TAOCP 4.5.1: Fractions

Section 4.5.1 exercises: 9/9 solved.

9 items

Section 4.5.1. Fractions

Exercises from TAOCP Volume 2 Section 4.5.1: 9/9 solved.

#	Rating	Status	Time
1	[**]	verified	2m51s
2	[**]	verified	8m41s
3	[**]	verified	2m19s
4	[**]	verified	5m34s
5	[**]	verified	4m15s
6	▶ [**]	solved	9m14s
7	[**]	verified	3m51s
8	▶ [**]	verified	4m17s
9	[**]	verified	3m18s

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 1

A satisfactory method is based on continued reduction rather than cross multiplication, because the products $uv'$ and $vu'$ may overflow even when all four quantities fit in a single word.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 2

Let $d = \gcd(u, v)$.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 3

Let A=\gcd(u,v'), \qquad B=\gcd(u',v).

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 4

Let \frac{u}{u'},\qquad \frac{v}{v'} be fractions in canonical form, with

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 5

**Corrected Solution for Exercise 4.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 6

**Exercise 4.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 7

Let \frac{u}{u'},\qquad \frac{v}{v'} be the input fractions, with

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 8

The fractions $(1/0)$ and $(-1/0)$ arise naturally in the fraction representation scheme, because ordinary fractions are represented by pairs $(u,v)$ with $v>0$.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 4.5.1: Fractions ›

TAOCP 4.5.1 Exercise 9

Suppose $1 \le u' < 2^k$ and $1 \le v' < 2^k$.