### 7.3.14 modulo (plural)

`Syntax:`
  `modulo (` ideal_expression`,` ideal_expression `)`
  `modulo (` module_expression`,` module_expression `)`
`Type:`
  module
`Purpose:`
  `modulo(h1,h2)` represents , where and are considered as submodules of the same free module (l=1 for ideals).
  Let (resp. ) be the matrix of size (resp. ), having the generators of (resp. )as columns.
  Then , where is the induced map given by .
  `modulo(h1,h2)` returns generators of the kernel of this induced map.

`Note: If, for at least one of`
  or ,the attribute `isHomog` is st, then `modulo(h1,h2)` also sets this attribute (if the weights are compatible).

`Example:`

      LIB "ncalg.lib";
      def A = makeUsl2();
      setring A; // this algebra is U(sl_2)
      option(redSB);
      option(redTail);
      ideal H2 = e2,f2,h2-1;
      H2 = twostd(H2);
      print(matrix(H2)); // print H2 in a compact form
      ==> h2-1,fh-f,eh+e,f2,2ef-h-1,e2
      ideal H1 = std(e);
      ideal T = modulo(H1,H2);
      T = NF(std(H2+T),H2);
      T = std(T);
      T;
      ==> T[1]=h-1
      ==> T[2]=e

See also syz (plural).

User manual for Singular version 4.4.1, 2025, generated by texi2html.