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

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionFieldCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='NTL')

Bases: sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric, sage.rings.padics.generic_nodes.pAdicCappedRelativeFieldGeneric

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedAbsolute(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation)

Bases: sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric, sage.rings.padics.generic_nodes.pAdicCappedAbsoluteRingGeneric

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='NTL')

Bases: sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric, sage.rings.padics.generic_nodes.pAdicCappedRelativeRingGeneric

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingFixedMod(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='NTL')

Bases: sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric, sage.rings.padics.generic_nodes.pAdicFixedModRingGeneric

fraction_field()

Eisenstein extensions with fixed modulus do not support fraction fields.

EXAMPLES:

sage: S.<x> = ZZ[]
sage: R.<a> = ZpFM(5).extension(x^2 - 5)
sage: R.fraction_field()
Traceback (most recent call last):
...
TypeError: This implementation of the p-adic ring does not support fields of fractions.

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionFieldCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')

Bases: sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric, sage.rings.padics.generic_nodes.pAdicCappedRelativeFieldGeneric

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionFieldFloatingPoint(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')

Bases: sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric, sage.rings.padics.generic_nodes.pAdicFloatingPointFieldGeneric

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingCappedAbsolute(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')

Bases: sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric, sage.rings.padics.generic_nodes.pAdicCappedAbsoluteRingGeneric

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')

Bases: sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric, sage.rings.padics.generic_nodes.pAdicCappedRelativeRingGeneric

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingFixedMod(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')

Bases: sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric, sage.rings.padics.generic_nodes.pAdicFixedModRingGeneric

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingFloatingPoint(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')

Bases: sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric, sage.rings.padics.generic_nodes.pAdicFloatingPointRingGeneric