newRing -- make a copy of a ring, with some features changed

Synopsis

• Usage:

  S = newRing(R,options)

• Inputs:
  • R, a polynomial ring or a quotient of a polynomial ring
• Optional inputs:
  • Constants => ..., default value nothing
  • DegreeLift => ..., default value nothing
  • DegreeMap => ..., default value nothing
  • DegreeRank => ..., default value nothing
  • Degrees => ..., default value nothing
  • Global => ..., default value nothing
  • Heft => ..., default value nothing
  • Inverses => ..., default value nothing
  • Join => ..., default value nothing
  • Local => ..., default value nothing
  • MonomialOrder => ..., default value nothing
  • MonomialSize => ..., default value nothing
  • SkewCommutative => ..., default value nothing
  • VariableBaseName => ..., default value nothing
  • Variables => ..., default value nothing
  • Weights => ..., default value nothing
  • WeylAlgebra => ..., default value nothing
• Outputs:
  • S, a ring, a new ring, constructed in the same way R was, over the same coefficient ring, but with the newly specified options overriding those used before. See monoid for a description of those options. If R was a quotient ring, then the number of variables must be the same, and S will be a quotient ring, too, with defining ideal obtained from the old by substituting the new variables for the old, preserving their order.

Description

If a different number of variables is given with Variables, then the list of degrees in R will be ignored. If a new degree rank is specified with DegreeRank then the list of degrees and the heft vector of R will be ignored. If a new nonempty list of degrees is specified with Degrees, then the degree rank and and the heft vector of R will be ignored.

i1 : R = QQ[x,y,MonomialOrder => Lex,Degrees=>{3,5}];

i2 : describe newRing(R,MonomialOrder => GRevLex)

o2 = QQ[x..y, Degrees => {3, 5}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
                                                               {GRevLex => {3, 5} }
                                                               {Position => Up    }

i3 : describe newRing(R,Variables=>4)

o3 = QQ[p ..p , Degrees => {4:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
         0   3                                                  {Lex => 2          }
                                                                {Position => Up    }
                                                                {GRevLex => {2:1}  }

i4 : describe newRing(R,Heft=>{2})

o4 = QQ[x..y, Degrees => {3, 5}, Heft => {2}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
                                                               {Lex => 2          }
                                                               {Position => Up    }

i5 : S = R/(x^2+y^3);

i6 : describe newRing(R,Variables=>2)

o6 = QQ[p ..p , Degrees => {3, 5}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
         0   1                                                   {Lex => 2          }
                                                                 {Position => Up    }

The default values for the options of newRing are all set to a non-accessible private symbol whose name is nothing.