[Tutor] Basic terminology
Hi, I'm reading a Python book right now (Learning Python, a great book!), and there are few terms that come are brought up a few times but without any explanation. So what are: - remainders (in the context of remainders-of-division modulus for numbers) - modulus (in the same context; I have also seen it in different context, like 3D graphics programs to perform certain types of calculations). Thanks Bernard ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
Re: [Tutor] Basic terminology
A remainder is what's left over after a division: 10/3 = 3 remainder 1 12/5 = 2 remainder 2 27/3 = 9 remainder 0 and the modulus operator (which is % in python) gives you that remainder: 10%3 = 1 12%5 = 2 27%3 = 0 See http://mathworld.wolfram.com/Remainder.html and http://mathworld.wolfram.com/Modulus.html for more formal explanations. In particular, it explains some deeper meanings of the word modulus. Once you get into group theory, it can start to mean some related but different things. Peace Bill Mill bill.mill at gmail.com On Tue, 15 Feb 2005 16:16:44 -0500, [EMAIL PROTECTED] [EMAIL PROTECTED] wrote: Hi, I'm reading a Python book right now (Learning Python, a great book!), and there are few terms that come are brought up a few times but without any explanation. So what are: - remainders (in the context of remainders-of-division modulus for numbers) - modulus (in the same context; I have also seen it in different context, like 3D graphics programs to perform certain types of calculations). Thanks Bernard ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
Re: [Tutor] Basic terminology
A remainder is what's left over after a division: 10/3 = 3 remainder 1 12/5 = 2 remainder 2 27/3 = 9 remainder 0 and the modulus operator (which is % in python) gives you that remainder: 10%3 = 1 12%5 = 2 27%3 = 0 Hi Bernard, Another familiar example of modulo is checking to see if a number is even or odd: ### def isEven(n): Check to see if n is divisible by 2. return n % 2 == 0 ### The remainder of 'n' divided by 2, that is, n modulo 2, is zero if 'n' is even. Another cute thing about modulo is that we can use it to evenly distribute things. Let's make this more concrete, or at least a little sweeter. Imagine that it's Halloween, and we want to evenly distribute some candy out to some trick-or-treaters: ### people = ['fred', 'wilma', 'barney', 'betty'] candy = ['almond joy', 'take 5', 'cadbury', 'twizzlers', 'reeses', 'york', 'jolly rancher', 'nestle crunch'] ### There are two ways we can pass candy to the folks: we can give each people two candies each: ### for (i, c) in enumerate(candy): ... print people[i / (len(candy) / len(people))], gets, c ... fred gets almond joy fred gets take 5 wilma gets cadbury wilma gets twizzlers barney gets reeses barney gets york betty gets jolly rancher betty gets nestle crunch ### That is, since there are eight pieces of candy, and only four people, we can give each person two pieces of candy each. We use simple division: (i / (len(candy) / len(people)) == i / 2 to figure out, given the index number of the candy, which person can seize the sugary treat. So the first two pieces belong to fred, the second two pieces belong to wilma, and so on. Or we can do something that looks more round-robin: ### for (i, c) in enumerate(candy): ... print people[i % len(people)], gets, c ... fred gets almond joy wilma gets take 5 barney gets cadbury betty gets twizzlers fred gets reeses wilma gets york barney gets jolly rancher betty gets nestle crunch ### And here, we use the modulo operator to figure out which person each candy belongs to. In this case, we see the calculation involves: i % len(people) So there's this intimate relationship between division and modulo that corresponds to two main ways we pass things out to people. Does this make sense? ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
Re: [Tutor] Basic terminology
On Tue, 15 Feb 2005 14:26:52 -0800 (PST), Da Hi Bernard, Another familiar example of modulo is checking to see if a number is even or odd: snip lots of good stuff from danny Since Danny got it started with the examples, I'll give another canonical example of the use of the modulus operator. Imagine that we're trying to figure out what number the hour hand of a clock will be pointing at x hours from now. If it's one o'clock right now, in 5 hours, the hour hand will be pointing at the six, and in 10 hours, it will be pointing at the 11. However, where will it be pointing in 16 hours? Well, in 12 hours it will be at the one, then four more hours later it will be pointing at the five. This can be represented as: 1 + (16 % 12) = 1 + 4 = 5 In general, the hour at some point in the future will be: (start time) + (hours in the future % 12) Peace Bill Mill bill.mill at gmail.com ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
Re: [Tutor] Basic terminology
Well, thanks everyone who answered, much clearer now. Bernard Max Noel wrote: In a slightly more generic fashion (everybody started dropping examples), the goal of an integer (euclidian) division (say, a / b) is to express an integer as such: a = b * quotient + remainder Where all the numbers used are integers, and 0 = remainder b. When you perform integer division in Python, a / b (a // b in 2.4+) gives you the quotient, and a % b gives you the remainder. See the other posts for examples of use :p -- Max maxnoel_fr at yahoo dot fr -- ICQ #85274019 Look at you hacker... A pathetic creature of meat and bone, panting and sweating as you run through my corridors... How can you challenge a perfect, immortal machine? ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor ___ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
