## How to do this substitution?...

i am new on maple while usig maple i have to substitute a general value in an equation but could not do it like

> restart;
> taylor(f(x), x = gamma);

i typed this and want to replace x-gamma with e[n] which is easy and i did it but whn i want to substitute D(f)(gamma),(D@@2)(f)(gamma) and so on by (D@@k)(f)(gamma)=k!*c[k]*f(gamma) then i could not understand how can i do 2nd part
pls help in this i m very thanlful to you

## Square Free Factorization ...

Dear hope you will fine. I am try to make a program of square free factorization over a finite field whose alogrithm is below:

Algorithm: SFF (Square-Free Factorization)
Input: A monic polynomial f in Fq[x]
Output: Square-free factorization of f
i←1; R ← 1; g ← f′;
if g ≠ 0 then {
c ← gcd(f, g);
w ← f/c;
while w ≠ 1 do {
y ← gcd(w, c); z ← w/y;
R ← R·zi; i ← i+1; 
           w ← y; c ← c/y }
if c ≠ 1 then {
c ← c1/p;
           Output(R·SFF(c)p) }
     else  Output(R)
else {
f ← f1/p;
           Output(SFF(f)p) }
  end.The attached file my try to make this, please find and help me to complete this. I am waiting your kind response.Help.mw

With my best regards and sincerely.



## GCD of polynomials over finite field...

Dear

Hope everything going fine with you. I have question

f := x^11+2*x^9+2*x^8+x^6+x^5+2*x^3+2*x^2+1

g := 2*x^10+x^7+2*x^4+x

if we take gcd of infinite field its answer is x^6+1

and the GCD(3)[x]=Z_3[x] is given by x^9+2x^6+x^3+2

How we find GCD(3)[x] in maple.

With my best regards and sincerely.

## How to find exact solution of ODE?...

EF.3.mwHi, I want to ask that how to find the exact solution of equation without applying any technique

## Activation of new packages ? ...

Hello

I have maple 13, and I installed two new packages, the problem that I don't know where should I saved them and how to make them active to start using there routines ???

So pleas any one know how to add packages to maple 13, help me    :)

## Surface of Revolution...

Hi there

I use Maple13 for plotting the surface of revolution of y=x^2 around the line y=1 on the interval [1,2]. But the distance between the surface

and the vertical axis is ignored while there must be 1 unit distance.please specify the correct command.

Thanks for your cooperation

Regards

M. R. Yegan

## Plot of a certain curve...

I have the following code of a plot:

plot(
[
add(BS(bb[4], t, i, 3)*bb[1](i+1), i = 0..n),
add(BS(bb[4], t, i, 3)*bb[2](i+1), i = 0..n),
t = 0..1
],
color=red, axes=normal, scaling=constrained, numpoints=100, thickness=2
):

and I get the following error:

Error, (in BS) cannot determine if this expression is true or false: 0 <= t and t < .54901960784313725490196078431373

The problem is that, in the definition of BS, there are some conditions that depend on the variable t. It seems that Maple does not use a specific value of t when executing BS. My solution is to plot specific points, i.e.,

plot(
[
seq([add(BS(bb[4], h/5000, i, 3)*bb[1](i+1), i = 0..n),
add(BS(bb[4], h/5000, i, 3)*bb[2](i+1), i = 0..n)], h=0..5000)
],
color=red, axes=normal, scaling=constrained, numpoints=100, thickness=2
):

Can this be done in a more elegant way?

## Homotopy perturbation methods...

HPM_4.mwhi, I am using homotopy perturbation technique but there is arising an error in comaring coeffecient of p^0, p^1,.... plz help me

## Non linear part...

LE.2a.E.LGM.mwHi, my this programme is executing for linear part but does'nt show the proper results for non linear,plz tell me appropriate code

## error in simplify...

> coth;
coth
> restart;
> c := 0;
0
> w := -2*mu;
-2 mu
> a[-1] := 0;
0
> a[0] := mu*lambda*sqrt(-6*a);
(1/2)
mu lambda (-6 a)
> a[1] := (6*(mu*lambda^2+1))/sqrt(-6*a);
/         2    \
6 \mu lambda  + 1/
------------------
(1/2)
(-6 a)
> b[-1] := 0;
0
> b[0] := 0;
0
> b[1] := 0;
0
> xi := x+w*t;
x - 2 mu t
> P := sqrt(-mu)*coth(A+sqrt(-mu)*xi);
(1/2)     /         (1/2)             \
(-mu)      coth\A + (-mu)      (x - 2 mu t)/
> u := a[0]+a[1]*P/(1+lambda*P)+a[-1]*(1+lambda*P)/P+b[0]*sqrt(sigma*(1+P^2/mu))/P+b[1]*sqrt(sigma*(1+P^2/mu))+b[-1]*sqrt(sigma*(1+P^2/mu))/P^2;
(1/2)
mu lambda (-6 a)

/         2    \      (1/2)     /         (1/2)             \
6 \mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/
+ ---------------------------------------------------------------------
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//
> Diff(u, t)+a*u^2*(Diff(u, x))+Diff(u, \$(x, 3));
/    /
| d  |                (1/2)
|--- |mu lambda (-6 a)
| dt |
\    \

/         2    \      (1/2)     /         (1/2)             \   \\     /
6 \mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/   ||     |
+ ---------------------------------------------------------------------|| + a |mu lambda
(1/2) /                (1/2)     /         (1/2)             \\||     |
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)////     \

