\(p\)-adics#

Introduction to the \(p\)-adics
- Terminology and types of \(p\)-adics
Factory
- QpCR()
- QpER()
- QpFP()
- QpLC()
- QpLF()
- Qp_class
- Qq()
- QqCR()
- QqFP()
- ZpCA()
- ZpCR()
- ZpER()
- ZpFM()
- ZpFP()
- ZpLC()
- ZpLF()
- Zp_class
- Zq()
- ZqCA()
- ZqCR()
- ZqFM()
- ZqFP()
- get_key_base()
- is_eisenstein()
- is_unramified()
- krasner_check()
- pAdicExtension_class
- split()
- truncate_to_prec()
Local Generic
- LocalGeneric
\(p\)-adic Generic
- ResidueLiftingMap
- ResidueReductionMap
- local_print_mode()
- pAdicGeneric
\(p\)-adic Generic Nodes
- CappedAbsoluteGeneric
- CappedRelativeFieldGeneric
- CappedRelativeGeneric
- CappedRelativeRingGeneric
- FixedModGeneric
- FloatingPointFieldGeneric
- FloatingPointGeneric
- FloatingPointRingGeneric
- is_pAdicField()
- is_pAdicRing()
- pAdicCappedAbsoluteRingGeneric
- pAdicCappedRelativeFieldGeneric
- pAdicCappedRelativeRingGeneric
- pAdicFieldBaseGeneric
- pAdicFieldGeneric
- pAdicFixedModRingGeneric
- pAdicFloatingPointFieldGeneric
- pAdicFloatingPointRingGeneric
- pAdicLatticeGeneric
- pAdicRelaxedGeneric
- pAdicRingBaseGeneric
- pAdicRingGeneric
\(p\)-adic Base Generic
- pAdicBaseGeneric
\(p\)-adic Extension Generic
- DefPolyConversion
- MapFreeModuleToOneStep
- MapFreeModuleToTwoStep
- MapOneStepToFreeModule
- MapTwoStepToFreeModule
- pAdicExtensionGeneric
- pAdicModuleIsomorphism
Eisenstein Extension Generic
- EisensteinExtensionGeneric
Unramified Extension Generic
- UnramifiedExtensionGeneric
\(p\)-adic Base Leaves
- pAdicFieldCappedRelative
- pAdicFieldFloatingPoint
- pAdicFieldLattice
- pAdicFieldRelaxed
- pAdicRingCappedAbsolute
- pAdicRingCappedRelative
- pAdicRingFixedMod
- pAdicRingFloatingPoint
- pAdicRingLattice
- pAdicRingRelaxed
\(p\)-adic Extension Leaves
- EisensteinExtensionFieldCappedRelative
- EisensteinExtensionRingCappedAbsolute
- EisensteinExtensionRingCappedRelative
- EisensteinExtensionRingFixedMod
- UnramifiedExtensionFieldCappedRelative
- UnramifiedExtensionFieldFloatingPoint
- UnramifiedExtensionRingCappedAbsolute
- UnramifiedExtensionRingCappedRelative
- UnramifiedExtensionRingFixedMod
- UnramifiedExtensionRingFloatingPoint
Local Generic Element
- LocalGenericElement
\(p\)-adic Generic Element
- dwork_mahler_coeffs()
- evaluate_dwork_mahler()
- gauss_table()
- pAdicGenericElement
\(p\)-adic Capped Relative Elements
- CRElement
- ExpansionIter
- ExpansionIterable
- PowComputer_
- base_p_list()
- pAdicCappedRelativeElement
- pAdicCoercion_CR_frac_field
- pAdicCoercion_QQ_CR
- pAdicCoercion_ZZ_CR
- pAdicConvert_CR_QQ
- pAdicConvert_CR_ZZ
- pAdicConvert_CR_frac_field
- pAdicConvert_QQ_CR
- pAdicTemplateElement
- unpickle_cre_v2()
- unpickle_pcre_v1()
\(p\)-adic Capped Absolute Elements
- CAElement
- ExpansionIter
- ExpansionIterable
- PowComputer_
- make_pAdicCappedAbsoluteElement()
- pAdicCappedAbsoluteElement
- pAdicCoercion_CA_frac_field
- pAdicCoercion_ZZ_CA
- pAdicConvert_CA_ZZ
- pAdicConvert_CA_frac_field
- pAdicConvert_QQ_CA
- pAdicTemplateElement
- unpickle_cae_v2()
\(p\)-adic Fixed-Mod Element
- ExpansionIter
- ExpansionIterable
- FMElement
- PowComputer_
- make_pAdicFixedModElement()
- pAdicCoercion_FM_frac_field
- pAdicCoercion_ZZ_FM
- pAdicConvert_FM_ZZ
- pAdicConvert_FM_frac_field
- pAdicConvert_QQ_FM
- pAdicFixedModElement
- pAdicTemplateElement
- unpickle_fme_v2()
\(p\)-adic Extension Element
- pAdicExtElement
\(p\)-adic ZZ_pX Element
- pAdicZZpXElement
\(p\)-adic ZZ_pX CR Element
- make_ZZpXCRElement()
- pAdicZZpXCRElement
\(p\)-adic ZZ_pX CA Element
- make_ZZpXCAElement()
- pAdicZZpXCAElement
\(p\)-adic ZZ_pX FM Element
- make_ZZpXFMElement()
- pAdicZZpXFMElement
PowComputer
- PowComputer()
- PowComputer_base
- PowComputer_class
PowComputer_ext
- PowComputer_ZZ_pX
- PowComputer_ZZ_pX_FM
- PowComputer_ZZ_pX_FM_Eis
- PowComputer_ZZ_pX_big
- PowComputer_ZZ_pX_big_Eis
- PowComputer_ZZ_pX_small
- PowComputer_ZZ_pX_small_Eis
- PowComputer_ext
- PowComputer_ext_maker()
- ZZ_pX_eis_shift_test()
\(p\)-adic Printing
- pAdicPrinter()
- pAdicPrinterDefaults
- pAdicPrinter_class
Precision Error
- PrecisionError
Miscellaneous Functions
- gauss_sum()
- max()
- min()
- precprint()
- trim_zeros()
The functions in this file are used in creating new p-adic elements.
Frobenius endomorphisms on p-adic fields
- FrobeniusEndomorphism_padics

Indices and Tables#