restart;
Give the path to the package txt file. For example (linux):
read "/home/ekaterina/Desktop/work/package/lpdo_.txt";
Declare independent variables:
LPDO__set_vars([x,y]):
Use PDEtools package for pretty display of derivatives (can be skipped):
with(PDEtools): declare(a(x,y),b(x,y),c(x,y),p(x,y),q(x,y),r(x,y),g(x,y),u(x,y));
KigtSSJhRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJiRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJjRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJwRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJxRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJyRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJnRzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
KigtSSJ1RzYiNiRJInhHRiVJInlHRiUiIiJJOXdpbGx+bm93fmJlfmRpc3BsYXllZH5hc0dGJUYpRiRGKQ==
Create an operator:
L:= Create_LPDO_from_coeff([c(x,y),a(x,y),b(x,y)]): LPDO__print(L);
NiQ3JCIiIUYkLUkiY0c2IjYkSSJ4R0YnSSJ5R0Yn
NiQ3JCIiIiIiIS1JImFHNiI2JEkieEdGKEkieUdGKA==
NiQ3JCIiISIiIi1JImJHNiI2JEkieEdGKEkieUdGKA==
Pretty print:
LPDO__print(L);
NiQ3JCIiIUYkLUkiY0c2IjYkSSJ4R0YnSSJ5R0Yn
NiQ3JCIiIiIiIS1JImFHNiI2JEkieEdGKEkieUdGKA==
NiQ3JCIiISIiIi1JImJHNiI2JEkieEdGKEkieUdGKA==
Find degree of L and its characteristic symbol:
LPDO__degree(L); LPDO__Symbol(L);
IiIi
LCYqJi1JImFHNiI2JEkieEdGJkkieUdGJiIiIkkiWEdGJkYqRioqJi1JImJHRiZGJ0YqSSJZR0YmRipGKg==
Set the value of some coefficient of an LPDO.
Below we set the value of the coefficient at Dxy (which was zero before) as 1.
LPDO__set_value(L,1,[1,1]):
Now let us set the value of the coefficient at Dy as zero.
LPDO__set_value(L,0,[0,1]): LPDO__print(L);
NiQ3JCIiIUYkLUkiY0c2IjYkSSJ4R0YnSSJ5R0Yn
NiQ3JCIiIiIiIS1JImFHNiI2JEkieEdGKEkieUdGKA==
NiQ3JCIiIkYkRiQ=
The degree of L and its characteristic symbol have changed:
LPDO__degree(L); LPDO__Symbol(L);
IiIj
KiZJIlhHNiIiIiJJIllHRiRGJQ==
N:= Create_LPDO_from_coeff([r(x,y),q(x,y),1]): LPDO__print(N);
NiQ3JCIiIUYkLUkickc2IjYkSSJ4R0YnSSJ5R0Yn
NiQ3JCIiIiIiIS1JInFHNiI2JEkieEdGKEkieUdGKA==
NiQ3JCIiISIiIkYl
Apply to a function, and by this obtain the correponding partial differential equation.
