## how to obtain simpler integrate result...  This is the Maple code

```restart;
result:=int(1/tanh(u),u)

simplify(result,size) ;
simplify(result,symbolic);
simplify(result,ln);
simplify(result,trig);
```

Any suggestions?

## How to find a rational function with give horizont...

How to find a rational function with give horizontal asymptotes: y=0.7, y=-0.7 and vertical asymptotes: x=0.001, x=-0.001?

## How to partition a list fast? ...

Hello

I have a list with a large number of elements and I need to partition it in chunks of a specific size.  Here is my attempt

```listpart := proc(cond::list,nchunk::nonnegint:=1000)
if numelems(cond) < nchunk then
newcond:=[cond]:
else
ss:=[`\$`(1..numelems(cond))]:
sss:=map(`mod`,ss,nchunk):
ind:=[ListTools:-SearchAll(0,sss)]:
ind:=[0,op(ind),ifelse(ss[numelems(ss)]=ind[numelems(ind)],[],ss[numelems(ss)])]:
end if:
return(newcond):
end proc:```

It does not run as fast as I thought.  I am not even sure if Threads:-Seq could be used in this case.  Please tell me what I am doing wrong and how I can modify the code to get a faster response.

Many thanks

Ed

## need code, its very urgent...

Hello all

could anyone tell how to solve following nonliner equations numerically.

f '''' - c1(g'') + R(f ' f '' - f f ''' )=0

g'' + c2(f '' -2g) -c3(f g' - f ' g)=0

f ' (-1)=0,   f ' (1)=0,   f(-1)=1-A, F(1) =1, g(-1)=0, g(1)=0

c1=3.2, c2=3.3, c3=3.4, R= -10 and A=1.6 are constants.

## Why integration of dirac delta with argument sin i...

Hello,

I am trying to calculate an integral involving dirac delta as given below

```int(Dirac(sin(x)),x=-3/2*Pi..3/2*Pi)
```

However, Maple returns the integral unevaluated as How can I get it evaluated? the result should be 3 here.

## Physics package update...

Hello each and everyone,

I have a problem with updating the Physics Package. (At the moment I run version 709)

But when I try to update to version 710 I have the following error (see the screenshot)

I don't know what's happening.

Kind regards to all.

Jean-Michel ## Drawing a polygonal approximation of a curve C...

I try to make a procedure for this

Was it by a example of Riemann sum that  x-values in a array are stored for  numerical value, but in this task it seems that the array must be filled with the symbol x1,x2 , etc

Should this be needed ?

blz64.pdf

blz_65.pdf

Was it first for a partition about a interval ( example Riemannn sum) that i got  a list of numeric values

 > a:= 0: b:= 5: N:= 30: i= 0..N :
 > X:= Array(0..N, [seq(j, j=a..b, (b-a)/N)]); (1)

Now i want  to get a list  of  x-values in Array X ,  starting from  0  to N  :

example: array X =[x0= 0, x1=1/6, ...]

 > x[i]:= a+(b-a)*i/N; # for i = 0..N # endpoints subintervals
 > # generate X-values for interval [a,b]
 > X:= Array(0..N, [seq(j, j=a..b, x[i])]);
 >

the values  x1,x2....stored  in Array X are used in further calulations
If there is a need for naming x1= 0 , x2= ..  in the Array A ? , probably not .

 >

## how did Maple obtain this ode solution?...

I can't figure out how Maple obtained this solution and looking for some ideas to try.

It is first order non-linear ode in y(x), which is separable.

```ode:=diff(y(x),x)=x*ln(y(x));
dsolve([ode,y(1)=1],y(x))
``` But the general solution is

`sol:=dsolve(ode)` Setting up manually an equation using the given condition in order to solve for _C1, produces no solution.

```eq:=subs([y(x)=1,x=1],sol);
solve(eq,_C1)
``` Warning, solutions may have been lost

Also

`coulditbe(exp(RootOf(1 + 2*Ei(1, -_Z) + 2*_C1))=1)`

FAIL

So how did Maple solve for the constant of integration which results in particular solution y(x)=1 that is supposed to satisfy the condition y(1)=1?

It is clear that y(x)=1 satisfies the ODE itself. But I am asking about how it also satisfies y(1)=1

(odetst says it does satisfy the ODE and condition as well. So Maple must have done something very smart under the cover)

Next I tried

```ode:=diff(y(x),x)=x*ln(y(x));
sol:=dsolve(ode,y(x));
sol:=DEtools:-remove_RootOf(sol);
sol:=subs([y(x)=1,x=1],sol)
``` And now

