I Residue or Modular Arithmetic. - 1. Introduction. - 2. Single-Modulus Residue Arithmetic. - 3. Multiple-Modulus Residue Arithmetic. - 4. Mapping Standard Residue Representations onto Integers. - 5. Single-Modulus Residue Arithmetic with Rational Numbers. - 6. The Forward Mapping and the Inverse Mapping. - 7. Multiple-Modulus Residue Arithmetic with Rational Numbers. - II Finite-Segment p-adic Arithmetic. - 1. Introduction. - 2. The Field of p-adic Numbers. - 3. Arithmetic in Qp. - 4. A Finite-Segment p-adic Number System. - 5. Arithmetic Operations on Hensel Codes. - 6. Removing a Leading Zero from a Hensel Code. - 7. Mapping a Hensel Code onto a Unique Order-N Farey Fraction. - III Exact Computation of Generalized Inverses. - 1. Introduction. - 2. Properties of g-inverses. - 3. Applications of g-inverses. - 4. Exact Computation of A+ if A Is a Rational Matrix. - 5. Failures of Residue Arithmetic and Precautionary Measures. - IV Integer Solutions to Linear Equations. - 1. Introduction. - 2. Theoretical Background. - 3. The Matrix Formulation of Chemical Equations. - 4. Solving the Homogeneous System. - 5. Solving a Non-Homogeneous System. - 6. Solving Interval Linear Programming Problems. - 7. The Solution of Systems of Mixed-Integer Linear Equations. - V Iterative Matrix Inversion and the Iterative Solution of Linear Equations. - 1. Introduction. - 2. The Newton-Schultz Method for the Matrix Inverse. - 3. Iterative Solution of a Linear System. - 4. Iterative Computation of g-inverses. - VI The Exact Computation of the Characteristic Polynomial of a Matrix. - 1. Introduction. - 2. The Algorithm Applied to Lower Hessenberg Matrices. Language: English