selectVariables(List,PolynomialRing) -- make a subring of a polynomial ring generated by selected variables

Synopsis

Function: selectVariables
Usage:

(S,f) = selectVariables(v,R)
Inputs:
- v, a list, a sorted list of numbers specifying which variables to select
- R, a polynomial ring
Outputs:
- S, a polynomial ring, a polynomial ring generated as a subring of R by the variables whose indices occur in the list v, together with the induced monomial ordering
- f, a ring map, the inclusion map from S to R

Description

i1 : (S,f) = selectVariables({2,4}, QQ[a..h,Weights=>1..8]);

i2 : describe S

o2 = QQ[c, e, Degrees => {2:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}]
                                                              {Weights => {3, 5} }
                                                              {GRevLex => {2:1}  }
                                                              {Position => Up    }

i3 : options S

o3 = OptionTable{Constants => false                   }
                                  1
                 DegreeGroup => ZZ
                 DegreeLift => null
                 DegreeMap => null
                 DegreeRank => 1
                 Degrees => {{1}, {1}}
                 Global => true
                 Heft => {1}
                 Inverses => false
                 Join => null
                 Local => false
                 MonomialOrder => {MonomialSize => 32}
                                  {Weights => {3, 5} }
                                  {GRevLex => {1, 1} }
                                  {Position => Up    }
                 SkewCommutative => {}
                 Variables => {c, e}
                 WeylAlgebra => {}

o3 : OptionTable

i4 : f

o4 = map (QQ[a..h], S, {c, e})

o4 : RingMap QQ[a..h] <-- S

Ways to use this method: