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Package sage :: Package rings :: Module polynomial_ring :: Class PolynomialRing |
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Gens
--+ |Ring
--+ |object
--+ | | |_uniqPolynomialRing
--+ | PolynomialRing
MPolynomialRing
,
PowerSeriesRing
Univariate polynomial ring.
EXAMPLES:>>> import rings >>> Q = rings.RationalField() >>> R = PolynomialRing(Q) >>> x = R.gen() >>> R(-1) + R(1) 0 >>> (x - '2/3')*(x**2 - 8*x + 16) x^3 - 26/3*x^2 + 64/3*x - 32/3
Method Summary | |
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__init__(self,
base_ring,
variable,
sparse)
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__call__(self,
*args,
**kwds)
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__cmp__(self,
other)
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__contains__(self,
x)
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__repr__(self)
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base_ring(self)
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characteristic(self)
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The nth cyclotomic polynomial, which is irreducible and has a primitive nth root of unity as root. | |
If this is R[x], this intrinsic returns x. | |
is_field(self)
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is_sparse(self)
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name(self)
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ngens(self)
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polynomial(self,
*args,
**kwds)
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Return a random polynomial. | |
set_variable(self,
variable)
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Returns the string which is used to print the generator of the polynomial ring. | |
Inherited from object | |
x.__delattr__('name') <==> del x.name | |
x.__getattribute__('name') <==> x.name | |
x.__hash__() <==> hash(x) | |
helper for pickle | |
helper for pickle | |
x.__setattr__('name', value) <==> x.name = value | |
x.__str__() <==> str(x) | |
Inherited from Ring | |
True if the elements have atomic string representations, in the sense that they print if they print at s, then -s means the negative of s. | |
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Inherited from Gens | |
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Instance Method Details |
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cyclotomic_polynomial(self, n)The nth cyclotomic polynomial, which is irreducible and has a primitive nth root of unity as root. |
gen(self, n=0)If this is R[x], this intrinsic returns x. |
random(self, degree, bound=10)Return a random polynomial. INPUT: degree -- an int bound -- an int OUTPUT: Polynomial A polynomial whose coefficients of x^i, for i up to degree, are coercisions to the base ring of random integers between -bound and bound. |
variable(self)Returns the string which is used to print the generator of the polynomial ring. OUTPUT: str -- generator name |
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