## Difficult with Lambert W in implicitplot...

I'm trying plot  with implicitplot a expresion which involve Lambert W, but the result is very confuse, is it normal? Could i improve the result?, how?. Thank!

## run code for plot the region...

can anyone run my code?
please do it and send it for me.
thanks.

restart;
with(plottools): with(LinearAlgebra): with(plots):
ode := assuming([diff(Y(X), $(X, 2))+2*alpha*(diff(Y(X), X))+beta^2*Y(X) = 0], [alpha >= 0, beta >= 0, alpha+beta > 0]): F := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), $(X, 2)) = yz}, ode), yz), x, y, yp):
Fp := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), $(X, 2)) = yz, diff(Y(X), $(X, 3)) = yt}, diff(ode, X)), yt), x, y, yp, yz):
Ni := seq(i, i = 0 .. 9), 15, 20:
for ni in Ni do
print(ni);
st := time[real]();
f[0, ni] := F(x[0], y[0, ni], yp[0, ni]);
fp[0, ni] := Fp(x[0], y[0, ni], yp[0, ni], f[0, ni]);
f[1, ni] := F(x[1], y[1, ni], yp[1, ni]);
fp[1, ni] := Fp(x[1], y[1, ni], yp[1, ni], f[1, ni]);
y[2, 0] := y[0, ni]+2*h*yp[0, ni]+(6/5)*f[0, ni]*h^2+(4/15)*fp[0, ni]*h^3+(4/5)*f[1, ni]*h^2+(4/15)*fp[1, ni]*h^3;
yp[2, 0] := yp[0, ni]+2*f[0, ni]*h+(2/3)*fp[0, ni]*h^2+(4/3)*fp[1, ni]*h^2;
for j to ni do
f[2, j-1] := F(x[2], y[2, j-1], yp[2, j-1]);
fp[2, j-1] := Fp(x[2], y[2, j-1], yp[2, j-1], f[2, j-1]);
y[2, j] := y[1, ni]+h*yp[1, ni]+(7/20)*f[1, ni]*h^2+(1/20)*fp[1, ni]*h^3+(3/20)*f[2, j-1]*h^2-(1/30)*fp[2, j-1]*h^3;
yp[2, j] := yp[1, ni]+(1/2)*f[1, ni]*h+(1/12)*fp[1, ni]*h^2+(1/2)*f[2, j-1]*h-(1/12)*fp[2, j-1]*h^2;
end do:
Ms := Matrix(4, 4); Ms[1, 3] := 1; Ms[2, 4] := 1;
y[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(y[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[3, 1] := coeff(y[2, ni], y[0, ni]);
Ms[3, 2] := coeff(y[2, ni], yp[0, ni])/h;
Ms[3, 3] := coeff(y[2, ni], y[1, ni]);
Ms[3, 4] := coeff(y[2, ni], yp[1, ni])/h;
hyp[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(h*yp[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[4, 1] := coeff(hyp[2, ni], y[0, ni]);
Ms[4, 2] := coeff(hyp[2, ni], yp[0, ni])/h;
Ms[4, 3] := coeff(hyp[2, ni], y[1, ni]);
Ms[4, 4] := coeff(hyp[2, ni], yp[1, ni])/h;
sol := Eigenvalues(Ms);
print(time[real]()-st);
st := time[real]();
SR[ni, 1] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = 0 .. 3, H2 = 0 .. 3, filledregions, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
SR[ni, 2] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = -2 .. 3, H2 = -2 .. 3, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
print(time[real]()-st);
end do;
for i in Ni do
i;
display({SR[i, 1], SR[i, 2], line([-1, 0], [3, 0], color = red, linestyle = dash), line([0, -3], [0, 3], color = red, linestyle = dash)});
end do;
display({seq(SR[i, 2], i = 0 .. Ni)});

## plot ((1/2)*x*tan(log((1/5)*(2*(x^2+y^2)))) = y...

I want to plot the following equation

((1/2)*x*tan(log((1/5)*(2*(x^2+y^2)))) = y

I tried:

with(plots, implicitplot)

implicitplot((1/2)*x*tan(log((1/5)*(2*(x^2+y^2)))) = y, x = -5 .. 5, y =-5..5, numpoints = 1000, gridrefine = 6, color = red)

but result is strange...

## Bug in implicitplot

Maple

The command

plots:-implicitplot(evalc(argument((1+x+I*y)/(1-x-I*y))) <= (1/4)*Pi, x = -5 .. 5, y = -5 .. 5, crossingrefine = 1, gridrefine = 2, rational = true, filled, signchange = true, resolution = 1000);


produces an incorrect result

in view of

evalf(argument((1-4+4*I)/(1+4-4*I)));
2.889038378


There is a workaround

plots:-inequal(evalc(argument((1+x+I*y)/(1-x-I*y))) <= (1/4)*Pi, x = -5 .. 5, y = -5 .. 5);

