Dynamic Newton–Puiseux Theorem
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چکیده
A constructive version of Newton–Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular algebras over the base field and the expansions are given as formal power series over these algebras. 2000 Mathematics Subject Classification 03F65, 14Q05,68W30 (primary); 12Y05, 12E05, 12F05 (secondary)
منابع مشابه
Dynamic Newton–Puiseux Theorem
A constructive version of Newton–Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regula...
متن کاملDynamic Newton-Puiseux theorem
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansion of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular...
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تاریخ انتشار 2014