Part II: Polynomials and Expressions

Manipulating expressions is one of the core tasks of computer algebra. The goal of this part is to introduce the main tools and concepts to use SageMath to manipulate expressions.

• Lecture 11: Univariate and Multivariate Polynomials
  • Polynomials as Expressions
  • Univariate Polynomials
  • Multivariate Polynomials
  • Assignments
• Lecture 12: Rational Functions and Conversions
  • Rational Expressions
  • Conversions
  • Assignments
• Lecture 13: Representation of Expressions
  • Expression Trees
  • Evaluation of Expressions
  • Assignments
• Lecture 14: Substitution, Expansion, and Factorization
  • Substitution
  • Expansion
  • Factorization
  • Assignments
• Lecture 15: Normalizing Expressions
  • Normal and Canonical Form
  • Rewriting Multivariate Polynomials
  • A Numerical Test on Equality
  • Assignments
• Lecture 16: Review of the First 15 Lectures
• Lecture 17: the First Midterm Exam
  • Questions on the Spring 2017 First Midterm Exam
  • Questions on the Fall 2018 First Midterm Exam
  • Questions on the Spring 2019 First Midterm Exam
  • Questions on the Summer 2022 First Midterm Exam