Computational Algebra (MT5313)

None

• Computational Commutative Algebra 1
  M. Kreuzer, L, Robbiano
• Ideal Varieties And Algorithm
  D. Cox, L. O’Shea, Undergraduate Texts In Mathematics, Springer-Verlag,

A new field of mathematics, computational algebra, has been steadily growing significantly since past few decades. This field grew out of algorithms for computing Groebner bases of the ideal in multivariate polynomial rings. The focus of this course is to introduce these algorithms and their optimizations so that students can use these techniques and protocols for solving problems in the disciplines such as engineering, robotics, algebraic geometry and cryptography.

1-      Foundation

Polynomial rings, ideals, integral domain, monomials, term ordering, division algorithm, Varieties, examples and exercises.

2-      Groebner Bases

Monomial Order, Lex, DegLex, DegRevLex, Division Algorithm in multivariable polynomial rings, Monomial Ideals, Dickson’s Lemma, Hilbert Basis Theorem, Buchberger Algorithm, Computational Aspects

3-      Applications

Solution to Ideal Membership Problem, Eliminations, Polynomial System Solving, Intersection of Ideals