File: /home/runner/work/sage/sage/src/sage/rings/polynomial/commutative_polynomial.pyx (starting at line 1)

class sage.rings.polynomial.commutative_polynomial.CommutativePolynomial

Bases: CommutativeAlgebraElement

Abstract base class for commutative polynomials in any number of variables.

It is a common base for Polynomial, MPolynomial, and InfinitePolynomial.

EXAMPLES:

Sage

sage: from sage.rings.polynomial.commutative_polynomial import CommutativePolynomial
sage: K.<x> = PolynomialRing(QQ)
sage: isinstance(x, CommutativePolynomial)
True
sage: K.<x,y> = PolynomialRing(QQ)
sage: isinstance(x, CommutativePolynomial)
True
sage: X.<x,y> = InfinitePolynomialRing(ZZ, implementation='sparse')
sage: isinstance(x[2], CommutativePolynomial)
True

Python

>>> from sage.all import *
>>> from sage.rings.polynomial.commutative_polynomial import CommutativePolynomial
>>> K = PolynomialRing(QQ, names=('x',)); (x,) = K._first_ngens(1)
>>> isinstance(x, CommutativePolynomial)
True
>>> K = PolynomialRing(QQ, names=('x', 'y',)); (x, y,) = K._first_ngens(2)
>>> isinstance(x, CommutativePolynomial)
True
>>> X = InfinitePolynomialRing(ZZ, implementation='sparse', names=('x', 'y',)); (x, y,) = X._first_ngens(2)
>>> isinstance(x[Integer(2)], CommutativePolynomial)
True

Sage Live

from sage.rings.polynomial.commutative_polynomial import CommutativePolynomial
K.<x> = PolynomialRing(QQ)
isinstance(x, CommutativePolynomial)
K.<x,y> = PolynomialRing(QQ)
isinstance(x, CommutativePolynomial)
X.<x,y> = InfinitePolynomialRing(ZZ, implementation='sparse')
isinstance(x[2], CommutativePolynomial)

Make live