## Tracée de ellipse avec Maple et procédure la génér...

Y'a t-il des suggestion de résolution de ce qui suit? merci.

a) On pose F(-1,0) et F(1,0) les foyers de l'ellipse E, on veut déterminer son équation implicite f(x,y)=0,
des points A(x,y) sur l’ellipse en utilisant la description bifocale et sans utiliser Maple.
b) Utilisez la commande implicitplot de Maple et le résultat de a) pour tracer plusieurs ellipses sur
le même graphe en variant la valeur de la constante C,(la somme des distances aux foyers F, F’ est
une constante qui est C).

a) We put F (-1,0) and F (1,0) the foci of the ellipse E, we want to determine its implicit equation f (x, y) = 0,
A (x, y) points on the ellipse using the bifocal description and without using Maple.
b) Use the command implicitplot of Maple and the result of a) to draw several ellipses on
the same graph by varying the value of the constant C, ( FA +F'A = C ).

Give at the end a Maple procedure that generates this ellipse.

## How to draw Ford's circles ?...

with(plottools):F := proc (N) local a, b, L; L := NULL; L := sort([op({seq(seq(a/b, a = 0 .. b), b = 1 .. N)})]); return L end proc; F(6);
[   1  1  1  1  2  1  3  2  3  4  5   ]
[0, -, -, -, -, -, -, -, -, -, -, -, 1]
[   6  5  4  3  5  2  5  3  4  5  6   ]
Ford6 := proc (i) local d, k, n, r; k := i; n := numer(F(6)[k]); d := denom(F(6)[k]); r := (1/2)/d^2; return [n/d, r], r end proc; nops(F(6));
13
for i to 13 do C || i := Ford6(i) end do;

display(circle(C1), circle(C2), circle(C3), circle(C4), circle(C5), circle(C6), circle(C7), circle(C8), circle(C9), circle(C10), circle(C11), circle(C12), circle(C13), axes = normal, scaling = constrained, color = blue, size = [800, 800]);

## Printing slides...

Hello there,

I have created a MAPLE document in a slideshow format.

Is there a way to print a copy of my presentation with header and footer included and in a format that fits on letter format paper or pdf.

LL

## efficient operation on sets...

I have 2 questions here

1st I want to extend this set Ug3 := {1, 19, 23, 29} by repeatively subtracting 6 fron its elements. first pass should give

Ug3 := (Ug3-~ 6) union Ug3  Ug3 := {-5, 1, 13, 17, 19, 23, 29}

Now I dont want to add any elenments less than 6 so -5 need to go

Second pass produces

Ug3 := (Ug3-~ 6) union Ug3                Ug3 := {-11, -5, 1, 7, 11, 13, 17, 19, 23, 29}

Obiviously no elements less than 6 to be added on second pass either.

At this point there is no further elements that could be added to the set.

I am looking for an efficient method. I can use For loops and if then checks. The sets grow in length quickly. Repetition lengths are 6, 30 210, 2310,... I use sets because the numbers get ordered automaticially. Are sets efficient or should I use some form of table?

## integration by parts...

How I can perform integration by parts, with respect to the x[0..1],y[0..1],t

 >
 >
 >
 >
 >

## 3 little annoying things ....

1)  Copy/paste problem .

Looks like Maple is not able to copy/paste the output
from a summation command . Look at my example .
I have to use the  " lprint " command .
2)   Mysterious small box character .

Suppose I want to edit a command . I want to replace a character with a left bracket
(or right bracket or left accolade but strangely not the right accolade).
I put the cursor on the character and type the left bracket (or right...) .
The left bracket ( or right ...)  is inserted . Now when I try to delete the character,
a small box appear . The  character I am trying to delete is shifting to the right .
Like  I said , just a little annoying .

3)  Open file problem .

The first file I open in Maple with the  ctrl-o command , the "open file window" appears in
the center of the screen . All the others files I am opening , the "open file window"  show up
in the bottom left corner , top center or top right corner ... randomly .
Very annoying on a 27" screen . For this last one ,I am not shure  if it is a Maple 2018 problem
or a Windows 10 64 bits problem . I have few programs in my computer .
When I use Microsoft Paint or Wordpad ,I don't see this problem .

I don't know if somebody else can confirm those annoying things . If I am not the only one
then I am hoping the next updates or versions will fix that .

Thanks !

## Pythagora table which don't work...

with(plottools):with(plots): display(seq(seq(display(polygon([[i,j],[i,j+1],[i+1,j+1],[i+1,j]], color=if((j)::odd,ColorTools:-Color=magenta))), textplot([1+.5,j+.5,fprintf("%d",i*j)])),i=1..10), j=1..10),axes=none);

## pdsolve issue with heat PDE. map expects 2 or mo...

Hello Maple experts:

Using Maple 2018.2.1 on windows, with Physics package version 301.

