Maps are ring maps from a preimage ring into the basering.
The target of a map is ALWAYS the actual basering
The preimage ring has to be stored "by its name", that means, maps can only be
used in such contexts, where the name of the preimage ring can be
resolved (this has to be considered in subprocedures).
See also Identifier resolution, Names in procedures.
Maps between rings with different coefficient fields are
possible and listed below.
Canonically realized are
Possible are furthermore
Finally, in SINGULAR we allow the mapping from rings
with coefficient field Q to rings whose ground fields
have finite characteristic:
In these cases the denominator and the numerator
of a number are mapped separately by the usual
map from Z to Z/p, and the image of the number
is built again afterwards by division. It is thus
not allowed to map numbers whose denominator is
divisible by the characteristic of the target
ground field, or objects containing such numbers.
We, therefore, strongly recommend using such
maps only to map objects with integer coefficients.