Available operations between polynomials¶

Arithmetic operations¶

All basic arithmetic operations between polynomials are supported and exposed by standard Python operations.

Addition and subtraction between polynomials
Addition/subtraction of a scalar
Unary negation operation
Multiplication between polynomials
Multiplication/division with a scalar

The support of the resulting polynomial, i.e. the length of its coefficient list, will be the minimal required to keep all the coefficients.

Adding/subtracting a scalar means adding/subtracting it to the constant term of the polynomial.

from nlft_qsp import *

P = Polynomial([0.4, 0.3, 0.5, 0.7], support_start=-2)
print(P + 30)

(0.4+0j) z^-2 + (0.3+0j) z^-1 + (30.5+0j) z^0 + (0.7+0j) z^1

Truncating support¶

It is possible to use truncate() easily take only parts of a polynomial, discarding frequencies we are not interested in, or that are likely to contain negligible coefficients.

from nlft_qsp import *

P = Polynomial([1, 2, 3, 4, 5, 6, 7], support_start=-2)
print(P)
print(P.truncate(1, 3))

(1+0j) z^-2 + (2+0j) z^-1 + (3+0j) z^0 + (4+0j) z^1 + (5+0j) z^2 + (6+0j) z^3 + (7+0j) z^4
(4+0j) z^1 + (5+0j) z^2 + (6+0j) z^3

Note that both endpoints are included.

Conjugate polynomials¶

Given a Laurent polynomial $P(z) = \sum_k p_k z^k$, the conjugate polynomial is

$$ P^*(z) = \overline{P(1/\overline{z})} = \sum_k \overline{p_k} z^{-k} $$ Such polynomial can be easily obtain using the conjugate() method:

from nlft_qsp import *

P = Polynomial([7+3j, 4+2j, 5+1j])
print(P)
print(P.conjugate())

(7+3j) z^0 + (4+2j) z^1 + (5+1j) z^2
(5-1j) z^-2 + (4-2j) z^-1 + (7-3j) z^0