There is some strange issue in parsing somewhere.  This works

r:='r'; u:='u'; t:='t';theta:='theta';k:='k';
k:=1/25;
pde := diff(u(r,theta,t),t)=k*(diff(u(r,theta,t),r$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta$2));
bc1:= eval(diff(u(r,theta,t),r),r=1)=0;
bc2:= u(r,0,t)=0, u(r,Pi,t)=0;
ic := u(r,theta,0)=(r-1/3*r^3)*sin(theta);
sol:=pdsolve([pde, bc1, bc2, ic], u(r, theta, t),HINT = boundedseries(r = [0]));


No problem with the above, pdsolve gives solution. Now if I change k from 1/25 to 1, it gives parsing error in map

k:=1;
pde := diff(u(r,theta,t),t)=k*(diff(u(r,theta,t),r$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta$2));
bc1:= eval(diff(u(r,theta,t),r),r=1)=0;
bc2:= u(r,0,t)=0, u(r,Pi,t)=0;
ic  := u(r,theta,0)=(r-1/3*r^3)*sin(theta);
sol := pdsolve([pde, bc1, bc2, ic], u(r, theta, t),HINT = boundedseries(r = [0]));


Error, (in assuming) invalid input: map expects 2 or more arguments, but received 1

any K value less than one works.

Now I change K from 1 to 2, the error goes away. But no solution. Which is OK.

Why does the map error shows up when k=1 only? Same error shows up if K is missing all togother, as in

r:='r'; u:='u'; t:='t';theta:='theta';k:='k';
pde := diff(u(r,theta,t),t)=diff(u(r,theta,t),r$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta$2);
bc1:= eval(diff(u(r,theta,t),r),r=1)=0;
bc2:= u(r,0,t)=0, u(r,Pi,t)=0;
ic  := u(r,theta,0)=(r-1/3*r^3)*sin(theta);
sol := pdsolve([pde, bc1, bc2, ic], u(r, theta, t),HINT = boundedseries(r = [0]));


Error, (in assuming) invalid input: map expects 2 or more arguments, but received 1

## How can I use fsolve to interatively solve a probl...

I have been trying to use fsolve to iteratively solve a free convection heat transfer problem for a heated vertical plate using units and the ThermoPhysicalData library.  I have received some help and have managed to get rid of the eror messages but I still can't seem to get it to solve.

Here is the code

restart;
with(Units:-Standard); with(ThermophysicalData);

conv_VerticalPlate_proc := proc (T__side, T__amb, Area, L, varepsilon, q__i)

local sigma, g, T__s, T__&infin;, T__f, k, rho, Cp, Pr, mu, nu, alpha, beta, Ra__L, Nus__L, h, q__h, q__r, q__total;
g := 9.81*Unit('m'/'s'^2); sigma := 5.6703*Unit('W'/('m'^2*'K'^4))/10^8;

if type(T__side, with_unit) then
T__s := convert(T__side, temperature, kelvin)
elif T__side = 0 then
T__s := 273.15*Unit('K')
else
T__s := T__side*Unit('K')
end if;

if type(T__amb, with_unit) then
'T__&infin; := convert(T__amb, temperature, kelvin)
elif T__amb = 0 then
'T__&infin; := 273.15*Unit('K')
else
T__&infin; := T__amb*Unit('K')
end if;

T__f := (1/2)*T__s+(1/2)*T__&infin;;

k := Property(thermal_conductivity, temperature = T__f, pressure = Unit('atm'), air);
rho := Property(density, temperature = T__f, pressure = Unit('atm'), air);
Cp := Property(Cpmass, temperature = T__f, pressure = Unit('atm'), air);
Pr := Property(prandtl, temperature = T__f, pressure = Unit('atm'), air);
mu := Property(viscosity, temperature = T__f, pressure = Unit('atm'), air);

if type(k, with_unit) and type(rho, with_unit) and type(Cp, with_unit) and type(mu, has_unit) then
nu := mu/rho;
alpha := k/(rho*Cp);
beta := 1.0/T__f;
Ra__L := g*beta*abs(T__s-T__&infin;)*L^3/(alpha*nu);
Nus__L := (.825+.387*(Ra__L^(1/6))/(((1+(.492/Pr)^(9/16))^(8/27))))^2;
h := Nus__L*k/L; q__h := h*(T__s-T__&infin;)*Area;
q__r := varepsilon*sigma*(T__s^4-T__&infin;^4)*Area;
q__total := q__h+q__r
else
0.1e-6*Unit('W')
end if

end proc;

conv_VerticalPlate_proc(31.5*Unit('degC'), 20*Unit('degC'), Unit('m'^2), Unit('m'), .9);

100.8567010 Unit(W)

conv_VerticalPlate_proc(x*Unit('degC'), 20*Unit('degC'), Unit('m'^2), Unit('m'), .9);

0.001 Unit(W)

fsolve(100*Unit('W')-conv_VerticalPlate_proc(x, 20*Unit('degC'), Unit('m'^2), Unit('m'), .9), x = Unit('degC') .. 100*Unit('degC'));

I would appreciate help wih this.

