buildEMonomialMap -- builds an equivariant ring map

Synopsis

Usage:

m = buildEMonomialMap
Inputs:
- R, a ring, the target ring with symmetric action, produced by buildERing
- S, a ring, the source ring with symmetric action, produced by buildERing
- L, a list, a list of monomials in R, the images of each of the variable orbit generators of S
Outputs:
- m, a ring map, an equivariant monomial map to R from S

Description

R and S must be rings created by buildERing. Each orbit of variables in S consists of variables of the form x_{(i_1,...,i_k)} for some width k. L is a list that for each such orbit gives the desired image of x_{(0,...,k-1)}. The rest of the map is extrapolated from these value.

i1 : R = buildERing({symbol x, symbol y}, {1,1}, QQ, 3);

i2 : vars R

o2 = | x_2 x_1 x_0 y_2 y_1 y_0 |

             1      6
o2 : Matrix R  <-- R

i3 : n = buildEMonomialMap(R,R,{x_0,x_0^3})

                              3   3   3
o3 = map (R, R, {x , x , x , x , x , x })
                  2   1   0   2   1   0

o3 : RingMap R <-- R

i4 : n(x_1^3*y_0)

      3 3
o4 = x x
      1 0

o4 : R

i5 : S = buildERing({symbol z}, {2}, QQ, 3);

i6 : vars S

o6 = | z_(2,2) z_(2,1) z_(2,0) z_(1,2) z_(1,1) z_(1,0) z_(0,2) z_(0,1)
     ------------------------------------------------------------------------
     z_(0,0) |

             1      9
o6 : Matrix S  <-- S

i7 : m = buildEMonomialMap(R,S,{x_0^2*y_1})

                  2     2     2     2     2     2     2     2     2
o7 = map (R, S, {x y , x y , x y , x y , x y , x y , x y , x y , x y })
                  2 2   2 1   2 0   1 2   1 1   1 0   0 2   0 1   0 0

o7 : RingMap R <-- S

i8 : m(z_(1,2))

      2
o8 = x y
      1 2

o8 : R

Caveat

If a given variable orbit of S has k indices, then the target monomial list in L should only use indices between 0 and k-1.

Ways to use buildEMonomialMap :

buildEMonomialMap(Ring,Ring,List)

For the programmer