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!

In Maple 15.01, the commands

   f := x -> sin(2 x)
   h := n -> (1/Pi) int(f(x) sin(n x), x = -Pi .. Pi)
   g := x -> add(h(n) sin(n x), n = 1 .. 4)
   g(x)

result in

   sin(2 x)

which is what I expect.  However, the command

   evalhf(g(2))

results in the error message
   "Error, unable to evaluate function `int` in evalhf"
so evalhf is not being passed sin(4) as I want....

How does one simplify an expression and keep the base number, if it is a perfect square?

If for example I have  (16^j)/16  and I want  16^(j-1)

simplify(%)
                                  (4 j - 4)
             ...

I am new to Maple and trying to use it for a school project. I actually have this section of code written in a textbook and I want to use Maple to solve and plot this predator prey model. Here is what I have, Im not sure why it won't work any help will be geatly apprciated.

> e1 := diff(e(t), t)-0.325e-1*e(t)+.8*e(t)*w(t);
> e2 := diff(w(t), t)+.6*w(t)-0.5e-1*e(t)*w(t);
> sys := {e1, e2};
> ic := {e(0) = 18.0, w(0) = 0.21e-1};
> ivp := `union`(sys, ic);

Hello, I have a problem with plotting graphs with a constant.. I have one system of equations and one another equation:

dx/dt=x(t)

dy/dt=ky(t)

and 

|y|=C|x|^k

I need to compare theit curves.

k and C are constants. I thought it is alright if I would remove constants, BUT there is one in the power, so I have no idea what to do.. 

I just tried to plot the system, but it doesn't work either: