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7.3.21 preimage (plural)
Syntax:
preimage ( ring_name, map_name, ideal_name )
preimage ( ring_name, ideal_expression, ideal_name )
Type:
- ideal
Purpose:
- returns the preimage of an ideal under a given map.
The second argument has to be a map from the basering to the given ring
(or an ideal defining such a map),
and the ideal has to be an ideal in the given ring.
Note:
- To compute the kernel of a map, the preimage of zero has to be determined.
Hence there is no special command for computing the kernel of a map in
PLURAL.
Remark:
- In the non-commutative case, it is implemented only for maps
->
, where
is a commutative ring.
Example:
See
ideal (plural);
map (plural);
ring (plural).
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