Ordering Exponents and Variables
Date: 04/08/2000 at 14:53:25 From: Cherie Subject: Descending Order and Variables 1. Is there a rule for putting terms in descending order if the variables have the same exponent? 2. What about negative exponents and descending order? (Is there a connection?) Sincerely, Cherie
Date: 04/12/2000 at 09:12:01 From: Doctor Peterson Subject: Re: Descending Order and Variables Hi, Cherie. First, I'm assuming you are referring to polynomials, and probably to polynomials of more than one variable. The second question is odd, then, since polynomials can't have negative exponents, but I suppose you might try to extend the concept. Second, there is no rule about writing polynomials in descending order. It is conventional to do so when there is only one variable, because it makes it easier to operate on polynomials (compare, add, multiply) using methods similar to those for working with numbers written with their place value in descending order. With two variables, there may be a most common way to order the terms, but no real convention; with three, it becomes impossible in general. Third, I can't tell what you mean by "if the variables have the same exponent." Does this refer to two variables in one term having the same exponent, or to two terms having the same exponent for all variables, or to two terms having the same exponent for one variable and different exponents for another variable? I have to assume that you are looking simply for a rule for writing polynomials in two variables; the most common convention, I think, is to first order all terms by their total degree (the sum of the exponents), and then within each group to order them by their degree in one of the variables. There's no strong reason for doing this, as there is for a single variable, so it's hard to consider it a rule. You can see this style illustrated (though not prescribed) in Eric Weisstein's World of Mathematics: Polynomial: http://mathworld.wolfram.com/Polynomial.html Fourth, as I said, negative exponents don't exist in a polynomial, so there's no real convention here; if you have them, go ahead and keep sorting them in descending order. I don't see what connection this has to the other question. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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