Standard Bases and Primary Decomposition : The F4-Algorithm for Euclidean Rings and Efficient Algorithm for Primary Decomposition over Rings

ISBN-13: 9783846598528 / Angielski / Miękka / 2011 / 104 str.

Afshan Sadiq

Opis

The theory of standard bases in polynomial rings with coefficients in a ring with respect to local orderings is developed. Then the generalization of F4-Algorithm for polynomial rings with coefficients in Euclidean rings is given. This algorithm computes successively a Gröbner basis replacing the reduction of one single s-polynomial in Buchberger's algorithm by the simultaneous reduction of several polynomials. And finally we present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the rings. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama--Yokoyama resp. Eisenbud--Hunecke--Vasconcelos to extract primary ideals from pseudo-primary ideals.

O autorze

The author works as an Assistant professor of Mathematics in the Superior University Lahore, Pakistan. She has major interest in the Computational Aspects of Commutative Algebra. The author has given the more efficient algorithms for computing the Gröbner Basis and Primary Decomposition. She has been acting as member of SINGULAR team.