Maple Questions and Posts

A problem with integration...

Asked by: vfleurov 5

January 03 2020

1 11

I do a calculation o a simple integral

int(cosh(cos(2*t)), t = 0 .. 2*Pi)

and get the answer 0 (zero), which I know is incorrect. The cosh function of a real argument is always positive.

If I represent the cosh function as a sum of two exponentials

(1/2)*(int(cosh(cos(2*t)), t = 0 .. 2*Pi) + int(cosh(-cos(2*t)), t = 0 .. 2*Pi))

I get

2*Pi*BesselI(0, 1)

which looks much better.

What's the matter? Why Maple yields two different results? Victor.

Match parameter name of a function...

Asked by: Stretto 260

January 02 2020

1 15

I'm trying to create an iterator function

Iter := proc(ff, n)
    local i,f;
   if n = 0 then return (x->x); end;
    f := x->ff:
    f := apply(unapply(ff))(x);
    for i from 1 to n-1 do
        f := ff(f);
    end;
   return unapply(f,x);
end:

This seems to work except that it converts the independent variable to x, which can cause problems.

That is, if I pass something like n->sin(n) then it will output something like x->sin(sin(x))...

Of course, I do explicitly use x but it is because I don't know how to get the input's independent variable.

Ideally I'd like to be able to work on multiple arguments and iterate over the first, by default.

e.g., f#2(x,y,z) = f(f(x,y,z),y,z)

Ultimately the proc above doesn't work well as I want to be able to use it in all contexts(I could pass the value to Iter but I'd rather use function notation.

How to model a very simple phonetic voice generato...

Asked by: Fereydoon_Shekofte 223

January 02 2020

1 0

This must be so complicated process to describe the exact mechanism in human or animals ... and there are many reserchs on web for this subject ! Not expected Large answer !

By this way i am just curious to know by support of signal processing methods available in maple we can model a very basic vibrator as larynx and variable duct (what kind of filter we can call ?) or cavity that play the role of tongue or lips for changing of main stream to made various phonemes or frequencies

Here is a movie that show the section of human vocal system :

Anatomy

results of minimization iteration ...

Asked by: radaar 202

January 02 2020

1 8

is it possible to get all the iteration values for a minimization problem

How to animate linear transformation of multiple p...

Asked by: Ecco_Homolka 15

January 02 2020

3 2

Hey,

I want to animate action of linear transformation on multiple polygons, in the end, it should be a grid of multiple parallel lines that will get morphed. The transformation is defined by a matrix A.

So far I got this code to work:

with(plots):
with(plottools):
setoptions(style=patch,view=[-5..5,-5..5], scaling=constrained):
basis_i:=polygon([[0,0],[1,0]],color=red):

N:=20:
F:=(x,y) -> (1-k/N)*<x,y> + k/N*(A.<x,y>):
L := transform((x,y)->convert(F(x,y),list)):
A:=<<2,1>|<-1,1>>;

frames:=seq(L(basis_i),k=0..N):

display(frames, insequence=true);

It animates the basis vector nicely, but I can't seem to figure out, how to animate multiple lines, multiple polygons.

Anyone knows how to do this?

Any help will be much appreciated.

Filling Array with Procedure...

Asked by: eep8freak 5

January 01 2020

1 1

I try to fill an Array with a procedure to have pointpairs for a plot. Here is my problem. It doesn't work I wont it to.

Can someone help my please? The first procedure works, I tested it with some numbers, but the second one is the Problem.

a problem with integration...

Asked by: mehdi jafari 774

January 01 2020

0 7

Hi dear maple team. i have a question on integration and i need a "real" and "finite" solution with any assumption or options. thanks for the help.

