Algebraic Expression Calculation System Based on Plane Dynamic Geometry System

Plane Conics in Algebraic Geometry

We first examine points and lines within projective spaces. Then we classify affine conics based on the classification of projective conics. Based on the parametrization of conics, we also prove two easy cases of Bézout’s Theorem. In the end we turn to the discussion of the space of conics and the notion of pencils of conics.

Developing A Distributed System For Algebraic Geometry

A Java Based On-line Handwriting Interface for an Intelligent Algebraic Calculation Tutoring System

This paper describes our on-line handwriting mathematical expression input interface for our Intelligent Algebraic Calculation Tutoring System (ACTS). It consists of a Java-based client, which receives user’s handwriting input and displays output, and a C-based server, which recognizes hand-written symbols. Our interface provides simple and easy mathematical expression input environment. Its di...

DynBCN A Constructive Geometric Constraint-based Dynamic Geometry System

One of the goals of the Grup d’Informàtica a l’Enginyeria of the Universitat Politècnica de Catalunya at Barcelona is to conduct research on geometric constraint solving and its applications. Here we offer to the community dynBCN, a software prototype of a dynamic geometry system based on a constructive geometric constraint solving technology. So far we are offering a jar Java file. In the near...

An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...