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3.10 liftstd

Syntax:
liftstd ( ideal_expression, matrix_name )
liftstd ( module_expression, matrix_name )
Type:
ideal or module
Purpose:
returns a standard basis of an ideal or module and the transformation matrix from the given ideal, resp. module, to the standard basis.
That is, if m is the ideal or module, sm the standard basis returned by liftstd, and T the transformation matrix then transpose(matrix(sm))=transpose(T)*transpose(matrix(m)) and sm=ideal(transpose(T)*transpose(matrix(m))), resp. sm=module(transpose(transpose(T)*transpose(matrix(m)))).
Example:
 
  LIB "ncalg.lib";
  def A = sl2();
  setring A;
  ideal i = e2,f;
  option(redSB);
  option(redTail);
  matrix T;
  ideal j = liftstd(i,T);
  print(T);
==> 0,f2,         -f,1,
==> 1,-e2f+4eh+8e,e2,0 
  ideal tj = ideal(transpose(T)*transpose(matrix(i)));
  std(ideal(j-tj)); // test
==> _[1]=0
See ideal; @xref{matrix}; option; ring; std.


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            User manual for Singular version 2-1-99, August 2004, generated by texi2html.