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7.5.2.0. findInvo
Procedure from library involut.lib (see involut_lib).
- Usage:
- findInvo();
- Return:
- a ring containing a list L of pairs, 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:
- computed the ideal of linear involutions 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 "involut.lib";
def a = makeWeyl(1);
setring a; // this algebra is a first Weyl algebra
def X = findInvo();
setring X; // ring with new variables, corr. to unknown coefficients
L;
==> [1]:
==> [1]:
==> _[1]=a11+a22
==> _[2]=a12*a21+a22^2-1
==> [2]:
==> _[1,1]=-a22
==> _[1,2]=a12
==> _[2,1]=a21
==> _[2,2]=a22
// look at the matrix in the new variables, defining the linear involution
print(L[1][2]);
==> -a22,a12,
==> a21, a22
L[1][1]; // where new variables obey these relations
==> _[1]=a11+a22
==> _[2]=a12*a21+a22^2-1
| findInvoDiag, involution
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