p-Adic Extension Leaves¶
The final classes for extensions of Zp and Qp (ie classes that are not just designed to be inherited from).
AUTHORS:
- David Roe
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class
sage.rings.padics.padic_extension_leaves.
EisensteinExtensionFieldCappedRelative
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicCappedRelativeFieldGeneric
TESTS:
sage: R = Qp(3, 10000, print_pos=False); S.<x> = ZZ[]; f = x^3 + 9*x - 3 sage: W.<w> = R.ext(f); W == loads(dumps(W)) True
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class
sage.rings.padics.padic_extension_leaves.
EisensteinExtensionRingCappedAbsolute
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation)¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicCappedAbsoluteRingGeneric
TESTS:
sage: R = ZpCA(3, 10000, print_pos=False); S.<x> = ZZ[]; f = x^3 + 9*x - 3 sage: W.<w> = R.ext(f); W == loads(dumps(W)) True
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class
sage.rings.padics.padic_extension_leaves.
EisensteinExtensionRingCappedRelative
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicCappedRelativeRingGeneric
TESTS:
sage: R = Zp(3, 10000, print_pos=False); S.<x> = ZZ[]; f = x^3 + 9*x - 3 sage: W.<w> = R.ext(f); W == loads(dumps(W)) True
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class
sage.rings.padics.padic_extension_leaves.
EisensteinExtensionRingFixedMod
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicFixedModRingGeneric
TESTS:
sage: R = ZpFM(3, 10000, print_pos=False); S.<x> = ZZ[]; f = x^3 + 9*x - 3 sage: W.<w> = R.ext(f); W == loads(dumps(W)) True
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class
sage.rings.padics.padic_extension_leaves.
UnramifiedExtensionFieldCappedRelative
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicCappedRelativeFieldGeneric
TESTS:
sage: R.<a> = QqCR(27,10000); R == loads(dumps(R)) True
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class
sage.rings.padics.padic_extension_leaves.
UnramifiedExtensionRingCappedAbsolute
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicCappedAbsoluteRingGeneric
TESTS:
sage: R.<a> = ZqCA(27,10000); R == loads(dumps(R)) True
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class
sage.rings.padics.padic_extension_leaves.
UnramifiedExtensionRingCappedRelative
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicCappedRelativeRingGeneric
TESTS:
sage: R.<a> = ZqCR(27,10000); R == loads(dumps(R)) True
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class
sage.rings.padics.padic_extension_leaves.
UnramifiedExtensionRingFixedMod
(prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric
,sage.rings.padics.generic_nodes.pAdicFixedModRingGeneric
TESTS:
sage: R.<a> = ZqFM(27,10000); R == loads(dumps(R)) True