DefaultRing( r, s... )
DefaultRing( list )
In the first form
DefaultRing returns the default ring that contains
all the elements r, s... etc. In the second form
returns the default ring that contains all the elements in the list
list. If any element is not an element of a ring or if the elements
lie in no common ring an error is raised.
The ring returned by
DefaultRing need not be the smallest ring in which
the elements lie. For example for elements from cyclotomic fields
DefaultRing may return the ring of integers of the smallest cyclotomic
field in which the elements lie, which need not be the smallest ring
overall, because the elements may in fact lie in a smaller number field
which is not a cyclotomic field.
For the exact definition of the default ring of a certain type of elements read the chapter describing this type.
DefaultRing is used by the ring functions like
Gcd if no explicit ring is given.
gap> DefaultRing( 1, -1 ); Integers gap> DefaultRing( [10..20] ); Integers
Ring (see Ring) differs from
DefaultRing in that it returns the
smallest ring in which the elements lie, while
DefaultRing may return a
larger ring if that makes sense.
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