>

restart

>	f := ((1 - a)^2 + a^2((1 - exp(-y))(1 - exp(-x)) - 2 + exp(-x) + exp(-y)) + a(2 - exp(-x) - exp(-y) + (1 - exp(-y))(1 - exp(-x))))/(1 - aexp(-x)exp(-y))^3;

((1-a)^2+a^2*((1-exp(-y))*(1-exp(-x))-2+exp(-x)+exp(-y))+a*(2-exp(-x)-exp(-y)+(1-exp(-y))*(1-exp(-x))))/(1-a*exp(-x)*exp(-y))^3

(1)

>	a := 0.3;f

(.91+.39*(1-exp(-y))*(1-exp(-x))-.21*exp(-x)-.21*exp(-y))/(1-.3*exp(-x)*exp(-y))^3

(2)

>	s := 2evalf(int((int(fexp(-x)*exp(-y), x = 0 .. y + t,AllSolutions)), y = 0 .. infinity,AllSolutions)) assuming real ;

>

Download stat1.mw

simple random number construction...

Asked by: digerdiga 390

January 01 2020

0 14

Hello, Probably there is a way to do this easily but I do not quickly find it within the help.

I want

rand(0..1)

to give a true! random number and not always the same number; otherwise it should be called

predefinedlist()

Seed is deprecated, not sure it would help though. So how do I go abouts?

Rotating 3d letters...

Asked by: Christopher2222 6035

December 31 2019

2 1

In this code created by Acer a long while back. I can't figure out how to increase the length of the text rotating so the letters don't collide with one another.

Here is the code.

restart:

#
# One (of many) STL format collections of the English alphabet:
#     http://www.stlfinder.com/model/all-alphabet-letters-a-z
#
basedir:=cat(kernelopts(homedir), "/My Documents/stl/All_Alphabet_Letters_A-Z"):

getletter:=L->Import(cat(basedir, "/Letter_", L, ".stl"),
                     orientation=[-90,0,0],title=""):

letters := [m,a,p,l,e]:

for letter in letters do
  if not assigned(AZ[letter]) then
    AZ[letter]:=getletter(letter);
  end if;
end do:

with(plottools): with(plots):

Rplot:=display(AZ[letters[1]],
               seq(translate(AZ[letters[i]], 40*(i-1)+15, 0, 0),
                   i=2..nops(letters))):

Rplot:=transform((x,y,z)->[z,x,y])(scale(Rplot, 5/6*2*Pi/200, 1/5, 1/20, [0,0,10])):

display(changecoords(Rplot,cylindrical), scaling=constrained, axes=none,
        orientation=[0,90,0], viewpoint=[circleright], frames=50);

Here is the file with the letters

All_Alphabet_Letters_A-Z.zip

The series is not substituting...

Asked by: kencom1 115

December 31 2019

0 5

Good day everyone and happy new year in advance. I'm trying to write a code for a series but its not substituting. Below is the attached file. Thanking you very much in anticipation for your help.

Testing.mw

No query from Maple when saving worksheet with lar...

Asked by: Christopher2222 6035

December 31 2019

0 2

I went to save a file in Maple and it had large amounts of calculated data.

Maple didn't ask me if I also wanted to save that data like it usually does - it just saved it. Saved a 13Mb worksheet that took 5 minutes to relinquish control on my laptop.

Happy New Year!

by: vv 14042 Product: Maple

December 31 2019

8 6

with(plots):
S:=cat("Happy New Year 2020!   "$3):
N:=length(S): a:=0.77*Pi: h:=2*Pi/N:
display(seq(textplot([cos(a-k*h), sin(a-k*h),S[k+1]], 
        rotation=-Pi/2+a-k*h, 'font'=["times","roman",24]), k=0..N-4), axes=none);

A Parametric Happy New Year

by: Samir Khan 2151 Product: Maple

December 31 2019

2 4

When plotted, these parametric equations say "happy new year" (and were constructed with this worksheet)

