… of the 2009 international symposium on …, Jan 1, 2009
In this paper, we propose an efficient method to solve polynomial systems whose equations are lef... more In this paper, we propose an efficient method to solve polynomial systems whose equations are left invariant by the action of a finite group G. The idea is to simultaneously compute a truncated SAGBI-Gröbner bases (a generalisation of Gröbner bases to ideals of subalgebras of polynomial ring) and a Gröbner basis in the invariant ring K[σ1, . . . , σn] where σi is the i-th elementary symmetric polynomial.
The link between Gröbner basis and linear algebra was described by Lazard where he realized the G... more The link between Gröbner basis and linear algebra was described by Lazard where he realized the Gröbner basis computation could be archived by applying Gaussian elimination over Macaulay's matrix .
… of the 2009 international symposium on …, Jan 1, 2009
In this paper, we propose an efficient method to solve polynomial systems whose equations are lef... more In this paper, we propose an efficient method to solve polynomial systems whose equations are left invariant by the action of a finite group G. The idea is to simultaneously compute a truncated SAGBI-Gröbner bases (a generalisation of Gröbner bases to ideals of subalgebras of polynomial ring) and a Gröbner basis in the invariant ring K[σ1, . . . , σn] where σi is the i-th elementary symmetric polynomial.
The link between Gröbner basis and linear algebra was described by Lazard where he realized the G... more The link between Gröbner basis and linear algebra was described by Lazard where he realized the Gröbner basis computation could be archived by applying Gaussian elimination over Macaulay's matrix .
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