No immediate solution

Preben Alsholm — Mon, 09 Jul 2012 18:36:14 Z

I don't see any immediate solution, but the following at least works.

C:=Matrix([[D[1],0,D[2]],[0,D[2],D[1]]]);
B:=;
freeze~(B);
C.%;
evalindets(%,`*`,apply@op);
thaw~(%);
%;

#Putting this into a procedure:

`&p`:=proc(d,v) local a,b;
   a:=d.freeze~(v);
   b:=thaw~(evalindets(a,`*`,apply@op));
   eval(b)
end proc;

C &p B;

#####Later addition:
In the more general case where your differential operators in the matrix are polynomials in D[1] and D[2] you will have to freeze C too:

Take as a simple example the matrix A below which has the linear differential operator T as one of its elements:

T:=-3*D[1]+7*D[2]+(f->6*f);
#Testing it on a function g:
T(g);
A:=Matrix([[T,0,D[2]],[0,D[2],D[1]]]);
#Now just modify the procedure above so that A will be frozen too:
`&p`:=proc(d,v) local a,b;
   a:=freeze~(d).freeze~(v);
   b:=thaw~(evalindets(a,`*`,apply@op));
   eval(b)
end proc;

A &p B;

MaplePrimes - answers and comments on Question, Implementing Differential Operator applied to Matrix

No immediate solution