or advice will be greatly appreciated.

> restart

> with(LinearAlgebra):

> R := Vector(3, [x, y, z])

R := [x, y, z]

> V := Vector(3, [u, v, w])

V := [u, v, w]

>R x V

[-vz + wy, uz - wx, -uy + vx]

>'R x V'

Typesetting:-delayCrossProduct(R,V)

>CrossProduct(R, V)

[-vz + wy, uz - wx, -uy + vx]

>'CrossProduct(R,V)'

LinearAlgebra:-CrossProduct(R,V)

> R &x V

[-vz + wy, uz - wx, -uy + vx]

'R &x V'

LinearAlgebra:-&x(R,V)

https://www.maplesoft.com/support/help/maple/view.aspx?path=int%2Fdetails

I get a bug when I execute the page.

I copied pasted the last line using 1d math notation to replicate the error.

There is no addition symbol between x^2 + O(x^5)

On the help page I don't see an error.

I uploaded the help file   int-details_(2).mw

## Modifying expression....

Hello people in mapleprimes,

I hope you will help me about modifying an expression.

How can I factor the expression with w and Delta__1 in the attached file?

e2_3 := w^(1-sigma)*((f__11*sigma*Delta__1/L__1)^(-1/(sigma-1))/w)^(k-sigma+1)*k/(Delta__1*(k-sigma+1)*a__0^k);

Modifying_expression_factor.mw

## Can a smooth path of fastest descent be found betw...

The linked worksheet displays the geodesic between two points on a surface z(x,y).

Surfacepath.mw

Gradient descent will find a stepped approximate path of fastest descent between the points, but is there a way to find a function defining an exact i.e. smooth path of fastest descent? If so, how can a precise time of fastest descent be determined?