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7.5.2.0. findAuto
Procedure from library involution.lib (see involution_lib).
- Usage:
- findAuto();
- Return:
- a ring together with a list of pairs L, where
L[i][1] = Groebner Basis of an i-th associated prime,
L[i][2] = matrix, defining a linear map, with entries, reduced with respect to L[i][1]
- Purpose:
- computes the ideal of linear automorphisms of the basering
- Note:
- for convenience, the full ideal of relations
idJ
and the initial matrix with indeterminates matD are exported in the output ring
Example:
| LIB "involution.lib";
def a = makeWeyl(1);
setring a; // this algebra is a first Weyl algebra
def X = findAuto();
setring X; // ring with new variables - unknown coefficients
// look at matrices, defining linear automorphisms:
print(L[1][2]); // a first one: we see it is constant
==> 1,0,
==> 0,1
print(L[2][2]); // and a second possible matrix; it is constant too
==> -1,0,
==> 0, -1
L; // let us take a look on the whole list
==> [1]:
==> [1]:
==> _[1]=a22-1
==> _[2]=a21
==> _[3]=a12
==> _[4]=a11-1
==> [2]:
==> _[1,1]=1
==> _[1,2]=0
==> _[2,1]=0
==> _[2,2]=1
==> [2]:
==> [1]:
==> _[1]=a22+1
==> _[2]=a21
==> _[3]=a12
==> _[4]=a11+1
==> [2]:
==> _[1,1]=-1
==> _[1,2]=0
==> _[2,1]=0
==> _[2,2]=-1
| findInvo
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