## maple for theoretical physicists...

Could you tell about manual (book) at maple which tells how to make calculations in quantum field theory (Grassmann algebra, a Lie algebra, producing functional, fermionic determinants) and high-temperature quantum field theory (partition functions, thermodynamic potentials)?

## How to compute an extension of finite field?...

Hi EveryOne!

In the answer of the question "How to find roót of polynomial in finite field and extension finite field ", @Carl Love helped me to find roots of polynimial in finite field and extension finite field (At URL http://www.mapleprimes.com/view.aspx?sf=215097_Answer/Primfield.mw OR http://www.mapleprimes.com/view.aspx?sf=215285_Answer/Matrix_powers_finite_field.mw)

However, with matrix M: =< x^4+x^3+x^6+x^7+x, 1+x^2+x^4+x^5+x^6, 1+x+x^2+x^3, x^7+x^6+x^5+x^4;

x^7+x^5+x^4+x^3, x^6+x^4+x^2+1, x^4+x^3+x^6+x^7+x^2+x+1, 1+x^2+x^3+x^4+x^5;

x^7+x^5+x^2, x^7+x^5+x^3+x^2+1, x^2+x+x^6, x^2+x^3+x^5;
x^4+x^3+x^6+1, 1+x^2+x^3+x^4, x^6+x^5+x^4+x^3, x^7+x^3 >;

and GF(2^8)/f(x)=x^8 + x^7 +x^6 + x +1 (i.e ext1:= Z^8+Z^7+Z^6+Z+1), then program Primfield.mw don't run!

## How to convert to matrix over finite field?...

Hi all

I need to convert int matrix into matrix over finite field.

E.g: Convert inform integer number

A := <140, 155, 162, 64;

218, 12, 245, 50;

36, 251, 34, 253;

171, 251, 184, 37>;

into B = <x^7+x^3+x^2,x^7+x^4+x^3+x+1,x^7+x^5+x, x^6;

x^7+x^6+x^4+x^3+x, x^3+x^2, x^7+x^6+x^5+x^4+x^2+1, x^5+x^4+x;

x^5+x^2, x^7+x^6+x^5+x^4+x^3+x+1, x^5+x, x^7+x^6+x^5+x^4+x^3+x^2+1;

x^7+x^5+x^3+x+1, x^7+x^6+x^5+x^4+x^3+x+1, x^7+x^5+x^4+x^3, x^5+x^2+1>;

(Matrix B over finite field GF(2^8)/f(x) =x^8 + x^6 +x^5 +x^3 +1)

Thanks alot.

## Flux through a cone...

I'm trying to calculate flux through a cone but gets the following:

Flux(VectorField(`<,>`(x, y, z), cartesian[x, y, z]), Surface(`<,>`(x,y,z), x^2+y^2<=2*a,z = 2*a-sqrt(x^2+y^2)))
Error, (in VectorCalculus:-Flux) error with surface input

## 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.

## Obtaining the splitting field...

I am trying to obtain the splitting field of New_polyq. evala@AFactor did not complete. Applying splitting sequentially produced independent extensions from the first 2 (3?) factors. evala@Indep did not complete for the union of all 4 extensions.

What libraries would handle this better?

restart; _EnvExplicit:=false;interface(labelwidth=200);
Rho_polys:=rho[3,1]^3-2, rho[3,2]^2+rho[3,2]*rho[3,1]+rho[3,1]^2, 2*rho[6,1]^3+rho[6,1]^6-2, rho[12,1]^2+rho[6,1]^2-1, 2*rho[12,2]^2-rho[6,1]^2*rho[3,2]*rho[3,1]^2-2*rho[6,1]^2-2;
New_poly:=1/16*(-rho[6,1]^4*rho[3,2]*rho[3,1]-2-rho[3,1]^2*rho[6,1]^4-2*rho[6,1]*rho[3,2]*rho[3,1]-2*rho[3,1]^2*rho[6,1]+2*lambda^2)*(rho[6,1]^4*rho[3,2]*rho[3,1]+2*rho[6,1]*rho[3,2]*rho[3,1]-2+2*lambda^2)*(-2+2*rho[3,1]^2*rho[6,1]+rho[3,1]^2*rho[6,1]^4+2*lambda^2)*(-2+rho[6,1]^2*rho[3,2]*rho[3,1]^2+2*lambda^2);
sol:=solve({Rho_polys});
alias(op(sol));
New_polyq:=subs(sol,New_poly);