x := piecewise(t <= 58, -15.0*sin(1.43 + 0.650*t) - 14.8*sin(-1.64 + 0.703*t) - 1.28*sin(-2.97 + 1.25*t) - 11.9*sin(-1.58 + 0.540*t) - 1.07*sin(-1.60 + 1.35*t) - 3.85*sin(-2.09 + 1.41*t) - 7.13*sin(1.13 + 1.73*t) - 4.40*sin(1.32 + 1.30*t) - 26.3*sin(1.53 + 0.380*t) - 9.42*sin(-4.65 + 0.433*t) - 3.43*sin(1.42 + 2.06*t) - 7.57*sin(-1.77 + 2.11*t) - 2.65*sin(-4.34 + 0.323*t) - 1.95*sin(-4.57 + 2.54*t) - 5.39*sin(-1.38 + 2.60*t) - 49.2*sin(1.52 + 0.487*t) - 0.754*sin(-4.38 + 2.87*t) - 9.67*sin(-1.58 + 2.65*t) - 7.88*sin(-4.59 + 1.95*t) - 2.39*sin(-1.67 + 2.71*t) - 15.1*sin(1.53 + 0.108*t) - 39.0*sin(1.47 + 0.757*t) - 1.80*sin(1.37 + 2.22*t) - 4.22*sin(-1.95 + 0.973*t) - 7.72*sin(-1.44 + 2.17*t) - 8.80*sin(-1.66 + 0.813*t) - 3.59*sin(1.13 + 1.57*t) - 15.4*sin(-1.64 + 1.62*t) - 6.70*sin(1.36 + 1.19*t) - 791.*sin(-1.57 + 0.0540*t) - 2.55*sin(-1.55 + 1.89*t) - 6.92*sin(-1.87 + 1.68*t) - 3.95*sin(1.17 + 1.08*t) - 44.1*sin(-1.67 + 1.14*t) - 25.8*sin(1.51 + 0.597*t) - 31.4*sin(1.42 + 1.46*t) - 96.8*sin(-1.59 + 0.162*t) - 18.7*sin(1.53 + 0.217*t) - 7.87*sin(-4.66 + 2.98*t) - 4.99*sin(1.22 + 3.03*t) - 6.92*sin(1.43 + 2.44*t) - 48.3*sin(1.47 + 1.03*t) - 24.2*sin(1.48 + 1.52*t) - 9.58*sin(1.43 + 2.49*t) - 4.29*sin(1.33 + 2.27*t) - 6.34*sin(1.22 + 2.33*t) - 12.0*sin(1.45 + 2.00*t) - 0.388*sin(-1.25 + 2.92*t) - 2.74*sin(-1.43 + 1.79*t) - 6.71*sin(-1.66 + 1.84*t) - 0.713*sin(-3.63 + 2.38*t) - 43.1*sin(-1.59 + 0.271*t) - 2.51*sin(1.12 + 2.76*t) - 1.29*sin(-3.92 + 2.82*t) - 21.3*sin(-1.70 + 0.867*t) - 12.4*sin(1.50 + 0.920*t), 58 < t and t <= 84, -500 - 321.*sin(-8.608 + 0.121*t) - 7.18*sin(-12.408 + 0.241*t) - 57.1*sin(-22.608 + 0.361*t) - 21.9*sin(-26.682 + 0.484*t) - 21.3*sin(-33.474 + 0.603*t) - 50.2*sin(-43.800 + 0.725*t) - 20.6*sin(-50.760 + 0.845*t) - 41.5*sin(-54.756 + 0.967*t) - 9.74*sin(-61.89 + 1.09*t) - 41.1*sin(-72.03 + 1.21*t) - 2.49*sin(-78.88 + 1.33*t) - 3.30*sin(-83.227 + 1.45*t) - 6.73*sin(-89.99 + 1.57*t) - 5.88*sin(-96.59 + 1.69*t) - 16.4*sin(-106.99 + 1.81*t) - 1.61*sin(-111.8982 + 1.93*t) - 1.84*sin(-117.970 + 2.05*t) - 0.464*sin(-127.83 + 2.17*t) - 1.64*sin(-134.90 + 2.30*t) - 3.94*sin(-142.37 + 2.41*t) - 2.35*sin(-149.22 + 2.54*t) - 2.72*sin(-154.3362 + 2.66*t) - 8.41*sin(-160.453 + 2.78*t) - 4.39*sin(-171.17 + 2.90*t), 84 < t, -300 - 2.66*sin(-205.04 + 2.41*t) - 1.26*sin(-207.397 + 2.46*t) - 2.21*sin(-196.59 + 2.31*t) - 2.31*sin(-166.83 + 1.96*t) - 48.9*sin(-39.688 + 0.452*t) - 0.697*sin(-252.158 + 3.01*t) - 2.51*sin(-179.22 + 2.11*t) - 1.57*sin(-222.14 + 2.66*t) - 0.745*sin(-226.24 + 2.71*t) - 49.4*sin(-10.020 + 0.100*t) - 0.289*sin(-159.628 + 1.91*t) - 95.9*sin(-32.358 + 0.402*t) - 60.0*sin(-43.928 + 0.502*t) - 3.76*sin(-73.736 + 0.854*t) - 3.05*sin(-183.97 + 2.16*t) - 0.629*sin(-158.50 + 1.86*t) - 9.25*sin(-49.272 + 0.603*t) - 4.46*sin(-74.716 + 0.904*t) - 10.4*sin(-79.040 + 0.955*t) - 2.65*sin(-103.67 + 1.21*t) - 1.99*sin(-145.57 + 1.71*t) - 1.52*sin(-197.315 + 2.36*t) - 0.685*sin(-258.12 + 3.06*t) - 1.04*sin(-247.58 + 2.96*t) - 64.8*sin(-18.514 + 0.201*t) - 68.5*sin(-31.278 + 0.352*t) - 579.*sin(-5.8068 + 0.0502*t) - 6.52*sin(-95.20 + 1.11*t) - 5.03*sin(-96.28 + 1.16*t) - 0.396*sin(-211.620 + 2.51*t) - 7.28*sin(-150.00 + 1.76*t) - 2.42*sin(-153.92 + 1.81*t) - 10.4*sin(-112.11 + 1.31*t) - 24.8*sin(-85.95 + 1.00*t) - 3.91*sin(-124.83 + 1.46*t) - 1.69*sin(-185.369 + 2.21*t) - 1.18*sin(-189.238 + 2.26*t) - 16.6*sin(-56.662 + 0.653*t) - 1.33*sin(-222.31 + 2.61*t) - 0.593*sin(-238.70 + 2.81*t) - 1.88*sin(-233.58 + 2.76*t) - 3.91*sin(-133.01 + 1.56*t) - 4.94*sin(-134.16 + 1.61*t) - 9.59*sin(-128.89 + 1.51*t) - 1.02*sin(-240.2714 + 2.86*t) - 2.15*sin(-247.83 + 2.91*t) - 5.52*sin(-90.85 + 1.06*t) - 3.83*sin(-171.25 + 2.01*t) - 0.523*sin(-171.66 + 2.06*t) - 0.284*sin(-141.80 + 1.66*t) - 23.2*sin(-11.174 + 0.151*t) - 1.58*sin(-114.615 + 1.36*t) - 2.67*sin(-120.75 + 1.41*t) - 5.83*sin(-19.524 + 0.251*t) - 13.7*sin(-23.774 + 0.301*t) - 14.8*sin(-107.89 + 1.26*t) - 15.5*sin(-60.842 + 0.703*t) - 37.7*sin(-65.176 + 0.754*t) - 2.02*sin(-217.95 + 2.56*t) - 13.2*sin(-69.466 + 0.804*t) - 37.7*sin(-45.052 + 0.553*t)):

