Algorithms for algebraic computation

 

 
• Algebraic structures
  • Number domains
  • Algebraic expression domains
• Representation of algebraic structures
  • Representation of integers
  • Representation of polynomials
  • Representation of Expressions
• Arithmetic
  • Numeric vs symbolic arithmetic
  • Arithmetic of integers
  • Arithmetic of polynomials
• Simplification
  • Canonical simplification on algebraic domains
  • Complexity of expressions
• Greatest common divisor
  • GCD of integers
  • GCD of polynomials with rational coefficients
  • GCD of polynomials with integer coefficients
• Resultant
• Solving polynomial equations
• Differentiation
• Summation
  • Simple example
  • Gosper algorithm
  • Examples using the Gosper algorithm
• Integration
  • Integration of rational functions
  • Integration of elementary transcendental functions
  • Integration examples
• Ordinary differential equations
• Polynomial factorization
• Quantifier elimination
  • Example with QEPCAD program