Course title
V05507003
Computer Algebra

 idogawa tomoyuki Click to show questionnaire result at 2018
Course description
Computer algebra, which is also called formula manipulation, treats each mathematical expression as a symbolic sequence, and perform some mathematical operations such as arithmetics, expansions/factorizations of polynomials, and even differentiations and integrations exactly in mathematical formulas. The central objects dealt by computer algebra are numbers and polynomials, and there are specific algorithms such as finding common factors of plural polynomials. At first, some of these algorithms will be talked as an introduction of computer algebra. After that, the concept of Groebner basis, which plays an important role in solving a system of algebraic equations, ideal membership problem, and so on, will be talked and some central topics of modern computer algebraic research will be discussed.
Purpose of class
To learn basic concepts on computer algebra.
Goals and objectives
  1. To recognize that calculation by computer is not limited to numerical calculation.
  2. To be able to treat polynomials as computational algebraic.
  3. To understand the concept of Groebner basis and to be able to embark the basic/applied research on computer algebra.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction to computer algebra systems Research on computational algebra systems in advance. 190minutes
2. Review of algebra Review of the subjects related to algebra. 190minutes
3. Eucledian algorithm Review the last lecture. 190minutes
4. Resultant and extended Eucledian algorithm Review the last lecture. 190minutes
5. Subresultant and polynomial remainder sequence (PRS) Review the last lecture. 190minutes
6. Improved PRS algorithm Review the last lecture. 190minutes
7. Modular algorithm (1): Chinese remainder theorem Review the last lecture. 190minutes
8. Modular algorithm (2): reconstruction of rational numbers and polynomials Review the last lecture. 190minutes
9. Modular algorithm (3):
Hensel lifting 		Review the last lecture. 190minutes
10. Factorization of polynomial (1): square free decomposition Review the last lecture. 190minutes
11. Factorization of polynomial (2): one variable polynomial over finite field Review the last lecture. 190minutes
12. Factorization of polynomial (3): one variable polynomial over rational number field Review the last lecture. 190minutes
13. Groebner basis (1): definition and Buchberger algorithm Review the last lecture. 190minutes
14. Groebner basis (2): some applications (system of algebraic equations, integer programing problem) Review the total lectures. 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Term-end assignment Exercises Total.
1. 0% 10% 10%
2. 30% 20% 50%
3. 30% 10% 40%
Total. 60% 40% -
Evaluation method and criteria
Term-end assignment (60%) and exercises (40%).
Textbooks and reference materials
No textbook.
Prerequisites
Students are expected to have taken subjects related to algebraic, e.g., "Fundamental Algebra", "Algebra 1", and so on.
Office hours and How to contact professors for questions
  • Tuesday 12:35 -- 13:05.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Tue Sep 01 04:22:16 JST 2020