5.1.67 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 matrix(sm)=matrix(m)*T and sm=ideal(matrix(m)*T),
resp. sm=module(matrix(m)*T).
Example:
  ring R=0,(x,y,z),dp;
  poly f=x3+y7+z2+xyz;
  ideal i=jacob(f);
  matrix T;
  ideal sm=liftstd(i,T);
  sm;
==> sm[1]=xy+2z
==> sm[2]=3x2+yz
==> sm[3]=yz2+3048192z3
==> sm[4]=3024xz2-yz2
==> sm[5]=y2z-6xz
==> sm[6]=3097158156288z4+2016z3
==> sm[7]=7y6+xz
  print(T);
==> 0,1,T[1,3],   T[1,4],y,  T[1,6],0,
==> 0,0,-3x+3024z,3x,    0,  T[2,6],1,
==> 1,0,T[3,3],   T[3,4],-3x,T[3,6],0 
  matrix(sm)-matrix(i)*T;
==> _[1,1]=0
==> _[1,2]=0
==> _[1,3]=0
==> _[1,4]=0
==> _[1,5]=0
==> _[1,6]=0
==> _[1,7]=0
See
ideal;
matrix;
option;
ring;
std.
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&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,
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