Part Two: Polynomials

Welcome back! So… we were talking about monomials, right?

When we tried sum and subtraction between monomials, the variables were the same between terms, as you can see by doing

>>> (3*x).similar_to(5*x)
True

but, what happens when you sum two monomials that aren’t similar? Let’s find out!

>>> (3*x) + (5*y)
3x + 5y

wow! a polynomial!

>>> (3*x) + (5*y) - 9
3x + 5y - 9

another polynomial!

“C-Can I do operations between polynomials?” Well, you can do sums, subtractions and multiplications:

>>> ((3*x) + (5*y)) + ((-3*y) - 2) # Sum!
3x + 2y - 2
>>>
>>> (x + 3) - (2y + 1) # Subtraction!
x + 2 - 2y
>>>
>>> ((3*x) + (5*y)) * ((3*y) - 2) # Multiplication!
9xy - 6x + 15y**2 - 10y

but I’ve not finished factorization yet, so division and power aren’t legal

>>> (x + 2) / 4
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for /: 'Polynomial' and 'int'

yeah, I know, it’s a sad story.

We know polynomials are a sum of monomials, so they could be considered tuples. In fact, they are. Therefore, indexing is enabled:

>>> (2*x + 3)[0]
2x

but they’re immutable objects

>>> (2*x + 3)[0] = 9
Traceback (most recent call last):
...
TypeError: 'Polynomial' object does not support item assignment

If we need the coefficient of a variable(s), we can use a new method, called term_coefficient:

>>> (5*x + 2*y - 3).term_coefficient(x)
5
>>> (5*x + 2*y - 3).term_coefficient(x=1)
5
>>> (5*x + 2*y - 3).term_coefficient({'x': 1})
5

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Yes. There is, again, a more verbous and less readable way. This time is really verbous. But, if you want…

>>> Polynomial(2*x, 5*y, -9)
2x + 5y - 9

more verbous!

>>> Polynomial(Monomial(2, x=1), Monomial(5, y=1), -9))
2x + 5y - 9

convinced?

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Eww, as I said before, factoring isn’t finished yet, so our tutorial ends here. If you have any question or everything else, you can can contact me at gianluparri03@gmail.com