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""" 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. """
#***************************************************************************** # Copyright (C) 2007 Robert Bradshaw <robertwb@math.washington.edu> # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 2 of the License, or # (at your option) any later version. # http://www.gnu.org/licenses/ #*****************************************************************************
from cpython.sequence cimport *
from cysignals.memory cimport sig_free
from sage.arith.long cimport pyobject_to_long from sage.cpython.string cimport char_to_str, str_to_bytes from sage.structure.sage_object cimport SageObject from sage.rings.integer cimport Integer from sage.libs.flint.fmpz_poly cimport *
cdef class Fmpz_poly(SageObject):
def __cinit__(self):
def __init__(self, v): """ 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 """ cdef Py_ssize_t i cdef long c cdef Integer w else: raise ValueError("Unable to create Fmpz_poly from that string.") #fmpz_poly_set_coeff_si(self.poly, i, v[i]) except OverflowError: raise ValueError("No fmpz_poly_set_coeff_mpz() method.")
def __dealloc__(self):
def __setitem__(self, i, value): """ Set the $i$-th item of self, which is the coefficient of the $x^i$ term.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly(range(10)) sage: f[7] = 100; f 10 0 1 2 3 4 5 6 100 8 9 sage: f[2] = 10**100000 sage: f[2] == 10**100000 True """ else : fmpz_poly_set_coeff_si(self.poly, i, value)
def __getitem__(self, i): """ Return the $i$-th item of self, which is the coefficient of the $x^i$ term.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly(range(100)) sage: f[13] 13 sage: f[200] 0 """
def __repr__(self): """ Print self according to the native FLINT format.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly([0,1]); f^7 8 0 0 0 0 0 0 0 1 """
def degree(self): """ 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 """
def list(self): """ 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] """
def __add__(left, right): """ Add together two Flint polynomials.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: Fmpz_poly([1,2,3]) + Fmpz_poly(range(6)) 6 1 3 5 3 4 5 """ raise TypeError
def __sub__(left, right): """ Subtract two Flint polynomials.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: Fmpz_poly([10,2,3]) - Fmpz_poly([4,-2,1]) 3 6 4 2 """ raise TypeError
def __neg__(self): """ Return the negative of self.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: -Fmpz_poly([2,10,2,3,18,-5]) 6 -2 -10 -2 -3 -18 5 """
def __mul__(left, right): """ Return the product of left and right.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly([0,1]); g = Fmpz_poly([2,3,4]) sage: f*g 4 0 2 3 4 sage: f = Fmpz_poly([1,0,-1]); g = Fmpz_poly([2,3,4]) sage: f*g 5 2 3 2 -3 -4
Scalar multiplication sage: f * 3 3 3 0 -3 sage: f * 5r 3 5 0 -5 """ fmpz_poly_scalar_mul_si(res.poly, (<Fmpz_poly>right).poly, left) else: raise TypeError else:
def __pow__(self, n, dummy): """ Return self raised to the power of n.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly([1,1]) sage: f**6 7 1 6 15 20 15 6 1 sage: f = Fmpz_poly([2]) sage: f^150 1 1427247692705959881058285969449495136382746624 sage: 2^150 1427247692705959881058285969449495136382746624
sage: f**(3/2) Traceback (most recent call last): ... TypeError: rational is not an integer """ raise TypeError
def pow_truncate(self, 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 """ raise ValueError("Exponent must be at least 0") raise ValueError("Exponent must be at least 0")
def __floordiv__(left, right): """ Return left // right, truncated.
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly([3,4,5]) sage: g = f^5; g 11 243 1620 6345 16560 32190 47224 53650 46000 29375 12500 3125 sage: g // f 9 81 432 1404 2928 4486 4880 3900 2000 625 sage: f^4 9 81 432 1404 2928 4486 4880 3900 2000 625 """ raise TypeError
def div_rem(self, Fmpz_poly 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 """
def left_shift(self, unsigned long 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 """
def right_shift(self, unsigned long 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 """
def pseudo_div(self, Fmpz_poly other): cdef ulong d cdef Fmpz_poly Q = <Fmpz_poly>Fmpz_poly.__new__(Fmpz_poly) fmpz_poly_pseudo_div(Q.poly, &d, self.poly, other.poly) return Q, d
def pseudo_div_rem(self, Fmpz_poly other): cdef ulong d cdef Fmpz_poly Q = <Fmpz_poly>Fmpz_poly.__new__(Fmpz_poly) cdef Fmpz_poly R = <Fmpz_poly>Fmpz_poly.__new__(Fmpz_poly) fmpz_poly_pseudo_divrem(Q.poly, R.poly, &d, self.poly, other.poly) return Q, R, d
def derivative(self) : """ 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 """
def __copy__(self):
def truncate(self, 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 """
def _unsafe_mutate_truncate(self, n): """ Return the truncation of self at degree n.
Don't do this unless you know there are no other references to this polynomial!!!!!
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._unsafe_mutate_truncate(5); g 5 1 10 45 120 210 """
def _sage_(self, var='x'): """ Return self as an element of the sage ZZ[var].
EXAMPLES::
sage: from sage.libs.flint.fmpz_poly import Fmpz_poly sage: f = Fmpz_poly([1,1]) sage: f._sage_('t') t + 1 sage: Fmpz_poly([-1,0,0,1])._sage_() x^3 - 1 """
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