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7.5.2.0. findAuto
Procedure from library involut.lib (see involut_lib).
- Usage:
- findAuto(n); n an integer
- 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, given by a matrix, n-th power of which gives identity (i.e. unipotent matrix)
- Note:
- if n=0, a matrix, defining an automorphism is not assumed to be unipotent. For convenience, the full ideal of relations
idJ
and the initial matrix with indeterminates matD are exported in the output ring
Example:
| LIB "involut.lib";
def a = makeWeyl(1);
setring a; // this algebra is a first Weyl algebra
def X = findAuto(2);
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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