lift standard basis matrix N to lift result L

Determine if each column of N belongs to the submodule M generated by the standard basis. If so, ``lift'' N, obtaining a matrix L satisfying N = M L. Otherwise display an error message.

For example,

%  type j
; b2-ac c2-bd -bc+ad 

%  lift-std j j
; 2.3.4.
; computation complete after degree 4

%  poly f (a+b+c2)*(b2-ac)-(a3+c4)*(c2-bd)+(a3+b3)*(ad-bc)

%  lift j f f'

%  type f'
; bd+a+b       
; -c4-a3+b2-ac 
; a3+b3        

%  mult j f' g

%  subtract f g h

%  ; f should equal g, i.e. h = 0:
%  type h
; 0

This command returns the same value L as would be returned by the reduce command. The same restrictions and caveats that apply to reduce apply here as well: a standard basis of M and a change of basis matrix from this standard basis to the columns of M must both have been computed. Otherwise either an error is generated or the matrix L will consist entirely of zeros.