```solve(sol,_C1)
```

Error, (in Ei) numeric exception: division by zero

Just wondering how did Maple decide that y(x)=1 satisfies y(1)=1? I do not see it.

Using Maple 2020.1. But same result on Maple 2019

## How to display Trigonométric values of the Explo...

Hi,

How to display only trigonometric values ( like 0,Pi/6,Pi/3..)  of the parameter alpha in the Explore Command?

Thanks

ROTATIONConiquesEllipseAnimation.mw

## Ellipse Equation ( rotation)...

Hi ,

i want to find simple equation of rotate Ellipse  ( El1,EL2,El3 in the  worksheet), with calssic formula Ideas? Thanks

QuestionConiqueRotation.mw

## Find the focus of an ellipse with a tangential gen...

Etude d'un cas particulier a := 5: b := 7: k := 9: A := [a, 0]: B := [0, b]: #A et B fixes P := [t, 0]: Q := [0, k/t]:#P et Q 2 points mobiles cir := -a*x-b*y+x^2+y^2 = 0: sol := solve(subs(y = 5, cir), x): cen := [solve(diff(cir, x)), solve(diff(cir, y))]: x0 := sol: y0 := 5: M := [x0, y0]: R := sqrt(cen^2+cen^2): beta := arctan(diff(solve(EQ(M, cen), y), x)): Recherche des valeurs de t pour que les 2 droites soient perpendiculaires eq := t^2*(y0-b)+t*(a*b-a*y0+b*x0-k)-x0*(a*b-k) = 0; sol := solve(eq, t); t := sol; tp := sol; P1 := [t, 0]; Q1 := [0, k/t]; PQ1 := simplify(x*(-a*b+b*t+k)+y*t*(t-a)-t*(-a*b+b*t+k)) = 0:#1ere tangente PQ2 := simplify(x*(-a*b+b*tp+k)+y*tp*(tp-a)-tp*(-a*b+b*tp+k)) = 0:#2ième tangente P2 := [tp, 0]; Q2 := [0, k/tp]; CIR := implicitplot(cir, x = -4 .. 8, y = -4 .. 12, color = red); Fig := proc (alpha) local Dr1, DR1, Dr2, DR2, N, u0, v0, Po, t, tp, sol; global a, b, k, cen, R; u0 := cen+R*cos(alpha); v0 := cen+R*sin(alpha); N := [u0, v0]; sol := solve(t^2*(v0-b)+t*(b*u0-a*v0+a*b-k)-u0*(a*b-k) = 0, t); t := sol; tp := sol; Dr1 := simplify(x*(-a*b+b*t+k)+y*t*(t-a)-t*(-a*b+b*t+k)) = 0; DR1 := implicitplot(Dr1, x = -4 .. 8, y = -4 .. 12, color = brown); Dr2 := simplify(x*(-a*b+b*tp+k)+y*tp*(tp-a)-tp*(-a*b+b*tp+k)) = 0; DR2 := implicitplot(Dr2, x = -4 .. 8, y = -4 .. 12, color = pink); Po := pointplot([N[]], symbol = solidcircle, color = [black], symbolsize = 8); display([Po, DR1, DR2]) end proc; DrPQ1 := implicitplot(PQ1, x = -4 .. 22, y = -4 .. 12, color = blue); DrPQ2 := implicitplot(PQ2, x = -4 .. 22, y = -4 .. 12, color = blue); Points := pointplot([A[], B[], M[], P1[], P2[], Q1[], Q2[], cen[]], symbol = solidcircle, color = [green], symbolsize = 10); T := plots:-textplot([[A[], "A"], [B[], "B"], [M[], "M"], [P1[], "P1"], [P2[], "P2"], [Q1[], "Q1"], [Q2[], "Q2"], [cen[], "cen"]], font = [times, 10], align = {below, left}); n := 19; display([seq(Fig(2*i*Pi/n), i = 0 .. n), Fig(beta), CIR, DrPQ1, DrPQ2, Points, T], scaling = constrained, size = [500, 500]); I would find out the focus of the ellipse. Thank you.

## Change RootOf solutions...

How I can change this solution or remove the RootOf, because i have to show variables and params in this solutions.

 > > > > > >  (1)
 >  ## Why did Maple miss the multiplication symbol but ...

Theoretically, if the multiplication sign  is missed Maple needs to give reminders or warnings.But the following is not the case, why？I am surprised its output.

x:=1
x := 1
x(2+1)Actually, I want to enter x*(2+1)

1
x(sin(y))Actually, I want to enter x*(sin(y))
1

## Error that should not really occur ...

I am a little confused by why this error occurs in the second line and not the first, as well as the weird details specified in it. I don't know if the commands that are being called are inbuilt or not, but it is a safe bet that they will be. thankyou.

 > > > ## "evalf" output depends upon style of input?...

In preparing to sample problems, I came across this difference in an output depending upon the input type: 2d Input vs. Maple Input. Is there a typo on my part?

 >   (1)

Very happy with the output of the following line:

 >  (2)

But I'm confused about the output of the next line. Is it a limit to the calculation or a display problem?

 > a := evalf(3.0^(1.2)) (3)

and yet this next output looks fine:

 > b := evalf( exp( 1.2 * ln(3))) (4)

Fortunately, there appears to be no difference between x and b:

 >  (5)

But these next  lines suggest there is an actual limit in the calculation of a.

 >  (6)
 > evalf(a - b); (7)

Note - when Digits is set to 30, the calculation difference between x and a disappears.

 > 