Complete Discrete Valuation Rings (CDVR) and Fields (CDVF)¶
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class
sage.categories.complete_discrete_valuation.
CompleteDiscreteValuationFields
(s=None)¶ Bases:
sage.categories.category_singleton.Category_singleton
The category of complete discrete valuation fields
EXAMPLES:
sage: Zp(7) in CompleteDiscreteValuationFields() False sage: QQ in CompleteDiscreteValuationFields() False sage: LaurentSeriesRing(QQ,'u') in CompleteDiscreteValuationFields() True sage: Qp(7) in CompleteDiscreteValuationFields() True sage: TestSuite(CompleteDiscreteValuationFields()).run()
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class
ElementMethods
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precision_absolute
()¶ Return the absolute precision of this element.
EXAMPLES:
sage: K = Qp(7) sage: x = K(7); x 7 + O(7^21) sage: x.precision_absolute() 21
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precision_relative
()¶ Return the relative precision of this element.
EXAMPLES:
sage: K = Qp(7) sage: x = K(7); x 7 + O(7^21) sage: x.precision_relative() 20
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CompleteDiscreteValuationFields.
super_categories
()¶ EXAMPLES:
sage: CompleteDiscreteValuationFields().super_categories() [Category of discrete valuation fields]
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class
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class
sage.categories.complete_discrete_valuation.
CompleteDiscreteValuationRings
(s=None)¶ Bases:
sage.categories.category_singleton.Category_singleton
The category of complete discrete valuation rings
EXAMPLES:
sage: Zp(7) in CompleteDiscreteValuationRings() True sage: QQ in CompleteDiscreteValuationRings() False sage: QQ[['u']] in CompleteDiscreteValuationRings() True sage: Qp(7) in CompleteDiscreteValuationRings() False sage: TestSuite(CompleteDiscreteValuationRings()).run()
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class
ElementMethods
¶ -
precision_absolute
()¶ Return the absolute precision of this element.
EXAMPLES:
sage: R = Zp(7) sage: x = R(7); x 7 + O(7^21) sage: x.precision_absolute() 21
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precision_relative
()¶ Return the relative precision of this element.
EXAMPLES:
sage: R = Zp(7) sage: x = R(7); x 7 + O(7^21) sage: x.precision_relative() 20
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CompleteDiscreteValuationRings.
super_categories
()¶ EXAMPLES:
sage: CompleteDiscreteValuationRings().super_categories() [Category of discrete valuation rings]
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class