nzmath.polynomial | (ÆüËܸì)
PolynomialRing is a class for polynomial rings, and it is a derivative class of nzmath.ring.CommutativeRing.
aRing is a coefficient ring, and vars is a string of variable name or a list of such strings.
Create a polynomial from seed.
Compute greatest common divisor of a and b in the ring.
Return the coefficient ring with respect to variable var. There is no need to specify var if the ring has only one variable. Or TypeError will be raised if var is not specified.
Return a common super ring of the polynomial ring and other ring.
Return the quotient field of the polynomial ring if the coefficient ring has the quotient field. Otherwise, raise an error.
Return a list of variable names.
Return whether the polynomial ring is a subring of other ring.
Return whether the polynomial ring is a superring of other ring.
If the polynomial ring is nested, i.e. the coefficient ring is also a polynomial ring, the method returns an unnested ring. For example, the result of:
PolynomialRing(PolynomialRing(Q, "x"), "y").unnest()
is
PolynomialRing(Q, sets.Set(["x","y"]))
If the method is called against non-nested polynomial ring, an error will bbe raised.
The methods below are defined in nzmath.ring.CommutativeRing:
isdomain(),
iseuclidean(),
isfield(),
isnoetherian(),
ispid(),
isufd()
operator | explanation |
e in r | whether an object e is in the polynomial ring r or not. |
r1 == r2 | whether two rings (r1,r2) are the same ring or not. |
str(r) | return str string of the polynomial ring r |