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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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            User manual for Singular version 3-0-1, October 2005, generated by texi2html.