Polynomial Ring on Sage

Question

Somebody can explain me what does this function do?

class fastfrac:

  def __init__(self,top,bot=1):

    if parent(top) == ZZ or parent(top) == R:
      self.top = R(top)
      self.bot = R(bot)
    elif top.__class__ == fastfrac:
      self.top = top.top
      self.bot = top.bot * bot
    else:
      self.top = R(numerator(top))
      self.bot = R(denominator(top)) * bot

For example, parent() function I don't know what does it do. I search information but I didn't find nothing.

Thank you so much

Well it looks like this function intializes an object of fastfrac class. What it does is that for efficiency it considers some special cases of the ring you work over. Why does it matter? — Michal Adamaszek, Sep 19 '18 at 15:32
Yes, but what does the init function do? Because I know that R is a ring, but I don't know what is R(top) or R(bot), and I don't know why the function compare with ZZ and R — ZacariasSatrustegui2, Sep 19 '18 at 15:53
Note: also asked as Ask Sage question 43714 and on this blog. — Samuel Lelièvre, Sep 21 '18 at 23:14

score 2 · Accepted Answer · answered Sep 21 '18 at 23:36

In Sage, every mathematical object has a parent structure.

For example, an integer's parent would be the ring of integers, a matrix's parents would be a matrix space, a polynomial's parent would be the corresponding polynomial ring, etc.

To know what the object's parent is, one can use the function parent or the method parent of this object.

For example, having defined:

sage: N.<u> = NumberField(x^2 - x - 1)
sage: P.<t> = PolynomialRing(QQ)
sage: R.<y, z> = PolynomialRing(QQ)

and

sage: a = 3
sage: b = 6/2
sage: c = x + 3 - x
sage: d = t + 3 - t
sage: e = y + 3 - y
sage: f = mod(3, 8)

you could see that they all display as 3 but all have different parents.

Polynomial Ring on Sage

1 Answers1