| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
What is a "rational" function?
is it one that its Domain and Range take in values only from
the rational field?
A formal defintion would help.
Thanks,
/naser
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1391.1 | GUESS::DERAMO | Dan D'Eramo | Sat Feb 23 1991 10:27 | 7 | |
A rational function is a ratio of two polynomials
(including polynomials, which are fractions with
denominator equal to one). Rational functions can be in
one or more variables, for example, (x + y^2)/(2xy) is a
rational function of x and y.
Dan
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| 1391.2 | is this same definition? | SMAUG::ABBASI | Sat Feb 23 1991 19:23 | 16 | |
thanks Dan,
can we then say similarly a rational function is
f(x,y,..z)+ f(x,y,..,z)+...+f(x,y,..,z)
1 2 n
where n is the number of "terms" in the "longer" polynomial, and
x,x,..,z are the independent varibles.
for example, your example will be
f1(y)+f2(x,y)
where f1 is 1/2y
f2 is y/2x
I guess what iam asking why not say a rational function is the sum of
functions in zero or more variable? (well, may this is the same in a
way as Dan's definition in .1 ?)
/naser
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| 1391.3 | I'm not sure what you are getting at. | GUESS::DERAMO | Dan D'Eramo | Sun Feb 24 1991 01:16 | 15 |
A sum of rational functions will be a rational function.
But a sum of functions isn't necessarily a rational
function.
x y
2 + e is not a rational function.
2x - 1
If you do take a rational function such as -----------
x^2 + x + 1
and split it into a sum based on the numerator ...
then what does that gain you?
Dan
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