## Did anyone notice...

that in Kip Thorne's book Maple is mentioned through out ?

Kip Thorne and Roger Blandford : "Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics"

also, courtesy of Caltech in Chapter 24

## linearize the complex conjugate function partial d...

restart;
alias(u = u(x, z, t), f = f(x, z, t));
u, f
u := (f+sqrt(R))*exp(I*R*x);
/     (1/2)\
\f + R     / exp(I R x)
pde1 := I*(diff(u, z))+diff(u, x, x)+diff(u, t, t)+u*abs(u)*abs(u)-(u*abs(u)*abs(u))*abs(u)*abs(u);
/ d   \              / d  / d   \\
I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
\ dz  /              \ dx \ dx  //

/ d   \                /     (1/2)\  2
+ 2 I |--- f| R exp(I R x) - \f + R     / R  exp(I R x)
\ dx  /

/ d  / d   \\
+ |--- |--- f|| exp(I R x)
\ dt \ dt  //

2
/     (1/2)\                           2 |     (1/2)|
+ \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     |

4
/     (1/2)\                           4 |     (1/2)|
- \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     |

simplify(%);
/ d   \              / d  / d   \\
I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
\ dz  /              \ dx \ dx  //

/ d   \                 2
+ 2 I |--- f| R exp(I R x) - R  exp(I R x) f
\ dx  /

(5/2)              / d  / d   \\
- R      exp(I R x) + |--- |--- f|| exp(I R x)
\ dt \ dt  //

2
|     (1/2)|
+ exp(I R x - 2 Im(R x)) |f + R     |  f

2
|     (1/2)|   (1/2)
+ exp(I R x - 2 Im(R x)) |f + R     |  R

4
|     (1/2)|
- exp(I R x - 4 Im(R x)) |f + R     |  f

4
|     (1/2)|   (1/2)
- exp(I R x - 4 Im(R x)) |f + R     |  R
collect(%, exp(I*R*x));
/  (5/2)       / d   \      2       / d   \   / d  / d   \\
|-R      + 2 I |--- f| R - R  f + I |--- f| + |--- |--- f||
\              \ dx  /              \ dz  /   \ dx \ dx  //

/ d  / d   \\\
+ |--- |--- f||| exp(I R x)
\ dt \ dt  ///

2
|     (1/2)|
+ exp(I R x - 2 Im(R x)) |f + R     |  f

2
|     (1/2)|   (1/2)
+ exp(I R x - 2 Im(R x)) |f + R     |  R

4
|     (1/2)|
- exp(I R x - 4 Im(R x)) |f + R     |  f

4
|     (1/2)|   (1/2)
- exp(I R x - 4 Im(R x)) |f + R     |  R

## How can yeild two polynomial ideals I and J with ...

Hi Dears

I need some random zero-dimensional binomial ideals (20 ideals or more) with two, three, or four ... generators with 4 variables atmost. Then I want to regenerate each of them such that some of their generators are not binomial and the obtained ideals are equal to the first corresponding original binomial ideals. How can do I this automatically?

As a simple example let I be an ideal generated by {x-1, y-1, z-1} which is zero-dim. We can obtain J=<x-z, x+z-2, y+z-2> that is equal to I.

## result less than 1 ...

Dear all

I have the following code that  compute a parameter labeled by A.

I used some input vectors and my aim is to get A <1

A_less_than_one.mw

I tried to change some values of input vectors but unfortunattely I can not have A<1

Maybe I have a mistake in the code or something else