Set complexity of construction of a regular polygon

نویسنده

  • Eugene Kogan
چکیده

Given a subset of $\mathbb C$ containing $x,y$, one can add $x + y,\,x - y,\,xy$ or (when $y\ne0$) $x/y$ or any $z$ such that $z^2=x$. Let $p$ be a prime Fermat number. We prove that it is possible to obtain from $\{1\}$ a set containing all the $p$-th roots of 1 by $12 p^2$ above operations. This result is different from the standard estimation of complexity of an algorithm computing the $p$-th roots of 1.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

متن کامل

The effect of language complexity and group size on knowledge construction: Implications for online learning

This  study  investigated  the  effect  of  language  complexity  and  group  size  on  knowledge construction in two online debates. Knowledge construction was assessed using Gunawardena et al.’s Interaction Analysis Model (1997). Language complexity was determined by dividing the  number  of  unique  words  by  total  words.  It  refers  to  the  lexical  variation.  The  results showed  that...

متن کامل

Embedding measure spaces

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

متن کامل

تعبیه ی هندسی درخت درنقاط داخل یک چندضلعی با حداقل تعداد خم

In this paper we consider to embed a tree T with N vertices on a set of N points inside a simple polygon on n vertices and the goal is to minimize the number of bends. The main idea of our algorithm is modeling the problem into graph matching problem and uses the graph matching algorithms. We apply the concept of error-correction transformation and find the appropriate cost function then we per...

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

عنوان ژورنال:
  • CoRR

دوره abs/1711.05807  شماره 

صفحات  -

تاریخ انتشار 2017