The call RingZZ() produces the CoCoA ring which represents ZZ, the
ring of integers. Calling RingZZ() several times will always produce
the same unique CoCoA ring representing ZZ.
Strictly, there is a limit on the size of elements you can create, but the limit is typically high enough not to be bothersome.
See RingElem for operations on its elements.
Efficiency of arithmetic on elements of RingZZ() should be reasonable
rather than spectacular. If you wish to compute purely with integers
(without exploiting CoCoALib's rings) then see the documentation in
BigInt.
RingZZ() -- produces the CoCoA ring which represents ZZ.
Calling RingZZ() several times will always produce the same unique
ring in CoCoALib.
Let R be a ring
IsZZ(R) -- says whether R is actually RingZZ()
Let S be a ring
NewZZEmbeddingHom(S) -- creates the homomorphism ZZ --> S
(but see also CanonicalHom).
ZZ argument is implicit because there is a
unique copy
The function RingZZ() simply returns the unique instance of the
CoCoALib ring representing ZZ. This instance is managed by
GlobalManager, see its documentation.
The function MakeUniqueInstanceOfRingZZ is the only function which can
call the ctor of RingZZImpl. The only function which is supposed to
call MakeUniqueInstanceOfRingZZ is the ctor of GlobalManager. I have
discouraged others from calling MakeUniqueInstanceOfRingZZ by not putting
it in the header file RingZZ.H -- see bugs section in GlobalManager.
The class RingZZImpl is really very simple. It may look daunting and
complex because it inherits lots of virtual functions from RingBase.
It contains just three data members: a MemPool for managing the storage
of the mpz_t headers, and pointers to the ring's own zero and one elements.
The member functions for arithmetic are all quite simple. The only
minor difficulty is in the function AsMPZ which gets at the mpz_t
hidden inside a RingElemRawPtr. I have decided to stick with the C
interface to GMP for the moment (even though GMP 4 does offer a C++
interface). This appears to be more a personal choice than a technical
one.
Recall (from ring) that arithmetic on ring elements always passes
via the virtual member functions of the concrete rings, and that these
expect arguments to be of type RawPtr or ConstRawPtr. The arguments
are pointers to the mpz_t headers which reside in a region of memory
controlled by the MemPool belonging to the RingZZImpl class.
Given that the mpz_t values must live on the free store, we use a MemPool
to handle the space for their headers (which are of fixed size). Note that
this MemPool is NOT what handles the memory used for the digits (or limbs)
of the GMP integer values! Currently limb space is handled by whatever is
the default allocator (malloc, I suppose).
The data members myZeroPtr and myOnePtr just hold auto_ptrs to the zero
and one elements of the RingZZImpl. I used an auto_ptr to avoid having
to worry about freeing it in the destructor; the zero and one values cannot be
RingElems because their creation must be deferred. I opted not to store the
values in RingElem fields to avoid any possible problem due to a "race
condition" where elements of the ring would be constructed before the
body of the constructor of the ring had begun execution (might be OK
anyway, but could easily lead to hair-raising bugs (e.g. in the dtor)).
This code is probably not exception safe; I do not know what the
mpz_* functions do when there is insufficient memory to proceed.
Making the code "exception safe" could well be non-trivial: I suspect
a sort of auto_ptr to an mpz_t value might be needed.
Should I switch to the C++ interface for GMP integers?
It is a shame that the mpz_t headers are "out of line". How much this may
affect run-time performance I don't know.
Generation of random elements in RingZZ is not possible (yet???).