MaplePrimes Questions

with(plots);
P1 := plot([-sin(t), t, t = 0 .. 2*Pi], coords = polar, color = red);
P2 := plot([cos(t), t, t = 0 .. 2*Pi], coords = polar, color = blue);
display(P1, P2, scaling = constrained);

I have two polar equation in the same graph but how do i shade the region between those two polar curve?

how to replace some part in a formula ?...

s1 := RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S)

s2 := -(D1*RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S)*D6-S*D6+RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))/(D2*D6*RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))
algsubs(s = RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S), s2)

I try to use s1 to represent s2, and I get the following result:

-(D1*__SELECTION(RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))*D6-S*D6+RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))/(D2*D6*RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))
what is mean of __SELECTION, If algsubs cannot work well, what should I do?

How can I load a .m file with the big green arrow ...

Hi,
How can I load a .m file with the big green arrow ?

TIA

Does printf have an issue with rand?...

If I execute a program like:

restart;
pathname := "C:\\Users\\Gregory McColm\\Desktop\\Scratch2";
filename := "WhatGives6.txt";
stream := cat(pathname, "\\", filename);
Y := seq(rand(1..10)(), j = 1..10);
writeto(stream);
for i from 1 to 10 do
printf("X[ %d ]:= %d;\n", i, Y[i]);
end do;
writeto(terminal);
printf("DONE\n");

Maple will print exactly what I told it to print.  But when I enter

restart;
pathname := "C:\\Users\\Gregory McColm\\Desktop\\Scratch2";
filename := "WhatGives44.txt";
stream := cat(pathname, "\\", filename);
writeto(stream);
for i from 1 to 10 do
Y := rand(1..10)();
printf("X[ %d ]:= %d;\n", i, Y);
end do;
writeto(terminal);
printf("DONE\n");

Maple prints:

YAssign7, [Typesetting:-mprintslash([Y := 7], [7])]

X[ 1 ]:= 7;
YAssign10, [Typesetting:-mprintslash([Y := 10], [10])]

X[ 2 ]:= 10;
YAssign6, [Typesetting:-mprintslash([Y := 6], [6])]

X[ 3 ]:= 6;
YAssign2, [Typesetting:-mprintslash([Y := 2], [2])]

X[ 4 ]:= 2;
YAssign4, [Typesetting:-mprintslash([Y := 4], [4])]

X[ 5 ]:= 4;
YAssign6, [Typesetting:-mprintslash([Y := 6], [6])]

X[ 6 ]:= 6;
YAssign5, [Typesetting:-mprintslash([Y := 5], [5])]

X[ 7 ]:= 5;
YAssign1, [Typesetting:-mprintslash([Y := 1], [1])]

X[ 8 ]:= 1;
YAssign8, [Typesetting:-mprintslash([Y := 8], [8])]

X[ 9 ]:= 8;
YAssign5, [Typesetting:-mprintslash([Y := 5], [5])]

X[ 10 ]:= 5;

This must be more than a matter of calling rand when I am writing to terminal, for if I enter:

restart;
pathname := "C:\\Users\\Gregory McColm\\Desktop\\Scratch2";
filename := "WhatGives8.txt";
stream := cat(pathname, "\\", filename);
writeto(stream);
X := rand(0..1)():
writeto(terminal);
printf("DONE\n");

then all Maple prints is "Mary is a little lamb".  I have tried this on Maple 2018 and Maple 2019, with the same results.

Any ideas or suggestions?

How to fix unexpected animation options, and bette...

Hi,

I'm having trouble converting a static plot to animated plot:

Also I've been considering using functional operators instead of expressions so that there's no reuse of variable s when drawing different curves, though I'm not sure if this will be harder to differentiate since diff(expr, s) does not work on a functional operator meaning I'd have to do unapply(diff(f(s),s),s) which seems a long route and I'm not sure if it's what I'm looking for (in terms of simplification).

Thanks guys

agentpath.mw

Why are different solutions of same equatio...

Hello everyone!

