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# poly

polynomial definition

### Syntax

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

### History

Version | Description |

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

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