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3.13 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:
 
  LIB "ncalg.lib";
  def A = sl2();
  setring A;
  option(redSB);
  option(redTail);

  ideal I = e2,f2,h2-1;
  I = twostd(I);
  I;
==> I[1]=h2-1
==> I[2]=fh-f
==> I[3]=eh+e
==> I[4]=f2
==> I[5]=2ef-h-1
==> I[6]=e2
  ideal E = std(e);
  ideal T = modulo(E,I);
  T = NF(std(I+T),I);
  T = std(T);
  T;
==> T[1]=h-1
==> T[2]=e
See syz.


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