I want to find all solutions of  following equations :

I used Maple 2019:

solutions:=solve([abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1=0],[lambda]);
evalf(solutions)

The output is:

So we have two solutions. But when I use Matlab 2018,
four solutions are returned.

syms lambda
eqn =abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1==0;
solx1=solve(eqn, lambda)
%%
solx1 =
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 1)
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 2)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 3)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 4)

solx3=solve(eqn, lambda,   'MaxDegree', 4)
double(solx3)
%%The solution is:
-4.2681 + 0.0000i
0.0000 + 0.0000i
5.1340 -11.2012i
5.1340
+ 11.2012i

It is easy to check that  first two in Maple and Matlab are  same.

Who is right? Does Maple miss complex solutions?

How do I get CPU time on Maple Worksheet...

Dear,

I need to attach CPU time to my iterations/Computations, please how do I obtain that in Maple. I tried

a:=time ()

Iterations code

cputime:=time() -a;

But the issue is that once I rerun the code, It produces different cpu time, kindly help me out here.

Thank you.

how do I find the limit with integral. ...

First make sure that  and  are unassigned variables and then enter the Maple command

This tells Maple that  is a postive real number.  (You will see more on using "assume" later.)

Next, calculate the improper definite integral of

(8sin(x)+11cos(x))e^(−52cx)

for  from 0 to ∞ and assign this to the variable .  (Notice that Maple displays  as  to indicate it that an assumption has been made about .)

Finally calculate the limit of  times  as  tends to infinity and enter the limit in the box below.  (Enter your answer exactly using Maple syntax, not as a decimal.)

How I could do those questions? its deadline is n...

1 discuss and show graphically the effects of decrease in wage on labor supply. if A, leisure is normal good. B, if leisure is inferior good.

animate cylinder width during animate...

How do I animate the cylinder width, or some variation of it as we trace it's path in the z-axes

with(plots);
with(plottools);
display([seq(cylinder([2, 2, 2], 3, i/10, capped = false), i = 1 .. 60)], insequence);

How to fix arctan sign, and solve tricky parametri...

Hi,

I'm trying to create an agent vehicle which drives along a path of a uniform width, and finds the distance to the edge of the path directly ahead of it. Like this:

The aim is to somewhat simulate how far the agent can see down the road.

Since the thickness of a plot curve is unrelated to the units of the axis, and has no means of interacting with objects this would be no use.

I also considered shadebetween function, however this only can shade between the y values of 2 functions, so for a vertical curve it cannot produce any width to the path.

I then realised using parametric equations of form (x(t), y(t)) would likely make most sense and wrote some code which roughly gets the boundarys at a fixed distance from the centre path equation, by adding the x-y components of the reciprocal of the gradient:

For certain simple path equations such as this one, it roughly works other than the areas between which the boundary curves overlap themselves (I would need to find these points of intersection and break the curves up to remove these squigly inner bits). Any advice on this would be much appreciated cause this seems like it will be tricky, if not computationally heavy.

More annoyingly, due to the nature of the trig functions involved, for more complex graphs which include a vertical turning point, the left and right boundaries seem to swap over:

and

Clearly this is not the behaviour I had in mind.. and I'm not sure what I can do to fix it, I think maybe using piecewise trig may be a potential solution to avoid the jumping from + to -, though I'm not sure where I would put these breakpoints (I've tried just using abs(arctan(...)) with no luck).

If anyone could help wih this that would be really appreciated, or even suggest a better approach to this problem!

Thanks

[code] agentpath.mw

Should one install Physics package on new Maple 20...

I just updated to Maple 2020

interface(version)

Standard Worksheet Interface, Maple 2020.0, Windows 10, March 4
2020 Build ID 1455132

Physics:-Version()
The "Physics Updates" package is not installed

My question is: For new Maple 2020 installation, should one go and install latest Physics package from the cloud, which I see is at version 619 now, or is it allready included in the new Maple 2020?

export data of 3d plot...

Help me to export data of 3d plot

Problem with BinarySearch sintax...

Dear,

I have a list, say, L:= [2,3,4,5];

and I need to find the position of several of its elements. However, when a apply the BinarySearch command I get a wrong return. For example, element >= 5:  BinarySearch(L, 5, `>=`);

Maple returns 0

Element = 4: BinarySearch(L, 4, `=`);

Maple returns 0

Element < 3: BinarySearch(L, 3, `<`);

Maple returns 2.

Obviusly, I'm doing something wrong. Could you please tell me what it is?