## Unexpected RootOf result, would like help with sol...

I am not sure why I am getting this RootOf result when I solve for x.

Here is my code.

restart:
eq:=4*x^2+2*y(x)^2=32.5625:
deq:=solve(  diff(eq,x), diff(y(x),x) ):
deq=3;
y(x)=solve(deq=3,y(x));
x=solve(deq=3,x);

The last equation we are solving is  -2x / y = 3.
So we should get y  = -2/3 x and  x = -3/2 y.

The Maple software correctly solves for y in terms of x,
but gives an odd Rootof answer when solving for x. Why is that?

I am not sure how to intepret RootOf(2*_Z+3*y(_Z)).

## Speed up evalf on integal of weighted sum of Beta ...

Dear All,

I have two beta distributed r.v. as:

my Maple stucks when i try to calculate numerically:

evalf(int(z*PDF(0.3*p1+0.7*p2, z), z = 0 .. 1))

Any help to speed this up or other solutions?

It seems PDF(0.3*p1+0.7*p2, z) is the pain.

Thanks!

## How do I ignore terms containing certain combinati...

I need to simplify a differential equation by ignoring higher order terms. The terms are of the following form:

180.495*theta_dot*beta_dot*zeta_dot*psi_dot*sin(beta)*cos(delta__3)*sin(delta__3)^3*zeta_dot*cos(zeta)*zeta*beta*sin(psi)*p

Here beta, zeta and theta are hinge deflections for a helicopter blade and thus can be assumed to be small. Everything other than delta__3 is a function of time, _dot represents a derivative wrt time. Higher order terms, such as those containing betan, zetan, thetan where n > 1, and terms containing combinations of the hinge deflections, i.e. betaj.zetak, betaj.thetak or zetaj.thetak where j,k >= 1 need to be neglected. Since beta, zeta and theta are functions of time, and the equation contains derivatives, maple functions like 'degree' and 'match' don't seem to work. Also, the solution suggested over here does not seem to be suitable for this problem, since my equation is very long (~70 pages) and the various derivatives appearing in it are not known.

## Would like help with op/nops in a function...

Hi. I wrote a command for finding second derivative.

#secondderiv test of f(x,y)
f:=x^2+2*x*y+2*y^3:
H:=hessian(f,[x,y]);
seq([subs(soln[k],eval(H)),det(subs(soln[k],eval(H)))],k=1..nops(op(soln)))

Everything runs fine ... except if I change the function f to
f:=x^2+2*x*y+2*y^2
Then I get error :
Error, invalid input: nops expects 1 argument, but received 2

I sort of understand the error, when there is a single solution
{x=0,y=0} , then the op removes the parentheses to get x=0, y=0
which is now two arguments, and nops requires one argument.
I tried to use  nops(op({soln} ) , but that is not the correct approach
since it overcounts. Also it throws an error if change back f to the original expression.

## Decrypt message...

f(a)(x) = a*x mod 256  for all x in Z[256]

## Christoffel symbols and Ricci tensor and scalar....

I am a little bit clueless here, about how to use maple to calculate Christoffel symbol and Ricci tensor and scalar?

I read the help, but it got me confused; I have the metric ds^2 = du*dv+F(y,z)du^2+dy^2+dz^2

It's not Minkowski nor Cartesian, so how to use maple to calculate these symbols?

I am sure it's easy, but I didn't quite follow maple's instructions.

## Plotting the free space diagram (Fréchet distance)...

Hello!

I am interested in plot the so-called "free space diagram", please see https://en.wikipedia.org/wiki/Fr%C3%A9chet_distance for a formal definition. Essentially, given two curves (i.e., two polygonal from [0,1] to the plane) the "free space" is the points (s,t) in the square [0,1]x[0,1] such that the distance from P(s) to Q(t) (if P and Q are the parametrizations of the curves) is less or equal than a prefixed epsilon>0. An image can be the following (the free space is, in the image, the area not colored in black):

Thanks!

## One-Liner Crashes Maple 2017...

In Maple 2017, a simple one-liner can crash the current worksheet (in any mode with any text type it seems).

z[x]:=z

z[x]:=z(x)

Note that z and x can be any two letters, and that you can replace z[x] with the equivalent z+(ctrl shift _)+x (which displays as zx)

## Decomposition fields of polynomials and generator ...

Hi all. I have two questions about polynomials over Q.

i) Let f,g be polynomials over Q. How to show (with Maple) that the decomposition field of f is included in the decomposition field of g?

ii) Let f be a polynomial of degree n  over Q with Galois group C_n, the cyclic group of order n. Then, there is a polynomial P with coefficients in Q, of degree n-1, s.t. the iteration: u0=some root of f, u_{k+1}=P(u_k) gives all the roots of f; how to find P (with Maple)?

## plotting x+2y=3. Just 10 points...

How do I plot just 10 points of the equation?

I got ..

with(plots):
a := x+2*y = 3;
implicitplot(a, x = -5 .. 5, y = -5 .. 5, style = point);

but I only need 10 points. How do I do that? Thank you

## Loop appearing before else in an if statement - se...

Does anyone know why the following gives an error of invalid loop statement termination?

if true then
for i from 1 to 2 do
end do
else
end if

while putting a semicolon after `end do' fixes it.

This seems to only occur in if else statements, when end do appears directly before the else

## Double integration and summation. How to speed up?...

Hello.

Regarding to my previous question I'd like to speed up calculations of the expression.

```restart;
tt := -0.689609e-3; T_c := .242731; mu := .365908; k := 1;
R1 := a*tanh((a^2-mu)/(2*T_c))*ln((2*a^2+2*a*q+q^2-2*mu-(I*2)*Pi*N)/(2*a^2-2*a*q+q^2-2*mu-(I*2)*Pi*N))/q-2;
R2 := Int(R1, a = 0 .. 10000);
R3 := q*ln((-q^2-k^2+mu+I*(2*N*Pi*T_c-(2*m+1)*Pi*T_c)+k*q)/(-q^2-k^2+mu+I*(2*N*Pi*T_c-(2*m+1)*Pi*T_c)-k*q))/(k*(tt+R2));
R4 := Sum(R3, N = -100 .. 100);
m := 1;
R5 := Int(R4, q = 0.1e-2 .. 10000);
R6 := evalf(R5);```

Here I have integration procedure inside the expression R3, then the summation over the integer parameter N and then finally the integration again.

Is it possible to speed up calculations of this cumbersome expression? Or actually was I correct to write this simple code?