# poly

polynomial definition

## Calling Sequence

    p = poly(a, vname, ["flag"])

## Arguments

a

  a matrix or real number

vname

  a string, the symbolic variable name. The string must be 4 characters max.

"flag"

  string (`"roots"`, `"coeff"`), default value is `"roots"`.

  Shortcuts can be also used: `"r"` for `"roots"` and `"c"` for `"coeff"`.

## Description

If `a` is a matrix,

  `p` is the characteristic polynomial i.e. `determinant(x*eye()-a)`, `x` being the symbolic variable.

If `v` is a vector,

  - `poly(v,"x",["roots"])` is the polynomial with `roots` the entries of `v` and `"x"` as formal variable. (In this case, `roots` and `poly` are inverse functions).

    Note that Infinite roots gives zero highest degree coefficients.

  - `poly(v,"x","coeff")` creates the polynomial with symbol `"x"` and with coefficients the entries of `v` (`v(1)` is the constant term of the polynomial). (Here `poly` and `coeff` are inverse functions).

`s=poly(0,"s")` is the seed for defining polynomials with symbol `"s"`.

## Examples

    s=poly(0,"s");
    p=1+s+2*s^2
    A=rand(2,2);
    poly(A,"x")
    //rational fractions
    h=(1+2*%s)/poly(1:4,'s','coeff')

## See Also

- coeff
- roots
- varn
- horner
- derivat
- matrices
- rational

## History

5.5.0
The only values allowed for the third argument are "roots", "coeff", "c" and "r".