## Polynomial ideals over Q(sqrt(2))...

How to create polynomial ideals over algebraic extensions of the field of  rationals Q with Maple?
The Maple help to PolynomialIdeals
"All package commands support computations over the rational numbers, algebraic number fields, rational function fields, and algebraic function fields, as well as finite fields. Coefficients from algebraic extension fields can be specified using radicals or RootOfs"
is too poor. I also don't find any example on this topic in examples,PolynomialIdeals.

## how to plot a scalar field?...

given a scalar field function f(x,y,z), how to plot it in maple?

I can't find a suitable command, if I missed, please tell me.

## Quantum Electrodynamics with Maple...

Hi!

I was trying to obtain the field equations for the QED Lagrangian and I was not sucessfull.

All my calculations are equal to 0.

Can someone give a hand?

QED.mw

Thanks a lot.

## einstein-hilbert action...

guys, is there any possibility to obtain field equations of einstein-hilbert action?

best regards

## Analyzing a differential equation system with vary...

Hi there,
I have a set of differential equations whose solution, Jacobian matrix and its eigenvalues, direction field, phase portrait and nullclines, need to be computed.

Each of the equations has a varying parameter.

I know how to get the above for a single parameter value, but when I set a range of values for the parameters, Maple is not able to handle all cases as I would expect: solving the differential equation system:

eq1 := x*(1.6*(1-(1/100)*x)-phi*y)
eq2 := (x/(15+x)-0.3e-1*x-.4)*y+.6+theta
desys := [eq1, eq2];
vars := [x, y];

Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {-600*y+(Array(1..2, {(1) = 8400, (2) = 15900})), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0})}

The equations are the following:
de1 := diff(x(t), t) = x(t)*(1.6*(1-(1/100)*x(t))-phi*y(t));
de2 := diff(y(t), t) = (x(t)/(15+x(t))-0.3e-1*x(t)-.4)*y(t)+.6+theta

the parameters being:
phi:=[0 0.5 1 1.5 2]
theta:=[5. 10.]

How can I handle the situation so that Maple computes each of the above for each combination of the parameters?

I would like to avoid using two for loops and having to store all results in increasingly bigger and complicated arrays.

The worksheet at issue is this: MaplePrimes_Tumour_model_phi_theta_variation.mw

Thanks,
jon

## Vector Field to "normal" function...

Hello everyone.

I have a vector field in 2d-cartesian coordinates which I would like to convert to a "normal" function, that is f(x, y) where when you put x and y in, you get the magnitude of the vector at that point.

Example vector field:

This one is very hard to handle by hand which is why I want to use Maple for it.

I tried VectorCalculus[Norm] but it gave me this:

## Finding the rank of a matrix over a field of order...

The question of how to do matrix operations over a finite field with p^k elements k>1 was raised in this forum in April 27 2010. I wonder if there has been any progress since then for recent versions of Maple.

I am expecially interested in finding the rank of a matrix over a field of order p^k, k > 1.

## error on plotting vector field...

Hello, I have a problem in plotting the vector field of dx/dt=sinx/sint

It shows me an error:

Error, (in DEtools/dfieldplot) unable to evaluate function `sin(x)` in evalhf

Dunno how to fix it

Here is my code:

DE := [diff(x(t), t) = sin(x)(t)/sin(t)];
with(DEtools):
DC:=[sin(x)/sin(t),.1]:
dfieldplot(DE, x(t), t = -2 .. 2, x = -1 .. 2, arrows = medium, title = 'Diff', color = DC);

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