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5.1.73 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. Depending on which algorithm is used, modules are represented by a standard basis, or not.
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) = ideal(matrix(m)*T)), where U is a diagonal matrix of units.
U is always the identity 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:
 
See division; ideal; module.

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            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.