(1/2)
(-6 a)

/         2    \      (1/2)     /         (1/2)             \   \
6 \mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/   |
+ ---------------------------------------------------------------------|^2
(1/2) /                (1/2)     /         (1/2)             \\|
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)///

/    /
| d  |                (1/2)
|--- |mu lambda (-6 a)
| dx |
\    \

/         2    \      (1/2)     /         (1/2)             \   \\
6 \mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/   ||
+ ---------------------------------------------------------------------|| +
(1/2) /                (1/2)     /         (1/2)             \\||
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)////

/ 3 /
|d  |                (1/2)
|-- |mu lambda (-6 a)
|   |
\   \

/         2    \      (1/2)     /         (1/2)             \   \\
6 \mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/   ||
+ ---------------------------------------------------------------------||
(1/2) /                (1/2)     /         (1/2)             \\||
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)////
> value(%);
/                                     2\
/         2    \   2 |        /         (1/2)             \ |
12 \mu lambda  + 1/ mu  \1 - coth\A + (-mu)      (x - 2 mu t)/ /
--------------------------------------------------------------------- -
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/
1                                    |
---------------------------------------------------------------------- \12
2
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/
/         2    \      (1/2)     /         (1/2)             \          2 |
\mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/ lambda mu  \1

2\\     /
/         (1/2)             \ ||     |                (1/2)
- coth\A + (-mu)      (x - 2 mu t)/ // + a |mu lambda (-6 a)
|
\

/         2    \      (1/2)     /         (1/2)             \   \
6 \mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/   |
+ ---------------------------------------------------------------------|^2
(1/2) /                (1/2)     /         (1/2)             \\|
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)///

/                           /                                     2\
|       /         2    \    |        /         (1/2)             \ |
|     6 \mu lambda  + 1/ mu \1 - coth\A + (-mu)      (x - 2 mu t)/ /
|- --------------------------------------------------------------------- +
|        (1/2) /                (1/2)     /         (1/2)             \\
|  (-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//
\

/
1                                    |  /
---------------------------------------------------------------------- \6 \mu
2
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/
2    \      (1/2)     /         (1/2)             \           |
lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/ lambda mu \1

\
2\\|
/         (1/2)             \ |||
- coth\A + (-mu)      (x - 2 mu t)/ //|
|
|
/

2
/                                     2\
/         2    \   2 |        /         (1/2)             \ |
12 \mu lambda  + 1/ mu  \1 - coth\A + (-mu)      (x - 2 mu t)/ /
- --------------------------------------------------------------------- +
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/
1                                   |   /
--------------------------------------------------------------------- \24 \mu
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

2 /
2    \   2     /         (1/2)             \  |
lambda  + 1/ mu  coth\A + (-mu)      (x - 2 mu t)/  \1

2\\
/         (1/2)             \ ||
- coth\A + (-mu)      (x - 2 mu t)/ // +

/
|
1                                    |
---------------------------------------------------------------------- \84
2
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/         2    \   2     /         (1/2)             \
\mu lambda  + 1/ mu  coth\A + (-mu)      (x - 2 mu t)/

2                  \
/                                     2\                   |
|        /         (1/2)             \ |       (1/2)       |
\1 - coth\A + (-mu)      (x - 2 mu t)/ /  (-mu)      lambda/

3
/                                     2\
/         2    \   3 |        /         (1/2)             \ |        2
36 \mu lambda  + 1/ mu  \1 - coth\A + (-mu)      (x - 2 mu t)/ /  lambda
- ------------------------------------------------------------------------- +
3
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/
|
1                                    |
---------------------------------------------------------------------- \36
4
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

/         2    \      (1/2)     /         (1/2)             \       3   3
\mu lambda  + 1/ (-mu)      coth\A + (-mu)      (x - 2 mu t)/ lambda  mu

3\
/                                     2\ |
|        /         (1/2)             \ | |
\1 - coth\A + (-mu)      (x - 2 mu t)/ / / +

/
|
1                                    |
---------------------------------------------------------------------- \72
3
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

2
/         2    \   3     /         (1/2)             \        2
\mu lambda  + 1/ mu  coth\A + (-mu)      (x - 2 mu t)/  lambda

2\
/                                     2\ |
|        /         (1/2)             \ | |
\1 - coth\A + (-mu)      (x - 2 mu t)/ / / -

/
1                                    |
---------------------------------------------------------------------- \24
2
(1/2) /                (1/2)     /         (1/2)             \\
(-6 a)      \1 + lambda (-mu)      coth\A + (-mu)      (x - 2 mu t)//

3        /
/         2    \   2     /         (1/2)             \         |
\mu lambda  + 1/ mu  coth\A + (-mu)      (x - 2 mu t)/  lambda \1

2\           \
/         (1/2)             \ |      (1/2)|
- coth\A + (-mu)      (x - 2 mu t)/ / (-mu)     /
> simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion
>
>
>
>
pls help

hi, I just want to calculate Adomian's polynomial but does not got  desire result,plz helpADMP.mw

## evaluation problem...

LE_EQ.mwWhat is problem with this programme,why it does'nt calculate the values but only shows the solution with integral sign instead of calculating it, there is also arising a problem in plots

## Lgrange multiplier...

lambdaaaaaa.mwI have calculated lambda(s), now I to substitute  its derivative(1st,2nd) in b[2], b[3]and b[4] in order to calculate the values of constants i.e C1,C2 and C3, plz help