Algorithm to Compute Ordinary Continued Fractions for a Kind of Real Algebraic Numbers
Shen Jian
Abstract
Shen Jian
Abstract
For the real algebraic numbers of degree bigger than 2,there is no general effective algorithm to compute their ordinary continued fractions.In the paper,taking the degree 4 real algebraic number 2+3 as example,for a kind of real algebraic numbers,we give an algorithm to compute their ordinary continued fractions.At first,we state the principle of the algorithm,and point out that one can compute the continued fractions effectively until the computer runs over.At last,a computer program basing the algorithm is given,so is the computing result.
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For the real algebraic numbers of degree bigger than 2,there is no general effective algorithm to compute their ordinary continued fractions.In the paper,taking the degree 4 real algebraic number 2+3 as example,for a kind of real algebraic numbers,we give an algorithm to compute their ordinary continued fractions.At first,we state the principle of the algorithm,and point out that one can compute the continued fractions effectively until the computer runs over.At last,a computer program basing the algorithm is given,so is the computing result.
Key concepts: Algebraic number, Degree (music), Real algebraic geometry, Mathematics, Algebraic operation, Point (geometry), Algebraic solution, Fraction (chemistry)