y := piecewise(t <= 58, -28.1*sin(1.45 + 1.62*t) - 2.23*sin(-2.39 + 1.89*t) - 17.8*sin(-1.51 + 1.19*t) - 4.85*sin(-1.61 + 2.38*t) - 2.52*sin(1.55 + 1.95*t) - 20.0*sin(1.55 + 2.11*t) - 24.8*sin(-1.62 + 2.00*t) - 19.9*sin(-1.81 + 2.06*t) - 4.22*sin(-0.422 + 2.60*t) - 6.94*sin(1.47 + 2.87*t) - 61.1*sin(1.49 + 0.323*t) - 13.9*sin(-4.68 + 0.540*t) - 3.97*sin(0.00256 + 2.33*t) - 69.8*sin(1.53 + 0.487*t) - 59.6*sin(1.50 + 0.813*t) - 132.*sin(-1.65 + 0.867*t) - 26.7*sin(-1.76 + 1.52*t) - 53.1*sin(1.40 + 1.57*t) - 139.*sin(1.57 + 0.0540*t) - 3.75*sin(-2.34 + 3.03*t) - 8.03*sin(1.24 + 1.73*t) - 22.9*sin(-4.61 + 0.217*t) - 16.7*sin(-1.67 + 0.703*t) - 23.3*sin(-1.82 + 1.68*t) - 78.9*sin(-4.70 + 0.271*t) - 2.72*sin(-2.38 + 2.49*t) - 3.45*sin(1.10 + 2.54*t) - 2.07*sin(-0.489 + 2.22*t) - 13.1*sin(-1.82 + 2.27*t) - 60.6*sin(-1.62 + 1.08*t) - 5.27*sin(1.55 + 2.44*t) - 4.17*sin(1.46 + 2.82*t) - 33.1*sin(-1.80 + 1.46*t) - 2.15*sin(-1.58 + 0.757*t) - 3.94*sin(-3.86 + 2.65*t) - 8.88*sin(1.51 + 1.79*t) - 9.97*sin(1.52 + 1.84*t) - 105.*sin(1.48 + 1.03*t) - 15.2*sin(-4.67 + 1.25*t) - 101.*sin(1.51 + 0.380*t) - 11.0*sin(-4.59 + 0.433*t) - 86.7*sin(1.50 + 0.973*t) - 170.*sin(1.53 + 0.597*t) - 41.2*sin(1.51 + 0.650*t) - 20.4*sin(-1.67 + 1.30*t) - 47.9*sin(-1.70 + 1.35*t) - 15.8*sin(-1.66 + 2.71*t) - 8.61*sin(-1.71 + 2.76*t) - 25.7*sin(-1.64 + 0.108*t) - 70.9*sin(1.55 + 0.162*t) - 0.668*sin(-2.42 + 2.92*t) - 4.78*sin(-4.60 + 2.98*t) - 106.*sin(1.49 + 0.920*t) - 17.6*sin(1.53 + 1.41*t) - 8.82*sin(1.05 + 2.17*t) - 113.*sin(-1.67 + 1.14*t), t <= 84, -800 - 7.30*sin(-171.17 + 2.90*t) - 3.28*sin(-6.550 + 0.121*t) - 1.46*sin(-17.878 + 0.241*t) - 20.4*sin(-22.438 + 0.361*t) - 28.9*sin(-29.862 + 0.484*t) - 9.13*sin(-36.364 + 0.603*t) - 45.3*sin(-40.650 + 0.725*t) - 97.4*sin(-50.770 + 0.845*t) - 13.1*sin(-54.916 + 0.967*t) - 80.8*sin(-61.97 + 1.09*t) - 39.1*sin(-71.92 + 1.21*t) - 42.8*sin(-78.87 + 1.33*t) - 108.*sin(-85.97 + 1.45*t) - 10.6*sin(-92.80 + 1.57*t) - 49.8*sin(-99.94 + 1.69*t) - 15.4*sin(-103.75 + 1.81*t) - 24.2*sin(-113.90 + 1.93*t) - 8.96*sin(-123.18 + 2.05*t) - 1.59*sin(-127.14 + 2.17*t) - 14.1*sin(-137.59 + 2.30*t) - 6.51*sin(-142.35 + 2.41*t) - 7.98*sin(-145.83 + 2.54*t) - 6.40*sin(-153.721 + 2.66*t) - 1.23*sin(-164.36 + 2.78*t), 84 < t, -1400 - 128.*sin(-32.358 + 0.402*t) - 68.5*sin(-43.928 + 0.502*t) - 2.55*sin(-242.18 + 2.86*t) - 6.86*sin(-219.136 + 2.61*t) - 5.76*sin(-222.904 + 2.66*t) - 2.39*sin(-226.835 + 2.71*t) - 101.*sin(-11.164 + 0.151*t) - 8.69*sin(-231.548 + 2.76*t) - 146.*sin(-31.268 + 0.352*t) - 8.30*sin(-179.37 + 2.11*t) - 2.68*sin(-261.69 + 3.06*t) - 10.4*sin(-162.98 + 1.91*t) - 30.1*sin(-73.606 + 0.854*t) - 24.1*sin(-77.946 + 0.904*t) - 10.0*sin(-146.01 + 1.71*t) - 72.5*sin(-69.416 + 0.804*t) - 8.91*sin(-85.97 + 1.00*t) - 8.58*sin(-175.51 + 2.06*t) - 27.4*sin(-109.01 + 1.31*t) - 16.8*sin(-113.17 + 1.36*t) - 162.