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(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedAbsolute(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedRelative(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingFixedMod(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionFieldCappedRelative(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingCappedAbsolute(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingCappedRelative(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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

class sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingFixedMod(prepoly, poly, prec, halt, print_mode, shift_seed, names)

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