## Bug in implicitplot

Maple

The following three commands

plots:-implicitplot(3*cos(x) = tan(y)^3, x = -Pi .. Pi, y = -(1/2)*Pi-1 .. (1/2)*Pi+1, thickness = 3, crossingrefine = 1, rational = true, signchange = true, resolution = 1000, gridrefine = 2);
plots:-implicitplot(3*cos(x) = tan(y)^3, x = -Pi .. Pi, y = -(1/2)*Pi-1 .. (1/2)*Pi+1, thickness = 3, crossingrefine = 1, rational = true, signchange = false, resolution = 1000, gridrefine = 2);
plots:-implicitplot(3*cos(x) = tan(y)^3, x = -Pi .. Pi, y = -(1/2)*Pi-1 .. (1/2)*Pi+1, thickness = 3, crossingrefine = 1, rational = true, resolution = 1000, gridrefine = 2);

produce the same incorrect plot

It is clear the sraight lines given by y=Pi/2 and y=-Pi/2 are superfluous. It should be noticed that the Mmma's ContourPlot command without any options produces a correct plot.

## Displaying the list of coordinates in plot...

Is there a way to display the list of coordinates for implicitplot and plot, rather than the displaying image itself?

In Maple Classic this happens automatically when the assignment operator is used  ( := ) together with a semi-colon, eg.   A:=implicitplot(F, x=-1..1, y=-1..1);

But is there a way to do this in the non-classic version?  Thanks very much.

- Graham

## Intersection of two implicit plots...

hello

i have some implicit plot that i want intersect between them.

for example:

implicitplot(x^2+y^2<1,x=-3..3,y=-3..3);
implicitplot((x-1)^2+y^2<1,x=-3..3,y=-3..3);

how can i do intersect between them!?

thanks for guidance

## Surface with discontinuity ...

Hello,

So I want to create an image of the cusp catastrophe that looks like this

but instead I have been getting this image where the discontinuity is plotted out to infinity

I have tried to split up the surfaces on either side of this but I haven't been able to display both on the same plot whilst using implicitplot3d.
This is the line of code for the image, there't not much too it
"
with(plots);

implicitplot3d(x^4+x^2*z+x*y, x = -7 .. 7, y = -50 .. 50, z = -10 .. 5, axes = boxed, style = surfacecontour, grid = [60, 60, 60], orientation = [180, 8, 175], 'transparency' = .1);
"
If anyone could help or point me in the right direction that would be great.
Cheers,
Darryl A.M.

## Quality of implicit plot...

Hi,

I am trying to solve an equation and plot it as an implicit plot, I would like to increase the number of points in the plot calculation but it seems that there is a limit for it, I chose 10^8 and for a bigger values I get an memorry error from Maple. Is there anyway I can solve this problem?

This is just for an example:

implicitplot(subs({values = ...}), function), for a given values, numpoints=10^8)

Regards,

Baharm31

## how to plot this function?...

plots:-implicitplot((-2.0)^x-y,x=-sqrt(2)..-exp(-1),y=-1.5..1.5);

I tried surd, but there is a limitation (integer order).

## How to combine Greek letters and math in labels?...

Hi,

I am trying to use implicit plot. The plot is OK but I want to put labels such as what Latex produces :

$\frac{\Omega}{\omega_n}$ for x axis and $a_0 \mathrm{(m)}$ for y axis

How can I apply this in my maple code as below:

plot1:=implicitplot(a3, Omega_r=1.5..2.5, a=0.00000001..0.1, labeldirections=[horizontal, horizontal], axes=boxed, labels=["W/w_n",typeset("a_0 (m)")], labelfont=[SYMBOL]):

What I have put as bold does not work for me, it is making everything in Greek :) . I want combination of Greek and math.

Thasnks,

Bahareh

## use of implicit plot...

I have written the code below, and received the error message in the bottom. Can any body help me?

> with(plots);

> u := 100*sin((1/2)*pi*x)*((1-cosh(pi))*sinh((1/2)*pi*y)+sinh(pi)*cosh((1/2)*pi*y))/sin(pi);

> implicitplot({u = 10, u = 20, u = 30, u = 40, u = 50, u = 60, u = 70, u = 80, u = 90}, x = 0 .. 2, y = 0 .. 2, grid = [100, 100]);

Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {pi}
>

## something wrong with implicitplot?...

code:

restart;
convert([92*x/790+18*x*(1-y)/1000=0.125,ln(46.59/x)=1/1.5*(ln(0.553/y)+2.5*ln((1-y)/(1-0.553)))],rational);
fsolve(%);
plots:-implicitplot(%%,x=0..2,y=0..1,numpoints=1000,thickness=2,gridlines,color=[blue,red]);

question:

there is something missing with the red line. I can't find the intersect point on the figure.

Is there something wrong with implicitplot?

## implicit differentiation ...

I've got a function y(x) that is initially defined as x^3+y^3=1 and need to plot it, and find y',y''.

At present, I've used implicitplot(x^3+y^3=1,x=0..5,y=0..5) to plot it, but that doesnt seem to work. Also, to find y'

I've used the statement

implicitdiff(g(x,y),y(x),x) where g:=(x,y)->x^3+y^3=1 but this gives me an error that my input is invalid; y(x) is expected to be of the form {(name, set(name), set(function(name))}.

I don't quite understand..