Real algebraic numbers and polynomial systems of small degree

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Real algebraic numbers and polynomial systems of small degree

Based on precomputed Sturm-Habicht sequences, discriminants and invariants, we classify, isolate with rational points, and compare the real roots of polynomials of degree up to 4. In particular, we express all isolating points as rational functions of the input polynomial coefficients. Although the roots are algebraic numbers and can be expressed by radicals, such representation involves some r...

متن کامل

Comparing Real Algebraic Numbers of Small Degree

We study polynomials of degree up to 4 over the rationals or a computable real subfield. Our motivation comes from the need to evaluate predicates in nonlinear computational geometry efficiently and exactly. We show a new method to compare real algebraic numbers by precomputing generalized Sturm sequences, thus avoiding iterative methods; the method, moreover handles all degenerate cases. Our f...

متن کامل

Computations with real algebraic numbers of degree up to 4

Our motivation comes from computer-aided design and geometric modeling, where algorithms and predicates rely on computations of real algebraic numbers (usually of small degree). Predicates must be decided exactly in all cases, including degeneracies. In computational geometry there is a growing need for robust manipulation of curved objects (see [2] for a modern approach), since the critical po...

متن کامل

Algebraic Degree of Polynomial Optimization

Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, we prove that the optimality conditions always hold on optimizers, and the coordinates of optimizers are algebraic functions of the coefficients of the input polynomials. We also give a general formula for the algebraic degree of the opti...

متن کامل

Algebraic Geometry and Computer Vision : Polynomial Systems , Real and Complex

We review the diierent techniques known for doing exact computations on polynomial systems. Some are based on the use of Grr obner bases and linear algebra, others on the more classical resultants and its modern counterparts. Many theoretical examples of the use of these techniques are given. Furthermore, a full set of examples of applications in the domain of artiicial vision, where many const...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2008

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2008.09.009