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7.3.11 lift (plural)
Syntax:
lift ( ideal_expression, subideal_expression )
lift ( module_expression, submodule_expression )
Type:
- matrix
Purpose:
- computes the (left) transformation matrix which expresses the (left) generators of a
submodule in terms of the (left) generators of a module. Uses different
algorithms for modules which are (resp. are not) represented by a
Groebner basis.
More precisely, if m is the module, sm the submodule, and T the
transformation matrix returned by lift, then transpose(matrix(sm)) = transpose(T)*transpose(matrix(m)) .
If m and sm are ideals, ideal(sm) = ideal(transpose(T)*transpose(matrix(m))) .
Note:
- Gives a warning if
sm is not a submodule.
Example:
See
ideal (plural);
liftstd (plural);
module (plural).
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