\(p\)-adic Extension Leaves#

The final classes for extensions of \(\ZZ_p\) and \(\QQ_p\) (i.e., 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: EisensteinExtensionGeneric, pAdicCappedRelativeFieldGeneric

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedAbsolute(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation)#: Bases: EisensteinExtensionGeneric, pAdicCappedAbsoluteRingGeneric

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

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

Bases: EisensteinExtensionGeneric, 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)                                    # needs sage.libs.ntl
sage: R.fraction_field()                                                    # needs sage.libs.ntl
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: UnramifiedExtensionGeneric, pAdicCappedRelativeFieldGeneric

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

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

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

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

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