Polyno

Polynomial object (class)

Installation

pip install polyno

Import Poly object

from polyno import Poly

Set 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)
14

Integral

>>> # integeral of P2 from 1 to 3
>>> P2.integral(1, 3)
50

Zero

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

Futures