Topic
Algebraic number
About: Algebraic number is a research topic. Over the lifetime, 20611 publications have been published within this topic receiving 315606 citations.
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01 Jan 1960
TL;DR: Divisibility congruence quadratic reciprocity and Quadratic forms some functions of number theory some diophantine equations Farey fractions and irrational numbers simple continued fractions primes and multiplicative number theory algebraic numbers the partition function the density of sequences of integers.
Abstract: Divisibility congruence quadratic reciprocity and quadratic forms some functions of number theory some diophantine equations Farey fractions and irrational numbers simple continued fractions primes and multiplicative number theory algebraic numbers the partition function the density of sequences of integers.
1,508 citations
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01 Jan 2003TL;DR: This chapter discusses computing roadmaps and Connected Components of Algebraic Sets, as well as the "complexity of Basic Algorithms" and "cylindrical Decomposition Algorithm".
Abstract: Algebraically Closed Fields- Real Closed Fields- Semi-Algebraic Sets- Algebra- Decomposition of Semi-Algebraic Sets- Elements of Topology- Quantitative Semi-algebraic Geometry- Complexity of Basic Algorithms- Cauchy Index and Applications- Real Roots- Cylindrical Decomposition Algorithm- Polynomial System Solving- Existential Theory of the Reals- Quantifier Elimination- Computing Roadmaps and Connected Components of Algebraic Sets- Computing Roadmaps and Connected Components of Semi-algebraic Sets
1,407 citations
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01 Jul 1982TL;DR: A new algorithm applicable to other functional forms, in particular to the summation of several gaussian density distributions is presented, created to model electron density maps of molecular structures but can be used for other artistically interesting shapes.
Abstract: The mathematical description of three dimensional surfaces usually falls in one of two classifications: parametric and algebraic. The form is defined as all points which satisfy some equation: F(x,y,z)=0. This form is ideally suited for image space shaded picture drawing, the pixel coordinates are substituted for x and y and the equation is solved for z. Algorithms for drawing such objects have been developed primarily for first and second order polynomial functions. This paper presents a new algorithm applicable to other functional forms, in particular to the summation of several gaussian density distributions. The algorithm was created to model electron density maps of molecular structures but can be used for other artistically interesting shapes.
1,057 citations
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TL;DR: In this paper, Dyson's systematic approach to the reduction of the Heisenberg $S$-Matrix into a sum of "graph" terms can be simplified, and a notation is introduced and an algebraic theorem is proved.
Abstract: Dyson's systematic approach to the reduction of the Heisenberg $S$-Matrix into a sum of "graph" terms can be simplified. A notation is introduced and an algebraic theorem is proved, which allow one to handle the reduction problem quite easily and in the same manner for any type of field.
1,048 citations