Wikipedia:Reference desk/Archives/Mathematics/2011 March 11

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March 11

Suffix notation

Why are prefix and infix functions common, but suffix notation is very rarely used? The only example of suffix notation in pure math that I can think of is the factorial function. 76.67.75.94 (talk) 19:51, 11 March 2011 (UTC)

Derivative ($f'$)? Cycle notation?--203.97.79.114 (talk) 22:48, 11 March 2011 (UTC)

Well, (x)f is a little hard on the eyes... --COVIZAPIBETEFOKY (talk) 23:10, 11 March 2011 (UTC)

Though incidentally, I believe it is more common to see postfix (aka Reverse Polish Notation) than prefix on a calculator. --COVIZAPIBETEFOKY (talk) 01:14, 12 March 2011 (UTC)

The notation Xƒ is used in differential geometry to mean the derivative of the function ƒ with respect to the vector field X. Equivalent notations are d_Xƒ of (dƒ)(X), where the d is the exterior derivative. The reason being that you can think of a vector field as a differential operator. — Fly by Night (talk) 01:52, 12 March 2011 (UTC)

Would you count powers/exponentials as suffix notation? I have seen functions written using suffix notions (ie. f(x) written as xf) which makes composition of functions a little less confusing (applying f and then g is written xfg, which is the intuitive order, rather than g(f(x)) which seems backwards). However, I've only seen that in really old books. The notation we now consider conventional won out, but I don't know why. --Tango (talk) 02:20, 12 March 2011 (UTC)

I've seen postfix notation for group homomorphisms in recent papers (Eastern European authors, I think). It's also used in GAP: f(x) is x^f. Staecker (talk) 16:32, 12 March 2011 (UTC)

OP here. The derivative is a good example. The others, such as exponents, don't really count; 3² is the exponential with base 3 of two just as much as it is the square of three. Tango actually hit on the reason I asked the question: xfg is a more intuitive way to compose functions than g(f(x)), especially if one must deal with many functions being composed without being applied to a variable. I think prefix notation won just because it was invented first, but I was wondering if anyone the details of this. 76.67.74.178 (talk) 04:51, 14 March 2011 (UTC)