Polyno
Polynomial object (class)
Installation
pip install polynoImport Poly object
from polyno import PolySet P1 and P2 for the examples below
The parameter of Poly object is
a vector of coefficients in descending
according to the degrees order
or a dictionnary {degree:coef}
>>> P1 = Poly([3, 1, 0])
>>> P2 = Poly({0:5, 3:2})>>> P2.coefficients()
[5.0, 0, 0, 2.0]
>>> Print polynomial
>>> P1.toString()
'3x^2 + x'
>>> print(P1)
3x^2 + x
>>> print(P2)
2x^3 + 5
>>> Addition (with Poly and scalar)
>>> P1 + P2
2x^3 + 3x^2 + x + 5
>>>
>>> P1 + 2
3x^2 + x + 2
>>>Substraction (with Poly and scalar)
>>> P1 - P2
-2x^3 + 3x^2 + x - 5
>>> P2 - P1
2x^3 - 3x^2 - x + 5
>>> P1 - 2
3x^2 + x - 2
>>>Multiplication with scalar
>>> P1 * -2
-6x^2 - 2x
>>> P2 * 3
6x^3 + 15
>>> Multiplication with Poly
>>> P1 * P2
6x^5 + 2x^4 + 15x^2 + 5x
>>> Division with scalar
>>> P2/2
x^3 + 2.5
>>> Derivative
>>> P1.derivative()
6x + 1
>>> k_th order Derivative
>>> print(P2.derivative()) # first order
6x^2
>>> print(P2.derivative(2)) # second order
12x
>>> print(P2.derivative(3)) # third order
12
>>>Other methods
eval: value of P(x)
integral: polynomial integral from a to b
zero: solution of P(x) = 0 for x in [a, b] interval
Eval
>>> P1.eval(2)
14Integral
>>> # integeral of P2 from 1 to 3
>>> P2.integral(1, 3)
50Zero
f(x) = 0 ==> x ?
>>> # solution of P(x) = 0 ?
>>> P = Poly({2:-1, 1:-1, 0:1})
>>> P.zero(0, 10)
0.6180338561534882
>>> P.zero(-3, 0)
-1.6180343627929688
>>>
>>> P.zero(3, 6) # no solution
>>> P.zero(-3, 3) # two solution,
>>> # but nothing is returned
>>> # because of dichotomy (binary search) algorithm
