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SubalgebraBases :: subduction

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



Performs subduction of the second argument by the elements of subGens. If the second argument is a one-row matrix, subduction is performed on each entry individually and the resulting one-row matrix is returned. If the second argument is a ring element f, subduction is performed on f and the result is returned. The generators of subR are not required to be a Sagbi basis.

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

o4 : gndR
i5 : subduction(G, t_1)

o5 = t

o5 : gndR

Ways to use subduction :

For the programmer

The object subduction is a method function.