*sin(-5.7968 + 0.0502*t) - 3.69*sin(-205.52 + 2.41*t) - 7.62*sin(-207.006 + 2.46*t) - 131.*sin(-53.522 + 0.653*t) - 95.3*sin(-60.882 + 0.703*t) - 8.53*sin(-197.627 + 2.36*t) - 1.74*sin(-247.32 + 2.91*t) - 27.2*sin(-121.51 + 1.46*t) - 51.7*sin(-49.332 + 0.603*t) - 8.81*sin(-104.925 + 1.26*t) - 10.2*sin(-100.703 + 1.21*t) - 9.35*sin(-183.90 + 2.16*t) - 7.82*sin(-188.20 + 2.21*t) - 42.8*sin(-26.964 + 0.301*t) - 16.8*sin(-48.312 + 0.553*t) - 15.2*sin(-9.980 + 0.100*t) - 213.*sin(-18.524 + 0.201*t) - 39.4*sin(-19.584 + 0.251*t) - 6.28*sin(-87.85 + 1.06*t) - 3.71*sin(-117.623 + 1.41*t) - 4.92*sin(-196.77 + 2.31*t) - 1.25*sin(-255.21 + 3.01*t) - 5.13*sin(-248.529 + 2.96*t) - 8.69*sin(-141.43 + 1.66*t) - 11.5*sin(-167.26 + 1.96*t) - 13.0*sin(-171.19 + 2.01*t) - 4.12*sin(-159.23 + 1.86*t) - 3.66*sin(-212.23 + 2.51*t) - 0.810*sin(-83.380 + 0.955*t) - 3.11*sin(-65.516 + 0.754*t) - 1.38*sin(-139.34 + 1.61*t) - 9.07*sin(-188.885 + 2.26*t) - 52.6*sin(-39.678 + 0.452*t) - 6.81*sin(-125.917 + 1.51*t) - 24.7*sin(-130.128 + 1.56*t) - 4.16*sin(-215.362 + 2.56*t) - 11.8*sin(-92.283 + 1.11*t) - 16.6*sin(-96.32 + 1.16*t) - 6.39*sin(-147.108 + 1.76*t) - 7.61*sin(-154.46 + 1.81*t) - 4.28*sin(-235.566 + 2.81*t)):

plot( [ x, y, t = 0 .. 146 ], scaling = constrained, discont = [ usefdiscont ], axes = boxed, thickness = 5, size = [600, 600]);

Plotting integers at specific locations in the pla...

Asked by: erik10 791

December 30 2019

0 4

Dear Maple users

I just created a sunflower in Maple using the Golden angle. See attached file. I am using a scatterplot with solidcircles as symbols. But what I would like now is to plot integers instead of the solidcircles in order to investigate the order of these different solidcircles. To make it clear: I have 500 solidcircles. They have been plottet using two vectors containing the x and y coordinates of the individual solidcircles. The n'th solidcircle I want to replace with the integer n. How can I create that different plot?

NB! The plot might need to be larger or the integers smaller, but that is fine.

Regards

Erik V

sunflower.mw

What is the equation of motion of a swinging, hang...

Asked by: Earl 985

December 30 2019

3 6

A flexible rope of constant linear density hangs from one fixed end.

The lower end is pulled aside and then released.

The rope swings back and forth with a whip-like action.

What equation of motion can be used to animate this action in Maple?

I cannot find any references through Google to the appropriate math.

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