Thanks

## Typesetting:-mparsed(...) error on latest 2018.2.1...

Hi

I've just upgraded from v2017.3 to 2018. It worked OK until I installed latest service pack 2018.2.1 (server license provided by my University). Ever since I cannot use Maple. Anything I type I get Typesetting:-mparsed(...) error and the text/command I typed.

I’ve contacted our software tech support and they told me to change the typesetting level from advanced to standard and it did fix the problem.

But why does it happen in the first place? I’m running Windows 8.1 64bit. Out tech support told me to has something to do with 3D display issue on my machine and told me to bring my laptop on Monday to see if they can resolve the issue.

Anyone else have this problem? Why didn’t it happen with older Maple versions? What am I missing by using standard typesetting instead of the default advanced?

Thanks

## What's wrong in matrix...

What's going wrong here?

The Matrix is created by using the Matrix Palette.

It seems that in a matix it is not possible to use division by a noninteger. Is that right?

(I use Maple 2018.2 and this is tested on both Windows and MacOS.)

Kind regards,

Mikkel

## How to improve a procedure ?...

Fract := proc (P::posint, Q::posint) local p, q; for p to P-1 do for q to Q-1 do if is((P-p)*q-p*(Q-q) = 1) then return p/q, P/Q, (P-p)/(Q-q) end if end do end do end proc:#this procedure works Fract1 := proc (P::posint, Q::posint) local p, q; ~[~[/`@op]](select(type, map2(eval, [[p, q], [P-p, Q-q]], [isolve((P-p)*q-P*(Q-q) = 1)]), [[posint$2]$2]))[] end proc:#this procedure don't work Fract(7, 81);Fract1(7,81); Fract(39, 97);Fract1(39,97); Fract(101, 143);Fract1(101,143); Fract(11, 80);Fract1(11,80); Fract(15, 37);Fract1(15,37); Fract(22, 39);Fract1(22,39); Fract(25, 37);Fract1(25,37); Fract(21, 91);Fract1(21,91); Fract(13, 19);Fract1(13,91);

## how I can Pdsolve this equation?...

is possible to solvethis equation via maple?

hank you

 >
 >
 (1)
 >
 (2)
 >

Boundary condition:

 >

#####################################

INITIAL CONDITIONS:

 >
 (3)

## a procedure which don't work...

restart;
A002487 := proc (m) local a, b, n; option remember; a := 1; b := 0; n := m; while 0 < n do if type(n, odd) then b := a+b else a := a+b end if; n := floor((1/2)*n) end do; b end proc; listeinverse := proc (L::list) local i; [seq(op(nops(L)-i, L), i = 0 .. nops(L)-1)] end proc; Brocot := proc (n) local c, i, L, M, r; L := NULL; r := 2^n; L := [seq(A002487(i), i = 0 .. r)]; M := listeinverse(L); c[0] := 0, 1/cat(0); for i to r do c[i] := L[i]/M[i] end do; c[r+1] := 1/cat(0); return [seq(c[i], i = 1 .. r+1)], r+1 end proc; for i from 0 to 4 do B || i := Brocot(i) end do;
[   1]
B0 := [0, -], 2
[   0]
[      1]
B1 := [0, 1, -], 3
[      0]
[   1        1]
B2 := [0, -, 1, 2, -], 5
[   2        0]
[   1  1  2     3        1]
B3 := [0, -, -, -, 1, -, 2, 3, -], 9
[   3  2  3     2        0]
[   1  1  2  1  3  2  3     4  3  5     5        1]
B4 := [0, -, -, -, -, -, -, -, 1, -, -, -, 2, -, 3, 4, -], 17
[   4  3  5  2  5  3  4     3  2  3     2        0]
rang := proc(M::list, a)  ...  end;;
/       1\
rang|B2[1], -|;
\       2/
/ d        \
|--- don(x)| t work;
\ dx       /

F := proc (N) local a, b, L; L := NULL; L := sort([op({seq(seq(a/b, a = 0 .. b), b = 1 .. N)})]); return L, nops(L) end proc; F(1); F(2); F(3); F(4);
[0, 1], 2
[   1   ]
[0, -, 1], 3
[   2   ]
[   1  1  2   ]
[0, -, -, -, 1], 5
[   3  2  3   ]
[   1  1  1  2  3   ]
[0, -, -, -, -, -, 1], 7
[   4  3  2  3  4   ]
rang(F(3)[1], 2/3);
/[   1  1  2   ]  2\
rang|[0, -, -, -, 1], -|
\[   3  2  3   ]  3/

## Computing a limit by maple....

I want to compute a limit via maple and that it will show me the way how to compute the limit.

The limit is:

\lim_{epsilon ->0, t\in [0,1]} 1/(exp((-1+(1-4*epsilon)^(0.5))/(2*epsilon))-exp((-1-(1-4*epsilon)^(0.5))/(2*epsilon)))*[exp((-1+(1-4*epsilon)^(0.5))/(2*epsilon)*t)-exp((-1-(1-4*epsilon)^(0.5))/(2*epsilon)*t)]/(exp(1-t)-exp(1-t/(epsilon)))

According to my book it should converge to 1.

I tried manually but got stuck.

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