Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi everybody, 

The sequence 
    writeto(MyFile)
    showstat(Myproc)

keeps printing the result on the screen

How is it possible to redirected the output of showstat(Myproc) into a file ?

Thanks in advance

Hello,

I've just started to use Maple 16, and I can't seem to get a neat result, when I use the solve function to solve 4 equations with 4 unknown constants.

I've posted my calculations.

 

How can I get a simpler result? I found a simplification command, but that didn't help

Where I made a mistake I got this error in for loop and how to fix it?


 

restart

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

 

N := 5:

c__1 := Matrix([[c1__11, c1__12, 0], [c1__12, c1__22, 0], [0, 0, c1__66]]):

c__2 := Matrix([[c2__11, c2__12, 0], [c2__12, c2__22, 0], [0, 0, c2__66]]):

c__3 := Matrix([[c3__11, c3__12, 0], [c3__12, c3__22, 0], [0, 0, c3__66]]):

c__4 := Matrix([[c4__11, c4__12, 0], [c4__12, c4__22, 0], [0, 0, c4__66]]):

c__5 := Matrix([[c5__11, c5__12, 0], [c5__12, c5__22, 0], [0, 0, c5__66]]):

NULL

Q := Array(1 .. 3, 1 .. 3, 1 .. N):

A := Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]]):

Z := Matrix([[h__1], [h__2], [h__3], [h__4], [h__5], [h__6]]):

for ii to 3 do for jj to 3 do Q(ii, jj, 1) := c__1(ii, jj); Q(ii, jj, 2) := c__2(ii, jj); Q(ii, jj, 3) := c__3(ii, jj); Q(ii, jj, 4) := c__4(ii, jj); Q(ii, jj, 5) := c__5(ii, jj) end do end do

"for i from 1  to 3 do for j from 1 to 3 do Ar:=0:for k from 1 to N do  Ar:=(Q (i,j,k)*(Z(k+1)-Z(k)))+Ar: end do A(i,j):=Ar: end do end do"

Error, invalid loop statement termination

"for i from 1  to 3 do for j from 1 to 3 do Ar:=0:for k from 1 to N do Ar:=(Q (i,j,k)*(Z(k+1)-Z(k)))+Ar: end do A(i,j):=Ar: end do end do"

 

``

``


 

Download quest.mw

I have a need to calculate base 2 math as would be done in an integrated circuit. Math will be done using 15 bit 2's complement mantissa and 8 bit exponent. (the exponent is always assumed to be negative) We need to perform multiplication and addition, where each internal operation is represented by such a number.

The goal is to best represent the errors associated with such calculations and export the resulting code to a hardware description language for implementation on an integrated circuit.

Is there a package in Maple that can do that? Any advice on how te proceed?

How to do for to built animation Cylinder inscribed in cone?( in optimization problem)

I'm trying to plot the velocity of a ball thrown upwards with air resistance proportional to v^2 and also some simpler forms of this.

But the solution to v^2 returns root of and the plot stops for some specific time value. How can I proceed this plot to let's say 10 sec?

Staffan


 

``

``

restart

``

deq1 := m*(diff(v(t), t)) = -m*g:

``

sol := dsolve({deq1, v(0) = v__0}, v(t))

v(t) = -g*t+v__0

(1)

V := unapply(rhs(sol), t):

``

``

``

deq2 := m*(diff(v2(t), t)) = -m*g-k*v2(t):

``

sol2 := dsolve({deq2, v2(0) = v__0}, v2(t))

v2(t) = -g*m/k+exp(-k*t/m)*(v__0+g*m/k)

(2)

V2 := unapply(rhs(sol2), t):

``

deq3 := m*(diff(v3(t), t)) = -m*g-k*v3(t)*abs(v3(t))

m*(diff(v3(t), t)) = -m*g-k*v3(t)*abs(v3(t))

(3)

sol3 := dsolve({deq3, v3(0) = v__0}, v3(t))

v3(t) = RootOf(t+m*piecewise(_Z <= 0, arctanh(k*_Z/(k*m*g)^(1/2))/(k*m*g)^(1/2), 0 < _Z, arctan(k*_Z/(k*m*g)^(1/2))/(k*m*g)^(1/2))-m*piecewise(v__0 <= 0, arctanh(k*v__0/(k*m*g)^(1/2))/(k*m*g)^(1/2), 0 < v__0, arctan(k*v__0/(k*m*g)^(1/2))/(k*m*g)^(1/2)))

