axiom-source 20170501-3 / usr / share / axiom-20170501 / src / algebra / RGCHAIN.spad

)abbrev domain RGCHAIN RegularChain
++ Author: Marc Moreno Maza
++ Date Created: 01/1999
++ Date Last Updated: 23/01/1999
++ Description: 
++ A domain for regular chains (regular triangular sets) over
++ a Gcd-Domain and with a fix list of variables.
++ This is just a front-end for the \spadtype{RegularTriangularSet}
++ domain constructor.

RegularChain(R,ls) : SIG == CODE where
  R : GcdDomain
  ls : List Symbol

  V ==> OrderedVariableList ls
  E ==> IndexedExponents V
  P ==> NewSparseMultivariatePolynomial(R,V)
  TS ==> RegularTriangularSet(R,E,V,P)

  SIG ==> RegularTriangularSetCategory(R,E,V,P) with

     zeroSetSplit : (List P, Boolean, Boolean) -> List $
       ++ \spad{zeroSetSplit(lp,clos?,info?)} returns a list \spad{lts} of
       ++ regular chains such that the union of the closures of their regular
       ++ zero sets equals the affine variety associated with \spad{lp}. 
       ++ Moreover, if \spad{clos?} is \spad{false} then the union of the 
       ++ regular zero set of the \spad{ts} (for \spad{ts} in \spad{lts}) 
       ++ equals this variety.
       ++ If \spad{info?} is \spad{true} then some information is 
       ++ displayed during the computations. See 
       ++ zeroSetSplit from RegularTriangularSet.

  CODE ==> RegularTriangularSet(R,E,V,P)