selectVariables -- make a subring of a polynomial ring generated by selected variables

i1 : R = QQ[a..h, Weights => 1..8]

o1 = R

o1 : PolynomialRing

i2 : (S,F) = selectVariables({2,4}, R);

i3 : describe S

o3 = QQ[c, e, Degrees => {2:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}]
                                                              {Weights => {3, 5} }
                                                              {GRevLex => {2:1}  }
                                                              {Position => Up    }

i4 : options S

o4 = 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 => {}

o4 : OptionTable

i5 : F

o5 = map (R, S, {c, e})

o5 : RingMap R <-- S