Xideal Grr Obner Bases for Exterior Algebra

1 Description The method of Grr obner bases in commutative polynomial rings introduced by Buchberger (e.g. 1]) is a well-known and very important tool in polynomial ideal theory, for example in solving the ideal membership problem. XIDEAL extends the method to exterior algebras using algorithms from 2]. There are two main departures from the commutative polynomial case. First, owing to the non-commutative product in exterior algebras, ideals are no longer automatically two-sided, and it is necessary to distinguish between left and right ideals. Secondly, because there are zero divisors, connu-ent reduction relations are no longer suucient to solve the ideal membership problem: a unique normal form for every polynomial does not guarantee that all elements in the ideal reduce to zero. This leads to two possible deenitions of Grr obner bases as pointed out by Stokes 3]. XIDEAL constructs Grr obner bases for solving the left ideal membership problem: Grr obner left ideal bases or GLIBs. For graded ideals, where each form is homogeneous in degree, the distinction between left and right ideals