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Rational functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26080] Rational functions
• From: Jack Goldberg <jackgold at math.lsa.umich.edu>
• Date: Tue, 28 Nov 2000 01:55:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi group,

In my work I need to know whether the expression f[x] is a rational
function of x (the quotient of two polynomials).  I devised the following
obvious test:

	RationalQ[f_,x_] := Module[ { f1 = Together[f] },
		PolynomialQ[ Numerator[f1]*Denominator[f1], x ]
			]

I would like to hear from those who can find a flaw in this code, or who
can offer a better solution.  I probably should mention that I want
RationalQ to return True when f is a polynomial in x and that I don't
expect RationalQ to free of the subtle peculiarities that are inherent in  
PolynomialQ.   

Thanks,

Jack

• Follow-Ups:
  • Re: Rational functions
    • From: Daniel Lichtblau <danl@wolfram.com>