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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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