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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 $h_1/(h_1 \cap h_2) \cong (h_1+h_2)/h_2$ where $h_1$ and $h_2$ are considered as submodules of the same free module $R^l$ (l=1 for ideals). Let $H_1$, resp. $H_2$, be the matrices of size $l \times k$, resp. $l \times m$, having the generators of $h_1$, resp. $h_2$, as columns. Then $h_1/(h_1 \cap h_2) \cong R^k / ker(\overline{H_1})$ where $\overline{H_1}: R^k \rightarrow R^l/Im(H_2)=R^l/h_2$ 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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            User manual for Singular version 2-0-4, October 2002, generated by texi2html.