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`desing/rotation`

When the skewcover configuration variable is true the blowing up varieties are covered by chart which are obtained by first describing the blowing up center in some rotated coordinate system such that in a chart of the covering of the blowing up allows the elimination of maximal number of variables, i.e. the number of generators for the k-algebra of the new chart remains constant. The procedure applies such a rotation.

Input:

 

S

the variables of the original chart without DEP2V,

C

the generators of the nonsingular blowing up center with DEP2V being eliminated from them,

m

the codimension of the center,

SR1

(output parameter) the rotated variables,

SR2

(output parameter) the variables with respect to which we rotated the ones in SR1 (the unchanged ones),

SROT

(output parameter) the equations of the substitution of the rotation,

ISROT

(output parameter) the equations of the substitution of the inverse rotation.

Output:

The Gröbner basis of the center computed with elimination order for variables in SR2, after a rotation such that the projection to the subspace of the rotated variables is generically one-to-one.