How to resolve the algorithm Averages/Pythagorean means step by step in the Oz programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Averages/Pythagorean means step by step in the Oz 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 Oz programming language
Source code in the oz programming language
declare
%% helpers
fun {Sum Xs} {FoldL Xs Number.'+' 0.0} end
fun {Product Xs} {FoldL Xs Number.'*' 1.0} end
fun {Len Xs} {Int.toFloat {Length Xs}} end
fun {AMean Xs}
{Sum Xs}
/
{Len Xs}
end
fun {GMean Xs}
{Pow
{Product Xs}
1.0/{Len Xs}}
end
fun {HMean Xs}
{Len Xs}
/
{Sum {Map Xs fun {$ X} 1.0 / X end}}
end
Numbers = {Map {List.number 1 10 1} Int.toFloat}
[A G H] = [{AMean Numbers} {GMean Numbers} {HMean Numbers}]
in
{Show [A G H]}
A >= G = true
G >= H = true
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