\BOOKMARK [0][-]{chapter.1}{Integration}{}
\BOOKMARK [1][-]{section.1.1}{Rational Functions}{chapter.1}
\BOOKMARK [2][-]{subsection.1.1.1}{The full partial-fraction algorithm}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.2}{The Hermite reduction}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.3}{The Rothstein-Trager and Lazard-Rioboo-Trager algorithms}{section.1.1}
\BOOKMARK [1][-]{section.1.2}{Algebraic Functions}{chapter.1}
\BOOKMARK [2][-]{subsection.1.2.1}{The Hermite reduction}{section.1.2}
\BOOKMARK [2][-]{subsection.1.2.2}{Simple radical extensions}{section.1.2}
\BOOKMARK [2][-]{subsection.1.2.3}{Liouville's Theorem}{section.1.2}
\BOOKMARK [2][-]{subsection.1.2.4}{The integral part}{section.1.2}
\BOOKMARK [2][-]{subsection.1.2.5}{The logarithmic part}{section.1.2}
\BOOKMARK [1][-]{section.1.3}{Elementary Functions}{chapter.1}
\BOOKMARK [2][-]{subsection.1.3.1}{Differential algebra}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.2}{The Hermite reduction}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.3}{The polynomial reduction}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.4}{The residue criterion}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.5}{The transcendental logarithmic case}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.6}{The transcendental exponential case}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.7}{The transcendental tangent case}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.8}{The algebraic logarithmic case}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.9}{The algebraic exponential case}{section.1.3}
\BOOKMARK [0][-]{chapter.2}{Singular Value Decomposition}{}
\BOOKMARK [1][-]{section.2.1}{Singular Value Decomposition Tutorial}{chapter.2}
\BOOKMARK [0][-]{chapter.3}{Quaternions}{}
\BOOKMARK [1][-]{section*.2}{Preface}{chapter.3}
\BOOKMARK [1][-]{section.3.1}{Quaternions}{chapter.3}
\BOOKMARK [1][-]{section.3.2}{Vectors, and their Composition}{chapter.3}
\BOOKMARK [1][-]{section.3.3}{Examples To Chapter 1.}{chapter.3}
\BOOKMARK [1][-]{section.3.4}{Products And Quotients of Vectors}{chapter.3}
\BOOKMARK [1][-]{section.3.5}{Examples To Chapter 2.}{chapter.3}
\BOOKMARK [1][-]{section.3.6}{Interpretations And Transformations}{chapter.3}
\BOOKMARK [1][-]{section.3.7}{Examples to Chapter 3}{chapter.3}
\BOOKMARK [1][-]{section.3.8}{Axiom Examples}{chapter.3}
\BOOKMARK [0][-]{chapter.4}{Clifford AlgebraFl09}{}
\BOOKMARK [1][-]{section.4.1}{Introduction}{chapter.4}
\BOOKMARK [1][-]{section.4.2}{Clifford Basis Matrix Theory}{chapter.4}
\BOOKMARK [1][-]{section.4.3}{Calculation of the inverse of a Clifford number}{chapter.4}
\BOOKMARK [2][-]{subsection.4.3.1}{Example 1: Clifford \(2\)}{section.4.3}
\BOOKMARK [2][-]{subsection.4.3.2}{Example 2: Clifford \(3\)}{section.4.3}
\BOOKMARK [2][-]{subsection.4.3.3}{Example 3: Clifford \(2,2\)}{section.4.3}
\BOOKMARK [2][-]{subsection.4.3.4}{Conclusion}{section.4.3}
\BOOKMARK [0][-]{chapter.5}{Package for Algebraic Function Fields}{}
\BOOKMARK [0][-]{chapter.6}{Groebner Basis}{}
\BOOKMARK [0][-]{chapter.7}{Greatest Common Divisor}{}
\BOOKMARK [0][-]{chapter.8}{Polynomial Factorization}{}
\BOOKMARK [0][-]{chapter.9}{Cylindrical Algebraic Decomposition}{}
\BOOKMARK [0][-]{chapter.10}{Pade approximant}{}
\BOOKMARK [0][-]{chapter.11}{Schwartz-Zippel lemma and testing polynomial identities}{}
\BOOKMARK [0][-]{chapter.12}{Chinese Remainder Theorem}{}
\BOOKMARK [0][-]{chapter.13}{Gaussian Elimination}{}
\BOOKMARK [0][-]{chapter.14}{Diophantine Equations}{}
\BOOKMARK [0][-]{chapter.15}{Index}{}
