Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

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. 

Thanks in advance for your help.

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?

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

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)

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'. 

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)

When I download the help document here

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 

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);

Thank you for advance.

Modifying_expression_factor.mw

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?

The following procedure describes the path of a projectile fired from the origin with a launch angle of alpha and a launch velocity of u.

z := proc (x) options operator, arrow; tan(alpha)*x-(1/2)*g*x^2/(u^2*cos(alpha)^2) end proc

The projectile's path must pass through the point [a, h], both values greater than zero.

Can an expression be found for the minimum value of u and its related value for alpha?

Hi, I am currently using the embedded components to make an interface in maple 2016. However, when I executed the startup code, an error was reported, which is 0, "recursive assignment". The recursions are not allowed in the startup code? Anyone can help me with this problem? By the way, how to cancel the warning of executing the startup code when I open the .mw?

Many thanks!

When I launch Maple, I have to activate my license, so I type my purchase code and then I fill the form, but I receive the message "not enough activations left on this account". I used and installed Maple on an old computer and sold it because it was really old, now with my new computer I would like to re-install Maple, is there a way I can use my old activation key, instead of buying Maple again ? 

Hi, there.

I have a program, and I want to make an interface where I can text in the figures and show the results. But I have no idea about this. Anyone can give me some instructions? Thanks!

I am trying to solve a vector calculus problem, find r(t) given:

a(t) = < 4t, sin t, cos(2t) > ,  v(0) = <1,0,0>  , r(0) = <0, 1, 0 >

My approach below seems kind of complicated for such a straightforward problem.  I am trying to do this without copying pasting previous results. Also there might be a recursion issue when i defined v in terms of v(t).

 

 

Question on the ditto operator, labels, and unapply, using three examples.

 

Example 1:

The ditto operator produces no output. Why is that? I presumed that the ditto operator is equivalent to copying pasting the last output.

 

Example 2:

Here the label approach seems to work, but in example three, both the ditto and label approach fails.

 

Example 3:

Someone earlier said that I should use unapply.

Why isn't    " v := x->% " equivalent to "v:=unapply(%,x)"

And why does the label approach fail in the vector calculus example.

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