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.
<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
</font>

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