# FLINT fmpz_poly class wrapper¶

AUTHORS:

• Robert Bradshaw (2007-09-15) Initial version.
• William Stein (2007-10-02) update for new flint; add arithmetic and creation of coefficients of arbitrary size.
class sage.libs.flint.fmpz_poly.Fmpz_poly

Construct a new fmpz_poly from a sequence, constant coefficient, or string (in the same format as it prints).

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: Fmpz_poly([1,2,3])
3  1 2 3
sage: Fmpz_poly(5)
1  5
sage: Fmpz_poly(str(Fmpz_poly([3,5,7])))
3  3 5 7

degree()

The degree of self.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,2,3]); f
3  1 2 3
sage: f.degree()
2
sage: Fmpz_poly(range(1000)).degree()
999
sage: Fmpz_poly([2,0]).degree()
0

derivative()

Return the derivative of self.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,2,6])
sage: f.derivative().list() == [2, 12]
True

div_rem(other)

Return self / other, self, % other.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,3,4,5])
sage: g = f^23
sage: g.div_rem(f)[1]
0
sage: g.div_rem(f)[0] - f^22
0
sage: f = Fmpz_poly([1..10])
sage: g = Fmpz_poly([1,3,5])
sage: q, r = f.div_rem(g)
sage: q*f+r
17  1 2 3 4 4 4 10 11 17 18 22 26 30 23 26 18 20
sage: g
3  1 3 5
sage: q*g+r
10  1 2 3 4 5 6 7 8 9 10

left_shift(n)

Left shift self by n.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,2])
sage: f.left_shift(1).list() == [0,1,2]
True

list()

Return self as a list of coefficients, lowest terms first.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([2,1,0,-1])
sage: f.list()
[2, 1, 0, -1]

pow_truncate(exp, n)

Return self raised to the power of exp mod x^n.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,2])
sage: f.pow_truncate(10,3)
3  1 20 180
sage: f.pow_truncate(1000,3)
3  1 2000 1998000

pseudo_div(other)
pseudo_div_rem(other)
right_shift(n)

Right shift self by n.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,2])
sage: f.right_shift(1).list() == [2]
True

truncate(n)

Return the truncation of self at degree n.

EXAMPLES:

sage: from sage.libs.flint.fmpz_poly import Fmpz_poly
sage: f = Fmpz_poly([1,1])
sage: g = f**10; g
11  1 10 45 120 210 252 210 120 45 10 1
sage: g.truncate(5)
5  1 10 45 120 210


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