# factors

factorization in ℝ of a polynomial or a rational fraction

### Syntax

[lnum, gain] = factors(pol) [lnum, gain] = factors(pol, flag) [lnum, lden, gain] = factors(rat) [lnum, lden, gain] = factors(rat, flag) rat = factors(rat, flag)

### Arguments

- pol
- real polynomial.
- rat
- real rational (
`rat=pol1/pol2`

). - lnum, lden
- lists of polynomials (of degrees 1 or 2).
- gain
- real number.
- flag
- character string:
`'c'`

, or`'d'`

.

### Description

returns the factors of polynomial `pol`

in the list `lnum`

,
and the "`gain`

".

One has pol = gain times product of entries of the list `lnum`

(if `flag`

is not given). If `flag='c'`

is given, then
one has `|pol(i omega)|`

= `|gain*prod(lnum_j(i omega)|`

.
If `flag='d'`

is given, then
one has `|pol(exp(i omega))|`

= `|gain*prod(lnum_i(exp(i omega))|`

.
If argument of `factors`

is a 1x1 rational `rat=pol1/pol2`

,
the factors of the numerator `pol1`

and the denominator `pol2`

are returned in the lists `lnum`

and `lden`

respectively.

The "gain" is returned as `gain`

,i.e. one has:
rat= gain times (product entries in lnum) / (product entries in lden).

If `flag`

is `'c'`

(resp. `'d'`

),
the roots of `pol`

are reflected wrt the imaginary axis (resp. the unit circle), i.e.
the factors in `lnum`

are stable polynomials.

Same thing if `factors`

is invoked with a rational arguments:
the entries in `lnum`

and `lden`

are stable polynomials if
`flag`

is given. `R2=factors(R1,'c')`

or `R2=factors(R1,'d')`

with `R1`

a rational function or SISO `syslin`

list then the
output `R2`

is a transfer with stable numerator and denominator and
with same magnitude as `R1`

along the imaginary axis (`'c'`

)
or unit circle (`'d'`

).

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