subduction -- Performs subduction by the generators of a subring.

Synopsis

• Usage:

  result = subduction(subGens, f)

  resultMat = subduction(subGens, M)

• Inputs:
  • f, a ring element, an element of ring M.
  • M, a matrix, a one-row matrix containing elements ring M.
  • subGens, a matrix, a one-row matrix containing elements ring M.
• Outputs:
  • result, a ring element, of ring M
  • resultMat, a matrix, of elements of ring M

Description

i1 : gndR = QQ[symbol t_1, symbol t_2, symbol t_3];

i2 : G = matrix {{t_1^4*t_2^4*t_3^4, (t_1^8)*t_2*t_3^8}}

o2 = | t_1^4t_2^4t_3^4 t_1^8t_2t_3^8 |

                1          2
o2 : Matrix gndR  <--- gndR

i3 : subduction(G, G_(0,0))

o3 = 0

o3 : gndR

i4 : subduction(G, G_(0,0)*G_(0,1) + t_1)

o4 = t
      1

o4 : gndR

i5 : subduction(G, t_1)

o5 = t
      1

o5 : gndR