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WittVectors : Table of Contents
WittVectors
-- computations with finite-length Witt vectors
baseMap
(missing documentation)
baseMap(WittRingMap)
-- Returns the underlying RingMap of a WittRingMap
createEquations
-- Finds explicit equations satisfied by the parameters of a Frobenius lift up to a given degree
explicit
(missing documentation)
explicit(WittIdeal)
-- Obtains the explicit version of a WittIdeal.
explicit(WittPolynomialRing)
-- Expresses a WittPolynomialRing as a finitely generated algebra over the integers.
explicit(WittQuotientRing)
-- Expresses a WittQuotientRing as a finitely generated algebra over the integers.
findFrobeniusLift
-- Finds a random lift of the Frobenius
findFrobeniusLiftConstraints
-- Finds the equations satisfied by a delta structure on a ring R
fSplittingHeight
-- Finds the quasi-F-split height ht(S/I) of the quotient of the polynomial ring S=(ZZ/p)[x1,...,xn] by an ideal I generated by a regular sequence (f1,...,fm).
generators(WittIdeal)
-- Extract the generators of a WittIdeal.
makeCoefficientFieldPrime
(missing documentation)
MaxHeight
(missing documentation)
Nontrivial
(missing documentation)
overring
(missing documentation)
overringMap
(missing documentation)
PerturbationTerm
(missing documentation)
ring(WittRingElement)
-- Returns the Witt ring that a WittRingElement belongs to
toList(WittRingElement)
-- Converts a WittRingElement into a List
truncate(ZZ,WittPolynomialRing)
-- Crop Witt ring to the ring of Witt vectors of a given length
truncate(ZZ,WittQuotientRing)
-- Crop Witt Quotient ring to the ring of Witt vectors of a given length
truncate(ZZ,WittRingElement)
-- Crop Witt Vector to have a given length.
truncation
(missing documentation)
unWitt
-- Returns the underlying ring R of a Witt ring W_n(R)
verschiebung
(missing documentation)
verschiebung(WittRingElement)
-- The Verschiebung map on an element
witt
(missing documentation)
witt(List)
-- Forms a WittRingElement from a list of ring elements
witt(ZZ,PolynomialRing)
-- Builds a Witt ring.
witt(ZZ,QuotientRing)
-- Forms the n-th Witt ring of a quotient ring
witt(ZZ,RingMap)
-- The map induced on Witt rings by a RingMap.
witt(ZZ,ZZ,RingMap)
-- The map induced on Witt rings by a RingMap.
wittFrobenius
(missing documentation)
wittFrobenius(WittPolynomialRing)
-- The (Witt) Frobenius map of a Witt ring
wittFrobenius(WittRingElement)
-- The (Witt) Frobenius map on an element
wittFrobenius(ZZ,Ring)
-- The (Witt) Frobenius map on the Witt vectors of a ring
wittGenerators
(missing documentation)
WittIdeal
-- Ideals in Witt rings.
wittIdeal
-- Make an ideal in a Witt ring.
wittLength
-- Returns the length of the Witt vectors in a given Witt ring
WittOverring
(missing documentation)
wittOverring
-- Returns the n-th WittOverring of a ring R, or the overring of a witt ring.
wittOverringIdeal
-- The expansion of the witt ideal to the witt overring.
wittOverringToTuple
-- Converts an element of the explicit overring of a Witt ring into a tuple.
WittPolynomialRing
-- The class of the n-th Witt ring of a polynomial ring.
WittQuotientRing
-- The class of the n-th Witt ring of a quotient of a polynomial ring.
WittRing
(missing documentation)
WittRingElement
-- The Type for elements of WittPolynomialRing and WittQuotientRing.
WittRingElement * WittRingElement
-- Multiplication of WittRingElements.
WittRingElement + WittRingElement
-- Addition of WittRingElements.
wittRingIdeal
-- Returns the n-th witt ideal in explicit form.
WittRingMap
-- The class of maps between Witt rings.
wittRingToTuple
-- Converts an element of the explicit presentation of a Witt ring into a tuple.
wittSub
(missing documentation)
wittTupleToOverring
-- Converts an element of a Witt ring to an element of the overring of its explicit presentation.
wittTupleToRing
-- Converts an element of a Witt ring to an element of its explicit presentation.