2.4 Polynomials and Polynomial Matrices

Polynomials are easily created and manipulated in Scilab.
Manipulation of polynomial matrices is essentially identical
to that of constant matrices.
The `poly`
primitive in Scilab can be used to specify the coefficients
of a polynomial or the roots of a polynomial.

-->p=poly([1 2],'s') //polynomial defined by its roots p = 2 2 - 3s + s -->q=poly([1 2],'s','c') //polynomial defined by its coefficients q = 1 + 2s -->p+q ans = 2 3 - s + s -->p*q ans = 2 3 2 + s - 5s + 2s --> q/p ans = 1 + 2s ----------- 2 2 - 3s + sNote that the polynomial

--> poly([1 2;3 4],'s') ans = 2 - 2 - 5s + sPolynomials can be added, subtracted, multiplied, and divided, as usual, but only between polynomials of same formal variable.

Polynomials, like real and complex constants, can be used as elements in matrices. This is a very useful feature of Scilab for systems theory.

-->s=poly(0,'s'); -->A=[1 s;s 1+s^2] A = ! 1 s ! ! ! ! 2 ! ! s 1 + s ! --> B=[1/s 1/(1+s);1/(1+s) 1/s^2] B = ! 1 1 ! ! ------ ------ ! ! s 1 + s ! ! ! ! 1 1 ! ! --- --- ! ! 2 ! ! 1 + s s !From the above examples it can be seen that matrices can be constructed from polynomials and rationals.