# rational

rational fractions

### Description

A rational `r`

is the quotient of two polynomials `r=num/den`

.

An array `R`

of rationals can be directly defined as the elementwise
quotient of two polynomials arrays `Num`

and `Den`

:
`R = Num./Den`

.

The internal representation of a rational is a list of type "r":
`R = tlist(['r','num','den','dt'], Num, Den,[])`

, or
`R = rlist(Num, Den, [])`

.

All usual operators can be used with arrays of rationals:
`' .' + - * .* / ./ .^ .*. [,] [;]`

,

As for polynomials, the `horner()`

function allows to compute
the value of rationals for some value of their variable.

Many other Scilab functions can be used with rationals input : `permute`

,
`cat`

, `real`

, `imag`

,
`conj`

, `isreal`

, etc.

Addressing some components of an array `R` of rationals with their
linearized indices can be done using the syntax `R(k,0)` where
`k` is the vector of linearized indices, and 0 is used instead of
`j` or higher order indices. |

### Examples

s=poly(0,'s'); W=[1/s,1/(s+1)] W'*W Num=[s,s+2;1,s];Den=[s*s,s;s,s*s]; rlist(Num,Den,[]) H=Num./Den syslin('c',Num,Den) syslin('c',H) [Num1,Den1]=simp(Num,Den)

--> R = (1-%s).^[1 0 2] ./ %s.^[1 2 0] R = 2 1 - s 1 1 - 2s + s ------ -- ----------- 2 s s 1 --> horner(R,[-1 0 2 -2]') ans = -2. 1. 4. Inf Inf 1. -0.5 0.25 1. -1.5 0.25 9. --> R = (1-%s)/(1+%s) R = 1 - s ------ 1 + s --> horner(R, 1-%z^2) ans = 2 z ------ 2 2 - z

### See also

### History

Version | Description |

6.0.2 | The syntax `R(k,0)` is now available to address components
with their linearized indices k. |

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