polyno 1.2.5

Polyno: polynomial object

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