parent, [x=False], [check=False], [is_gen=True], [construct=None]) |
copy,
degree,
int_list,
is_irreducible,
list,
ntl_ZZ_pX,
quo_rem,
set_directly
Further documentation:
) |
Return the degree of this polynomial. The zero polynomial has degree -1.
) |
sage: x = PolynomialRing(Integers(100)).gen() sage: f = x**3 + 3*x - 17 sage: f.list() [83, 3, 0, 1]
) |
Return underlying NTL representation of this polynomial. Additional ``bonus'' functionality is available through this function.
right) |
Returns a tuple (quotient, remainder) where self = quotient*other + remainder.
v) |
Set the value of this polynomial directly from a vector or string.
Polynomials over the integers modulo n are stored internally using NTL's ZZ_pX class. Use this function to set the value of this polynomial using the NTL constructor, which is potentially very fast. The input v is either a vector of ints or a string of the form '[ n1 n2 n3 ... ]' where the ni are integers and there are no commas between them. The optimal input format is the string format, since that's what NTL uses by default.
sage: R = PolynomialRing(Integers(100)) sage: R([1,-2,3]) 3*x^2 + 98*x + 1 sage: f = R(0) sage: f.set_directly([1,-2,3]) sage: f 3*x^2 + 98*x + 1 sage: f.set_directly('[1 -2 3 4]') sage: f 4*x^3 + 3*x^2 + 98*x + 1
Instances of class Polynomial_dense_mod_n also have the following special methods:
__getitem__,
__getslice__,
__pow__,
__reduce__,
__setitem__,
_add,
_mul,
_pari_,
_sub
Further documentation:
right) |
sage: x = PolynomialRing(Integers(100)).gen() sage: (x - 2)*(x**2 - 8*x + 16) x^3 + 90*x^2 + 32*x + 68
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