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Each CoCoA object has a type. The possible types are:

BOOL : A boolean. The boolean constants are TRUE and FALSE.
DEVICE : For input/output.
ERROR : Objects of this type are used in error-handling.
FUNCTION : A CoCoA-defined function.
IDEAL : An ideal.
INT : An arbitrary precision integer.
LIST : A list.
MAT : A matrix.
MODULE : A submodule of a free module.
NULL : The null constant is Null.
POLY : A polynomial.
RAT : An arbitrary precision rational number.
RATFUN : A rational function.
RECORD : A record is a set of bindings, name --> object.
RING : A base ring, a polynomial ring, or a quotient ring.
STRING : A string.
TAGGED : Used to help in printing complicated objects.
TYPE : Returned by the function `Type`, for example.
VECTOR : A vector.
ZMOD : An integer modulo another integer, e.g. 3 % 5.

The types are partially ordered by inclusion of the sets that they
represent, as follows:

MAT < LIST
VECTOR < LIST
INT < RAT < POLY < RATFUN
ZMOD < POLY < RATFUN (if compatible).

In the manual, OBJECT is used to refer to an arbitrary CoCoA type. It
is not a type itself.