nzmath.poly.multiutil

PolynomialRingAnonymousVariables

The class of multivariate polynomial ring. There's no need to specify the variable names.

This class inherit ring.CommutativeRing.

Constructors

PolynomialRingAnonymousVariables(coeffring, number_of_variables)

Initialize a PolynomialRingAnonymousVariables instance.

PolynomialRingAnonymousVariables.getInstance(coeffring, number_of_variables)

Return an instance of the class with specified coefficient ring and the number of variables. This class method is the preferable way to obtain the ring.

Methods

getCoefficientRing()

Return the coefficient ring.

getQuotientField()

Return the quotient field of the ring if coefficient ring has its quotient field. Otherwise, an exception will be raised.

issubring(other)

Report whether another ring contains this polynomial ring.

issuperring(other)

Report whether this polynomial ring contains another ring.

getCommonSuperring(other)

Return common superring of two rings.

createElement(seed)

Return an element of the polynomial ring made from seed.

gcd(a, b)

Return the greatest common divisor of given polynomials. The polynomials must be in the polynomial ring. If the coefficient ring is a field, the result is monic.

extgcd(a, b)

Return the tuple (u, v, d): d is the greatest common divisor of given polynomials, and they satisfy d = u*a + v*b. The polynomials must be in the polynomial ring. If the coefficient ring is a field, the result is monic.

Operators

r == sequality
e in rmembership test
hash(r)hash
repr(r)repr string
str(r)string like "R[][]"

Properties