How to resolve the algorithm Averages/Pythagorean means step by step in the GAP programming language

Published on 12 May 2024 09:40 PM
#Gap

How to resolve the algorithm Averages/Pythagorean means step by step in the GAP programming language

Table of Contents

Problem Statement

Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive). Show that

A (

x

1

, … ,

x

n

) ≥ G (

x

1

, … ,

x

n

) ≥ H (

x

1

, … ,

x

n

)

{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}

for this set of positive integers.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Averages/Pythagorean means step by step in the GAP programming language

Source code in the gap programming language

# The first two work with rationals or with floats
# (but bear in mind that support of floating point is very poor in GAP)
mean := v -> Sum(v) / Length(v);
harmean := v -> Length(v) / Sum(v, Inverse);
geomean := v -> EXP_FLOAT(Sum(v, LOG_FLOAT) / Length(v));

mean([1 .. 10]);
# 11/2
harmean([1 .. 10]); 
# 25200/7381

v := List([1..10], FLOAT_INT);;
mean(v);
# 5.5
harmean(v); 
# 3.41417
geomean(v);
# 4.52873

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