{"id":1659,"date":"2009-08-30T13:11:00","date_gmt":"2009-08-30T12:11:00","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=1659"},"modified":"2009-08-30T13:11:00","modified_gmt":"2009-08-30T12:11:00","slug":"rationalq-testing-for-rationals-in-mathematica","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=1659","title":{"rendered":"RationalQ – Testing for rationals in Mathematica"},"content":{"rendered":"

Mathematica<\/a> has a large set of functions that you can use to test the properties of numbers.\u00a0 For example<\/p>\n

IntegerQ[x]<\/strong><\/p>\n

returns True if x is an integer and False if it isn’t.\u00a0 Of course you are not just restricted to asking if x is an integer or not.\u00a0 For example, you can ask if it is an even number<\/p>\n

EvenQ[x]<\/strong><\/p>\n

or an odd number<\/p>\n

OddQ[x]<\/strong><\/p>\n

Perhaps you are wondering if x is prime<\/p>\n

PrimeQ[x]<\/strong><\/p>\n

or even if it is an algebraic integer<\/a><\/p>\n

AlgebraicIntegerQ[x]<\/strong><\/p>\n

The observant reader will notice that all of these functions end with a capital Q and a way of remembering this is to think that you are asking a question of the variable x.\u00a0 So the question ‘Is x an integer<\/strong><\/em>‘ becomes, in Mathematica notation, IntegerQ[x]<\/strong>.<\/p>\n

I am currently working on a piece of code where I need to determine whether or not a particular number belongs to the set of rationals<\/a> and I assumed that a suitable function would exist in Mathematica and that it would be called RationalQ[]<\/strong> so I was rather surprised to see that there is no such function in Mathematica 7.<\/p>\n

So, I’ll just have to come up with my own.\u00a0 A quick search resulted in the following function definition from Bob Hanlon<\/p>\n

RationalQ[x_] := (Head[x] === Rational)<\/strong><\/p>\n

Which almost does what I need.\u00a0 It handles the following correctly<\/p>\n

RationalQ[1\/2] <\/strong>(gives True)<\/p>\n

RationalQ[Sqrt[2]]<\/strong> (Gives False)<\/p>\n

but I needed a version of RationalQ that also returned True when passed an integer.\u00a0 After all, the integers are just a subset of the rationals.\u00a0 A moments thought resulted in<\/p>\n

RationalQ[x_] := (Head[x] === Rational || IntegerQ[x]);<\/strong><\/p>\n

Which seems to work perfectly.\u00a0 So, I offer the above function for anyone who is googling for a RationalQ function and I also ask the following questions to any Mathematica gurus who might be reading this<\/p>\n