Package sage :: Package rings :: Package polynomial :: Module polynomial_element

Module polynomial_element

File: sage/rings/polynomial/polynomial_element.pyx (starting at line 1)

Univariate Polynomial Base Class

AUTHORS:
    -- William Stein: first version
    -- Martin Albrecht: Added singular coercion.
    -- Robert Bradshaw: Move Polynomial_generic_dense to SageX

TESTS:
     sage: R.<x> = ZZ[]
     sage: f = x^5 + 2*x^2 + (-1)
     sage: f == loads(dumps(f))
     True

Classes

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Polynomial
File: sage/rings/polynomial/polynomial_element.pyx (starting at line 134) A polynomial.

Polynomial_generic_dense
File: sage/rings/polynomial/polynomial_element.pyx (starting at line 3967) A generic dense polynomial.

Functions

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is_Polynomial(...)
File: sage/rings/polynomial/polynomial_element.pyx (starting at line 70) Return True if f is of type univariate polynomial.

make_generic_polynomial(...)
File: sage/rings/polynomial/polynomial_element.pyx (starting at line 4327)

Variables

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CC = Complex Field with 53 bits of precision

CDF = Complex Double Field

QQ = Rational Field

RDF = Real Double Field

RR = Real Field with 53 bits of precision

ZZ = ['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1...

pari = Interface to the PARI C library

singular_default = Singular

Function Details

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is_Polynomial(...)

File: sage/rings/polynomial/polynomial_element.pyx (starting at line 70)

Return True if f is of type univariate polynomial.

INPUT:
    f -- an object

EXAMPLES:
    sage: R.<x> = ZZ[]
    sage: is_Polynomial(x^3 + x + 1)
    True
    sage: S.<y> = R[]
    sage: f = y^3 + x*y -3*x; f
    y^3 + x*y - 3*x
    sage: is_Polynomial(f)
    True

However this function does not return True for genuine multivariate
polynomial type objects or symbolic polynomials, since those are not
of the same data type as univariate polynomials:
    sage: R.<x,y> = QQ[]
    sage: f = y^3 + x*y -3*x; f
    y^3 + x*y - 3*x
    sage: is_Polynomial(f)
    False
    sage: var('x,y')
    (x, y)
    sage: f = y^3 + x*y -3*x; f
    y^3 + x*y - 3*x
    sage: is_Polynomial(f)
    False

Variables Details

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ZZ

Value:

['4ti2-20061025',
 'R-2.6.0',
 'atlas-3.7.37',
 'atlas-3.8.1',
 'atlas-3.8.1.p1',
 'atlas-3.8.1.p3',
 'atlas-3.8.p11',
 'atlas-3.8.p6',
...