LPDO__apply(N,u(x,y));
LCgqJi1JInJHNiI2JEkieEdGJkkieUdGJiIiIi1JInVHRiZGJ0YqRioqJi1JInFHRiZGJ0YqLUklZGlmZkclKnByb3RlY3RlZEc2JEYrRihGKkYqLUYxNiRGK0YpRio=
Compute the commutator [N,L]:
F:= LPDO__minus(LPDO__mult(N,L),LPDO__mult(L,N)): LPDO__print(F);
NiQ3JCIiIUYkLCoqJi1JInFHNiI2JEkieEdGKUkieUdGKSIiIi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJjR0YpRipGK0YtRi0tRi82JEYyRixGLSomLUkiYUdGKUYqRi0tRi82JC1JInJHRilGKkYrRi0hIiItRi82JEY5RixGPQ==
NiQ3JCIiIiIiISwsKiYtSSJxRzYiNiRJInhHRipJInlHRipGJC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJhR0YqRitGLEYkRiQtRi82JEYyRi1GJComRjJGJC1GLzYkRihGLEYkISIiLUYvNiQtSSJyR0YqRitGLUY5LUYvNiRGN0YtRjk=
NiQ3JCIiISIiIiwkLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInJHNiI2JEkieEdGLUkieUdGLUYvISIi
NiQ3JCIiIyIiISwkLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInFHNiI2JEkieEdGLUkieUdGLUYwISIi
NiQ3JCIiIkYkLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkicUc2IjYkSSJ4R0YsSSJ5R0YsRi4hIiI=
Compute the gauge transformation of LPDO F with function exp(alpha(x,y)):
F_conj:=LPDO__conj(F,exp(alpha(x,y))): LPDO__print(F_conj);
NiQ3JCIiIUYkLD4qJi1JInFHNiI2JEkieEdGKUkieUdGKSIiIi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJjR0YpRipGK0YtRi0tRi82JEYyRixGLSomLUkiYUdGKUYqRi0tRi82JC1JInJHRilGKkYrRi0hIiItRi82JEY5RixGPSooLUYvNiQtSSZhbHBoYUdGKUYqRitGLUYnRi0tRi82JEY3RitGLUYtKiZGQUYtLUYvNiRGN0YsRi1GLSooRkFGLUY3Ri0tRi82JEYnRitGLUY9KiZGQUYtLUYvNiRGO0YsRi1GPSomRkFGLS1GLzYkRktGLEYtRj0qJkY5Ri0tRi82JEZDRixGLUY9KiYtRi82JEYnRixGLS1GLzYkRkFGK0YtRj0qJkZXRi1GQSIiI0Y9KiZGS0YtLUYvNiRGQUYsRi1GPSooRktGLUZURi1GQUYtRj0=
NiQ3JCIiIiIiISwwKiYtSSJxRzYiNiRJInhHRipJInlHRipGJC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJhR0YqRitGLEYkRiQtRi82JEYyRi1GJComRjJGJC1GLzYkRihGLEYkISIiLUYvNiQtSSJyR0YqRitGLUY5LUYvNiRGN0YtRjkqJi1GLzYkRihGLUYkLUYvNiQtSSZhbHBoYUdGKkYrRixGJCEiIyomRjdGJC1GLzYkRkVGLUYkRjk=
NiQ3JCIiISIiIiwmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInJHNiI2JEkieEdGLUkieUdGLUYvISIiKiYtRig2JC1JInFHRi1GLkYvRiUtRig2JC1JJmFscGhhR0YtRi5GL0YlRjE=
NiQ3JCIiIyIiISwkLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInFHNiI2JEkieEdGLUkieUdGLUYwISIi
NiQ3JCIiIkYkLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkicUc2IjYkSSJ4R0YsSSJ5R0YsRi4hIiI=
Compute the formal transpose of the LPDO F_conj:
TR:=LPDO__transpose(F_conj): LPDO__print(TR);
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
NiQ3JCIiIiIiISwwLUklZGlmZkclKnByb3RlY3RlZEc2JC1GKDYkLUkicUc2IjYkSSJ4R0YvSSJ5R0YvRjFGMiEiIyomRi1GJC1GKDYkLUkiYUdGL0YwRjFGJCEiIi1GKDYkRjdGMkY5KiZGN0YkRitGJEYkLUYoNiQtSSJyR0YvRjBGMkYkKiYtRig2JEYtRjJGJC1GKDYkLUkmYWxwaGFHRi9GMEYxRiQiIiMqJkYrRiQtRig2JEZGRjJGJEYk
NiQ3JCIiISIiIiwoLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInJHNiI2JEkieEdGLUkieUdGLUYvRiUqJi1GKDYkLUkicUdGLUYuRi9GJS1GKDYkLUkmYWxwaGFHRi1GLkYvRiVGJS1GKDYkRjJGLyEiIg==
NiQ3JCIiIyIiISwkLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInFHNiI2JEkieEdGLUkieUdGLUYwISIi
NiQ3JCIiIkYkLCQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkicUc2IjYkSSJ4R0YsSSJ5R0YsRi4hIiI=