I need some sugestions how to expand terms raised to some exponent within an expression. How to simplify,How to collect terms with some conmon factor within the same expression relativistic_11.mw

Dear All,

I have an implicit function f(x,y) in terms of special functions. I need to optimize it.  So  I plotted it and found the location of the zero slope. However I cannot get the precise value of x and y, where the slope equals  zero.

Is there any better option to get the location of x and y, where the slope is zero?

Thanks in advance.

hard code in this way is quite complex, how to do without hard code

after i get G which is an array for below, 

Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4],a*G[5],a*G[6],a*G[7],a*G[8],a*G[9],a*G[10],a*G[11],a*G[12],a*G[13],a*G[14], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,r,u,v,w));

Does anyone here uses SemiAlgebraic or CylindricalAlgebraicDecompose commands often?

The following error (see file below) was not caused by a typo (with smaller polynomials, I do not get them). The system of polynomial inequalities is generated by a code so again there are no typos. Would any one know what this error means? Maple website has no information on it.

the goal is to check kernel belong to image in Maple

restart;
with(Groebner):
K := {r-x^4,u-(x^3)*y,v-x*y^3,w-y^4};
G := Basis(K, 'tord', degrevlex(r,u,v,w));
R1 := eliminate(G, {r,u,v,w}); # eliminate is the reverse of Basis
Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4],a*G[5],a*G[6],a*G[7],a*G[8],a*G[9],a*G[10],a*G[11],a*G[12],a*G[13],a*G[14], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,r,u,v,w));
Ga := remove(has, Ga, [x,y,a]);

am using this command in end of my code 

> Points := [seq(seq([x[i], y[j], U[i, j]], i = 0 .. M-1), j = 0 .. N)];
> Points1 := subs({BC, XY, op(SOL)}, Points);
> pointplot3d(Points1, symbol = solidsphere, labels = [x, y, U], shading = zhue, orientation = [50, 70], axes = boxed);

but at last line am getting error

Error, (in plots/pointplot) incorrect first argument
 

restart:
> Digits:=30:
> with(linalg):
>
> h[0]:=0.156;:
> d:=0.32*h[0]:
> l:=4:
> h[1]:=h[0]-d:
> h[2]:=h[0]+d:
> g:=9.8:
> Term:=12:
> Num:=3:
> n:=4:
>
> for N from 1 to Num do
> lambda:=2*n*Pi/l:## N1 wei sha ba tiao shu
> epsilon:=evalf(0.5+2*(N-1)/(Num-1)):
> k[0]:=evalf(0.5*Pi+2*(N-1)*Pi/(Num-1)):
> tau[0]:=evalf(k[0]*h[0]):
> omega:=evalf((g*k[0]*tanh(k[0]*h[0]))^(1/2)):

An implicitplot3d of an f(x,y,z)=0 results in an ISOSURFACE structure containing the samples of a function taken over a regular grid in 3-D space and is rendered as a 3-D surface approximating the zero surface of the function.
When I select the points with values of f(x,y,z) "close" to zero, I only get a few points on the surface:

restart;
q := plots:-implicitplot3d( x^2+y^3+z^4=1 ,x=-1..1,y=-1..1,z=-1..1, 
    style=wireframe, color=black ):
pdata := plottools:-getdata(q); # doesn't work...

Hi! Any help would be greatly appreciated :)

I have two matrices S and R, where 

S :=

Matrix([[a_1, a_2, a_3, a_4], [b_1, b_2, b_3, b_4], [c_1, c_2, c_3, c_4], [d_1, d_2, d_3, d_4]]);

such that 

a_1*d_1 = b_1*c_1
a_2*d_2 = b_2*c_2
a_3*d_3 = b_3*c_3
a_4*d_4 = b_4*c_4;

and 

R :=

Matrix([[s_1, t_1, r_1, l_1], [s_2, t_2, r_2, l_2], [s_3, t_3, r_3, l_3], [s_4, t_4, r_4, l_4]]);

Hey, I have a system of ODE and I can't draw it's phase curve. I tried to use DEplot and phaseportrait, but it doesn't work. Here is my system:

 dx/dt=x

dy/dt=ky              (k is a constant)

Here is my piece of code:

DE := [diff(x(t), t) = x(t)];

DF := [diff(y(t), t) = k*y(t)];

with(DEtools);

phaseportrait([DE, DF], [y, x], t = -5 .. 5, y = -5 .. 5, x = -5 .. 5, k...

Greetings

It occured to me to try to animate this spiral.

I found some code on the interweb. but when you run the animation, only one triangle appears, to be replaced by another. how to get them to stay?

Spiral_of_Theodoru.mw

Hey, I'm trying to plot the phase curve of the simple system of ODE, BUT it shows me an error which one I don't understand at all :)

Here is my code:

DE := diff(x(t), t) = x(t);
DF := diff(y(t), t) = k*y(t);
with(DEtools);
phaseportrait([DE, D], [y, x], t = -5 .. 5, [[y(0) = 1, x(0)], [y(0) = 0, x(0) = 2], [y(0) = 0, z(0) = -2]], y = -5 .. 5, x = -5 .. 5, color = black, linecolor = red);

Error, (in DEtools/phaseportrait) invalid initial...

Hi! Any help would be greatly appreciated :)

I have two matrices S and R, where 

S := Matrix( [ [a_1, a_2, a_3, a_4], [b_1, b_2, b_3, b_4], [c_1, c_2, c_3, c_4], [d_1, d_2, d_3, d_4] ] );

such that 

a_1*d_1 = b_1*c_1
a_2*d_2 = b_2*c_2
a_3*d_3 = b_3*c_3
a_4*d_4 = b_4*c_4;

and 

R := Matrix( [ [s_1, t_1, r_1, l_1], [s_2, t_2, r_2, l_2], [s_3, t_3, r_3, l_3], [s_4, t_4, r_4, l_4] ] );

such that 

I am trying to get Maple to calculate for me.. Let X and Y have a trinomial distribution with parameters n=3, p1=1/6 and p2=1/2. I am supposed to find E(X), E(Y), Var(X), Var(Y) and Cov (X,Y). Thank you to anyone who can assist with this. And if  you can help me understand the concept behind it.. Im having some troubles with bivariate distributions in my Stats course :( Thanks!