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WittQuotientRing -- The class of the n-th Witt ring of a quotient of a polynomial ring.

Description

Can be built by using the witt method.

i1 : R = (ZZ/3)[x,y,z] / ideal(x^2  + y^2 + z^2);
 
i2 : WR = witt(4, R)

o2 = Witt (R)
         4

o2 : WittQuotientRing

Methods that use an object of class WittQuotientRing:

  • explicit(WittQuotientRing) -- Expresses a WittQuotientRing as a finitely generated algebra over the integers.
  • net(WittQuotientRing) (missing documentation)
  • random(ZZ,WittQuotientRing) (missing documentation)
  • substitute(ZZ,WittQuotientRing) (missing documentation)
  • truncate(ZZ,WittQuotientRing) -- Crop Witt Quotient ring to the ring of Witt vectors of a given length
  • unWitt(WittQuotientRing) -- see unWitt -- Returns the underlying ring R of a Witt ring W_n(R)
  • wittFrobenius(WittQuotientRing) -- see wittFrobenius(WittPolynomialRing) -- The (Witt) Frobenius map of a Witt ring
  • wittLength(WittQuotientRing) -- see wittLength -- Returns the length of the Witt vectors in a given Witt ring
  • wittOverring(WittQuotientRing) -- see wittOverring -- Returns the n-th WittOverring of a ring R, or the overring of a witt ring.
  • ZZ _ WittQuotientRing (missing documentation)

For the programmer

The object WittQuotientRing is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/WittVectors/Documentation.m2:906:0.