(4)

V3 := unapply(rhs(sol3), t):

``

m := 0.258e-2:

``

plot([V(t), V2(t), V3(t)], t = 0 .. 5, color = [blue, red, black], gridlines = true)

 

``


 

Download tal_3.9_sid_66_b.mw

Dear all,

 

Is there any way to fill the upper region in plot3d?

e.g. if I put the filled option in 

plot3d(y^3+x^2, x = 0 .. 1, y = -1 .. 1, filled)

then the region between the x-y plane and my plot will be filled. What if I want to fill the upper region?

The reason is that I want to show the upper region is acceptable for me, but I couldn't find any other way. 

If you have any solutions for me, I appreciate it.

Hi,

I am a maths teacher and would like to create an ebook for my students with explanations, examples and quizes in the same time. They should be able to access and work through it, even on mobile devices, using the free Maple player. I am new in Maple and don't know if all this is possible. I would like to see some samples of code to learn from and of course, some advice. I would highly apprecaite your support. Thank you.

One of the things I like about Maple, is that I am able to look at most of the source code, and learn from it. But since I am newbie in Maple, sometimes I find it hard to know which next call I need to showstat() in order to see what happens next and follow the code.

Sometimes I do not know how to find the proc() being called in the listing shown by showstat().

For an example, I wanted to see how Maple implements AiryAi(x).

So I did  showstat(`AiryAi`) and I see the listing of AiryAi. The top level of the function. But then I see it calling, which must be some other level of `AiryAi` function? For example, at line 16, it says

     res := ('AiryAi')(x)

Since I am looking at AiryAi itself, this must be either recursive call or calling other internal AiryAi?

But if it recursive, then I do not see where the actual implementation is? I wanted to see if it uses the integral form of AiryAi or series form (not likely, uses GAMMA). I see the same recursive call in many places, such as line 35 and line 37 and othere places.

But looking at all the 42 lines, I do not see where the actual calculation of AiryAi(x) is done. Did I miss it?

There is a lot of error checking and looking at special cases and such. But how does one know from looking at this listing, which other function they need to showstat() in order to see the actual implementation? There must be more to it than those 42 lines?

This is on Maple 2016.2

 

Hi all,

I am using Maple 2016.

I have defined 5 polynomials: f1, f2, f3, f4 and f5 with 5 unknowns q1,q2 ,q3, q4 and lamda.

After this, I generated the Gröbner basis. But when I try to find the normal set I got an error.

 

with(Groebner);

f1 := lamda*q1-(3380075947548081*q1*(1/140737488355328)-259050600068343*q2*(1/140737488355328)-1826834460600733*q3*(1/1125899906842624)+4414049272733425*q4*(1/9007199254740992))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f2 := lamda*q2+(259050600068343*q1*(1/140737488355328)+3380075947548081*q2*(1/140737488355328)-4414049272733425*q3*(1/9007199254740992)-1826834460600733*q4*(1/1125899906842624))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f3 := (1826834460600733*q1*(1/1125899906842624)-4414049272733425*q2*(1/9007199254740992)+843667886835955*q3*(1/35184372088832)-862655592804515*q4*(1/18014398509481984))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)))+lamda*q3;
f4 := lamda*q4-(4414049272733425*q1*(1/9007199254740992)+1826834460600733*q2*(1/1125899906842624)+862655592804515*q3*(1/18014398509481984)+843667886835955*q4*(1/35184372088832))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f5 := q1^2+q2^2+q3^2+q4^2-1;
ord := tdeg(q1, q2, q3, q4, lamda);
                  tdeg(q1, q2, q3, q4, lamda)
G := Basis([f1, f2, f3, f4, f5], ord);

IsZeroDimensional(G);
                             false
ns, rv := NormalSet(G, ord);
Error, (in Groebner:-NormalSet) The case of non-zero-dimensional varieties is not handled.

 

Any help please ?

Thank you.

Hi!

