Tartalomjegyzék

Invariánsok annihilátorral (első próbálkozás)

Teljes Matlab script kiegészítő függvényekkel.

File: elso_probalkozas.m
Directory: 1_PhD_projects/01_demonstrative/01_invariansok
Author: Peter Polcz (ppolcz@gmail.com)

Created on 2019. March 31.

f = @(x1,x2) [
    -3*x1*x2
    0.5*x1
    ];

lfrs x1 x2
x = [ x1 ; x2 ];

Pi = @(x1,x2) [
    x1
    x2
    x1*x2
    ];
m = 3;

I = @(m) eye(m);

dx = f(x1,x2);

N_PI = @(x1,x2) [
    I(m)
    I(m)*x1
    I(m)*x2
    ];

d = @(lfr) diff(lfr,'x1') * dx(1) + diff(lfr,'x2') * dx(2);

d_N_PI_Pi = minlfr(d(N_PI(x1,x2)) * Pi(x1,x2) + N_PI(x1,x2) * d(Pi(x1,x2)));

C = P_constKerT_for_LFR(d_N_PI_Pi);

% itt tortenik a roundingolas !!
C_coeffs = rref(C);
C_coeffs = pround(C_coeffs, 5);

syms x1 x2 real
x = [ x1 ; x2 ];


N = C_coeffs * kron([1;x],eye(m))

% Invariánsok:

Invariansok = simplify(N * Pi)

Output:

 
N =
 
[   1, 3*x2, 0]
[ -x2,    0, 1]
[ -x2,   x1, 0]
 
 
Invariansok =
 
 3*x2^2 + x1
           0
           0
 

Published with MATLAB® R2018b, and sanitarized by BeautifulSoup (Python script using BSoup is written by Polcz).