How to perform polynomial addition and multiplication using python 3.x?

Question

For instance, 3x^4 - 17x^2 - 3x + 5. Each term of the polynomial can be represented as a pair of integers (coefficient, exponent). i.e. [(3,4),(-17,2), (-3,1), (5,0)]

We have the following constraints to guarantee that each polynomial has a unique representation:

Terms are sorted in descending order of exponent
No term has a zero cofficient
No two terms have the same exponent
Exponents are always nonnegative

Write Python functions for the following operations:

addpoly(p1,p2)
multpoly(p1,p2)

Some examples:

>>> addpoly( [(4,3),(3,0)], [(-4,3),(2,1)] )
[(2, 1),(3, 0)]

Explanation: (4x^3 + 3) + (-4x^3 + 2x) = 2x + 3

>>> addpoly( [(2,1)], [(-2,1)] )
[]

Explanation: 2x + (-2x) = 0

>>> multpoly( [(1,1),(-1,0)], [(1,2),(1,1),(1,0)] )
[(1, 3),(-1, 0)]

Explanation: (x - 1) * (x^2 + x + 1) = x^3 - 1

If you are allowed to use a library, just use sympy. No need to reinvent the wheel — user2341726, Aug 03 '17 at 13:52
@user2341726: OP was asked for an implementation: "Write Python functions for `addpoly, multpoly`" — smci, Sep 16 '18 at 01:36

Sebastian Wozny · Answer 1 · 2017-02-24T18:18:40.187

2

You want to define a function that takes an arbitrary amount of arguments of the form

[(4,3),(3,0)], [(-4,3),(2,1)]

addpoly could be done easily with a collections.defaultdict:

from collections import defaultdict

def addpoly(*polynoms):
    result = defaultdict(int)
    for polynom in polynoms:
        for factor, exponent in polynom:
            result[exponent] += factor
    return [(coeff, exponent) for exponent, coeff in result.items() if coeff]

In [68]: addpoly([(4,3),(3,0)],[(-4,3),(2,1)])
Out[68]: [(3, 0), (2, 1)]

edited Feb 24 '17 at 18:18

answered Feb 24 '17 at 17:12

Sebastian Wozny

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I just used floats because technically the exponents could be floats. If my answer answered your question, please accept it. – Sebastian Wozny Feb 24 '17 at 18:15
3

This code prints even those elements that have zero degree. instead we need a blank list. the compiler shows: when input is addpoly([(4,3),(3,0)],[(-4,3),(2,1)]) Expected Output: [(2, 1), (3, 0)] Actual Output [(0, 3), (1, 2), (3, 0)] and in another case: when input is addpoly([(2,1)],[(-2,1)]) Expected Output [] Actual Output [(1, 0)] – Sandeep Kumar Kushwaha Feb 24 '17 at 18:16
3

I am really sorry for my frequent edits. I am new here :) thanks for your support! – Sandeep Kumar Kushwaha Feb 24 '17 at 18:20
3

I understand what to be done...but cant find a way to do it. Can you take a look at the 2nd comment and see how can we fix the output problem... – Sandeep Kumar Kushwaha Feb 24 '17 at 18:22
I amended my code to do it there is a `if factor `in the last line – Sebastian Wozny Feb 24 '17 at 18:24
1

If my answer answered your question please accept it. – Sebastian Wozny Feb 25 '17 at 13:00
Should be an accepted answer. What is a reason to use defaultdict? Will a simple dict work? – Evgeny Sep 16 '18 at 01:51

How to perform polynomial addition and multiplication using python 3.x?

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