Base class for elements of Henselizations¶

AUTHORS:

Julian Rüth (2017-05-04): initial version

class henselization.sage.rings.padics.henselization.henselization_element.HenselizationElement_Field¶

Bases: henselization.sage.rings.padics.henselization.henselization_element.HenselizationElement_base

Abstract base class for elements of Henselization_Field

EXAMPLES:

sage: from henselization import *
sage: K = QQ.henselization(2)
sage: x = K(0); x
0

TESTS:

sage: from sage.rings.padics.henselization.henselization_element import HenselizationElement_Field
sage: isinstance(x, HenselizationElement_Field)
True
sage: TestSuite(x).run()

class henselization.sage.rings.padics.henselization.henselization_element.HenselizationElement_Ring¶

Bases: henselization.sage.rings.padics.henselization.henselization_element.HenselizationElement_base

Abstract base class for elements of Henselization_Ring

EXAMPLES:

sage: from henselization import *
sage: S = ZZ.henselization(2)
sage: x = S(0); x
0

TESTS:

sage: from sage.rings.padics.henselization.henselization_element import HenselizationElement_Ring
sage: isinstance(x, HenselizationElement_Ring)
True
sage: TestSuite(x).run()

euclidean_degree()¶

Return an Euclidean degree of this element.

EXAMPLES:

sage: from henselization import *
sage: S = ZZ.henselization(3)
sage: R.<x> = S[]
sage: T.<y> = S.extension(x^2 + 3)
sage: y.euclidean_degree()
1

class henselization.sage.rings.padics.henselization.henselization_element.HenselizationElement_base¶

Bases: IntegralDomainElement

Abstract base class for elements of Henselization_base

EXAMPLES:

sage: from henselization import *
sage: K = QQ.henselization(2)
sage: x = K(0); x
0

TESTS:

sage: from sage.rings.padics.henselization.henselization_element import HenselizationElement_base
sage: isinstance(x, HenselizationElement_base)
True
sage: TestSuite(x).run()