Construction of rational functions.

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`numer` |
in |

`denom` |
similar to |

A rational function object could be constructed either by
calling `rationalfun()`

or by calling
`rationalfun.poly()`

.

`rationalfun()`

constructs a rational function from
the coefficient vectors of the numerator and the
denominator. For example, consider a rational function
*R(x) = P(x) / Q(x)* where

*P(x) = p[1] + p[2] * x +
p[3] * x^2 + ... + p[k]* x^(k-1)*

and

*Q(x) = q[1] + q[2]
* x + q[3] * x^2 + ... + q[m]* x^(m-1)*

, you may call
`rationalfun(p[1:k], q[1:m])`

to build the object.

For `rationalfun.poly()`

, it receives two objects of
class "polynomial" from the polynom package,
representing the polynomials of the numerator and the
denominator respectively. Use this function if you
already have objects of "polynomial" class, typically by
calling `polynomial()`

,
`poly.calc()`

or
`poly.orth()`

.

`rfun()`

and `rfun.poly()`

are aliases of
`rationalfun()`

and `rationalfun.poly()`

in
order to type fewer letters.

The value returned by `rationalfun()`

and
`rationalfun.poly()`

is an object of class
"rationalfun". You can coerce the object to a function,
by calling `as.function.rationalfun()`

, or to
a character string, by calling
`as.character.rationalfun()`

.

Objects of "ratioanlfun" class support basic operators
including `"+"`

, `"-"`

, `"*"`

, `"/"`

and `"^"`

. To evaluate a rational function at a
given vector, use `predict.rationalfun()`

. To
compute the derivative and integral in **explicit**
form, call `deriv.rationalfun()`

and
`integral.rationalfun()`

respectively.

An object of class "rationalfun".

`polynomial`

,
`poly.calc`

,
`poly.orth`

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