I have seen th following procedure to compute the image of the points of [0,1] under the so called Peano space-filling curve (sorry, I have to pasted the code in "text plane" mode):

P[0] := (x, y) -> ((1/3)*y, (1/3)*x);

P[1] := (x, y) -> (-(1/3)*x+1/3, (1/3)*y+1/3); 

P[2] := (x, y) -> ((1/3)*x, (1/3)*y+2/3); 

P[3] := (x, y) -> ((1/3)*x+1/3, -(1/3)*y+1);

P[4] := (x, y) -> (2/3-(1/3)*y, 2/3-(1/3)*x); 

P[5] := (x, y) -> ( (1/3)*x+1/3, 1/3-(1/3)*y));

 P[6] := (x, y) -> (1/3)*x+2/3, (1/3)*y);

P[7] := (x, y) -> (-(1/3)*x+1, (1/3)*y+1/3);

P[8] := (x, y) -> ((1/3)*x+2/3, (1/3)*y+2/3);

peano := proc (t::numeric, depth::integer)

local q, r; global P;

if depth = 0 then return 0, 0 end if;

q := floor(9*t); r := 9*t-q;

return P[q](peano(r, depth-1))

end proc;

 

Now, I need to use the procedure "peanofun" as a function. For instance, if we define f:=(x,y)->x+y, I need to use (plot, compute, etc) for instance, the function f(peanofun(t,5))

Can you help me with this issue, please?

Many thanks for your time!

 

 

I have a list of sample values and I want to remove just one maybe two of them. 

list:=[13,16,16,29,34,33,33,12,22,26,25,25,25,11]:

How could I remove just one 25 from the list? 

I have a two graphics in two distinct Maple worksheets. How can I graph them on one graphic?

 

For example, 

 graphics of y=x^2 in one Maple worksheet named document 1, 

and graphics of y=x in an other Maple worksheet named document 2.

I want to graphics of them in document 1 by recalling the graphics of y=x in document 2.

Because, The codes that I will use in future are very long and complex, I need to write code like that. (if there is possibility) 

Suppose we have some simple animations. Our goal - to build a more complex animation, combining the original animations in different ways.
We show how to do it on the example of the three animations. The technique is general and can be applied to any number of animations.

Here are the three simple animations:

restart;
with(plots):
A:=animate(plot, [sin(x), x=-Pi..a, color=red, thickness=3], a=-Pi..Pi):
B:=animate(plot, [x^2-1, x=-2..a, thickness=3, color=green], a=-2..2): 
C:=animate(plot, [[4*cos(t),4*sin(t), t=0..a], color=blue, thickness=3], a=0..2*Pi):

 

In Example 1 all three animation executed simultaneously:

display([A, B, C], view=[-4..4,-4..4]);

                                

 

In Example 2, the same animation performed sequentially. Note that the previous animation disappears completely when the next one begins to execute:

display([A, B, C], insequence);

                                 

 

Below we show how to save the last frame of every previous animation into subsequent animations:

display([A, display(op([1,-1,1],A),B), display(op([1,-1,1],A),op([1,-1,1],B),C)], insequence);

                                 

 

Using this technique, we can anyhow combine the original animations. For example, in the following example at firstly animations   and  B  are executed simultaneously, afterwards C is executed:

display([display(A, B), display(op([1,-1,1],A),op([1,-1,1],B),C)], insequence);

                                     

 

The last example in 3D I have taken from here:

restart;
with(plots):
A:=animate(plot3d,[[2*cos(phi),2*sin(phi),z], z =0..a, phi=0..2*Pi, style=surface, color=red], a=0..5):
B:=animate(plot3d,[[(2+6/5*(z-5))*cos(phi), (2+6/5*(z-5))*sin(phi),z], z=5..a, phi=0..2*Pi, style=surface, color=blue], a=5..10):
C:=animate(plot3d,[[8*cos(phi),8*sin(phi),z], z =10..a, phi=0..2*Pi, style=surface, color=green], a=10..20):
display([A, display(op([1,-1,1],A),B), display(op([1,-1,1],A),op([1,-1,1],B),C)], insequence, scaling=constrained, axes=normal);

                        


 

AA.mw

Hello guys,

I have some system of differential equations,

How can i find  eigenvalues of this system?

If i have solution

res := evalf(dsolve(sys union ics, convert(x, list), type = numeric, method = rkf45))

and

sol := evalf(dsolve(sys union ics, convert(x, list), method = laplace))

AnSolution.mw

Thanks!

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