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5.1.75 modulo

Syntax:

modulo ( ideal_expression, ideal_expression )
modulo ( module_expression, module_expression )

Type:

module

Purpose:

modulo(h1,h2) represents h1(h1 h2)∼=(h1 + h2)∕h2 where h1 and h2 are considered as submodules of the same free module Rl (l=1 for ideals). Let H1, resp. H2, be the matrices of size l × k, resp. l × m, having the generators of h1, resp. h2, as columns. Then h1(h1 h2)∼=Rk∕ker(H1) where H1 : Rk Rl∕Im(H2) = Rl∕h2 is the induced map.
modulo(h1,h2) returns generators of the kernel of this induced map.

Example:
  ring r;
  ideal h1=x,y,z;
  ideal h2=x;
  module m=modulo(h1,h2);
  print(m);
→ 1,0, 0,0,
→ 0,-z,x,0,
→ 0,y, 0,x 

See syz.


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