Continued fraction/Arithmetic: Difference between revisions

My description follows [http://perl.plover.com/yak/cftalk/INFO/gosper.txt part of Gosper reproduced on perl.plover.com]. This document is text and unnumbered, you may wish to start by searching for "Addition, Multiplication, etc. of Two Continued Fractions" prior to reading the whole thing.

 

 

For these tasks continued fractions will be of the form:

so each may be described by the notation [<math>a_0 ; a_1, a_2, ..., a_n</math>]

 

During these tasks I shall use the function described in this task to create continued fractions from rational numbers.

 

So I can define arithmetic as operations on this matrix which make <math>a_{12}</math>, <math>a_1</math>, <math>a_2</math>, <math>b_{12}</math>, <math>b_1</math>, <math>b_2</math> zero and read the answer from <math>a</math> and <math>b</math>. This is more interesting when <math>N_1</math> and <math>N_2</math> are continued fractions, which is the subject of the following tasks.

 

Here we perform basic mathematical operations on a single continued fraction.

Here we perform basic mathematical operations on two continued fractions.

* Compare two continued fractions