5.1.66 lift
-----------
Syntax:
lift ( ideal_expression, subideal_expression )

lift ( module_expression, submodule_expression )

lift ( ideal_expression, subideal_expression, matrix_name )

lift ( module_expression, submodule_expression, matrix_name )
Type:
matrix
Purpose:
computes the transformation matrix which expresses the generators of a
submodule in terms of the generators of a module.  Uses different
algorithms for modules which are, resp. are not, represented by a
standard basis.

 More precisely, if  m is the
module (or ideal), sm the submodule (or ideal),
and T the transformation matrix returned by
lift, then matrix(sm)*U = matrix(m)*T
and module(sm*U) = module(matrix(m)*T)
(resp. ideal(sm*U) = ideal(matrix(m)*T)),
where U is a diagonal matrix of units.

U is always the unity matrix if the basering is a polynomial ring
(not power series ring). U is stored in the optional third argument.
Note:
Gives a warning if sm is not a submodule.
Example:
  ring r=32003,(x,y,z),(dp,C);
  ideal m=3x2+yz,7y6+2x2y+5xz;
  poly f=y7+x3+xyz+z2;
  ideal i=jacob(f);
  matrix T=lift(i,m);
  matrix(m)-matrix(i)*T;
==> _[1,1]=0
==> _[1,2]=0
See
division;
ideal;
module.
<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>.
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