## Archive for power

## battery recharged!

Posted in pictures, Travel with tags Amazon, battery, DIY, HP EliteBook, laptop, power on September 10, 2022 by xi'an## midnight run

Posted in Running, Travel with tags adaptivity, Banff, Canada, convenience, midnight run, midnight sun, power, UBC, Vancouver on December 8, 2019 by xi'an## Le Monde puzzle [#1114]

Posted in Kids, R with tags brute-force solution, cube, Le Monde, mathematical puzzle, perfect square, power, R on October 16, 2019 by xi'an**A**nother very low-key arithmetic problem as Le Monde current mathematical puzzle:

32761 is 181² and the difference of two cubes, which ones? And 181=9²+10², the sum of two consecutive integers. Is this a general rule, i.e. the root z of a perfect square that is the difference of two cubes is always the sum of two consecutive integers squared?

The solution proceeds by a very dumb R search of cubes, leading to

34761=105³-104³

The general rule can be failed by a single counter-example. Running

sol=0;while(!sol){ x=sample(2:1e3,1) y=sample(1:x,1)-1 sol=is.sqr(z<-x^3-y^3) z=round(sqrt(z)) if (sol) sol=(trunc(sqrt(z/2))^2+ceiling(sqrt(z/2))^2!=z)}

which is based on the fact that, if z is the sum of two consecutive integers squared, a² and (a+1)² then

2 a²<z<2 (a+1)²

Running the R code produces

x=14, y=7

as a counter-example. (Note that, however, if the difference of cubes of two consecutive integers is a square, then this square can be written as the sum of the squares of two different integers.) Reading the solution in the following issue led me to realise I had missed the consecutive in the statement of the puzzle!

## How many subjects? [not a book review]

Posted in Books, pictures, Statistics with tags Brett Kavanaugh, Christine Blasey, power, statistical significance, statistical tests, tests, textbook on September 24, 2018 by xi'an## take those hats off [from R]!

Posted in Books, Kids, R, Statistics, University life with tags exponent notation, exponentiation, functions in R, mantissa, power, R, scientific notation, system.time on May 5, 2015 by xi'an**T**his is presumably obvious to most if not all R programmers, but I became aware today of a hugely (?) delaying tactic in my R codes. I was working with Jean-Michel and Natesh [who are visiting at the moment] and when coding an MCMC run I was telling them that I usually preferred to code Nsim=10000 as Nsim=10^3 for readability reasons. Suddenly, I became worried that this representation involved a computation, as opposed to Nsim=1e3 and ran a little experiment:

> system.time(for (t in 1:10^8) x=10^3) utilisateur système écoulé 30.704 0.032 30.717 > system.time(for (t in 1:1e8) x=10^3) utilisateur système écoulé 30.338 0.040 30.359 > system.time(for (t in 1:10^8) x=1000) utilisateur système écoulé 6.548 0.084 6.631 > system.time(for (t in 1:1e8) x=1000) utilisateur système écoulé 6.088 0.032 6.115 > system.time(for (t in 1:10^8) x=1e3) utilisateur système écoulé 6.134 0.029 6.157 > system.time(for (t in 1:1e8) x=1e3) utilisateur système écoulé 6.627 0.032 6.654 > system.time(for (t in 1:10^8) x=exp(3*log(10))) utilisateur système écoulé 60.571 0.000 57.103

So using the usual scientific notation with powers is taking its toll! While the calculator notation with e is cost free… Weird!

I understand that the R notation 10^6 is an abbreviation for a power function that can be equally applied to pi^pi, say, but still feel aggrieved that a nice scientific notation like 10⁶ ends up as a computing trap! I thus asked the question to the Stack Overflow forum, getting the (predictable) answer that the R code 10^6 meant calling the R power function, while 1e6 was a constant. Since 10⁶ does not differ from π^{π}, there is no reason 10⁶ should be recognised by R as a million. Except that it makes my coding more coherent.

> system.time( for (t in 1:10^8) x=pi^pi) utilisateur système écoulé 44.518 0.000 43.179 > system.time( for (t in 1:10^8) x=10^6) utilisateur système écoulé 38.336 0.000 37.860

Another thing I discovered from this answer to my question is that negative integers are also requesting call to a function:

> system.time( for (t in 1:10^8) x=1) utilisateur système écoulé 10.561 0.801 11.062 > system.time( for (t in 1:10^8) x=-1) utilisateur système écoulé 22.711 0.860 23.098

This sounds even weirder.