Companions of fields of rational and real algebraic numbers

On approximation of real numbers by real algebraic numbers

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

Questions about algebraic properties of real numbers

This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w.r.t. {+, −, ×, >, ≥} in a constructive setting. Introduction This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w....

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...

Construction of Real Algebraic Numbers in Coq

This paper shows a construction in Coq of the set of real algebraic numbers, together with a formal proof that this set has a structure of discrete Archimedean real closed field. This construction hence implements an interface of real closed field. Instances of such an interface immediately enjoy quantifier elimination thanks to a previous work. This work also intends to be a basis for the cons...