RingQQ

• User documentation for RingQQ
  • Examples
  • Constructors and pseudo-constructors
  • Query
  • Operations on RingQQ
  • Homomorphisms
• Maintainer documentation for the class RingQQImpl
• Bugs, Shortcomings and other ideas

User documentation for RingQQ

The call RingQQ() produces the CoCoA ring which represents QQ, the field of rational numbers. Calling RingQQ() several times will always produce the same unique CoCoA ring representing QQ.

Strictly, there is a limit on the size of elements you can create, but the limit is typically high enough not to be bothersome.

RingQQ is the FractionField of RingZZ;

See RingElem for operations on its elements.

If you wish to compute purely with rationals (without exploiting CoCoALib's rings) then see the documentation in BigRat.

Examples

• ex-RingQQ1.C

Constructors and pseudo-constructors

• RingQQ() -- produces the CoCoA ring which represents QQ. Calling RingQQ() several times will always produce the same unique ring in CoCoALib.

Query

Let R be a ring

• IsQQ(R) -- says whether R is actually RingQQ()

Operations on RingQQ

See FractionField operations.

Homomorphisms

Let S be a ring

• NewQQEmbeddingHom(S) -- creates the (partial) homomorphism QQ --> S (but see also CanonicalHom). QQ argument is implicit because there is a unique copy

Maintainer documentation for the class RingQQImpl

The function RingQQ() simply returns the unique instance of the CoCoALib ring representing QQ. This instance is managed by GlobalManager, see its documentation.

The function MakeUniqueInstanceOfRingQQ is the only function which can call the ctor of RingQQImpl. The only function which is supposed to call MakeUniqueInstanceOfRingQQ is the ctor of GlobalManager. I have discouraged others from calling MakeUniqueInstanceOfRingQQ by not putting it in the header file RingQQ.H -- see bugs section in GlobalManager.

RingQQImpl is the implementation of the field of rational numbers following the scheme laid by RingBase and FractionFieldBase. Almost all member functions are trivial: indeed, virtually all the work is done by the GMP library. Once you have understood how RingZZImpl works, the implementation here should be easy to follow.

The implementation of RingQQImpl::InducedHomImpl::myApply turns out to be a bit lengthy, but I do not see how to improve it. Since partial homomorphisms can be built, myApply maps numerator and denominator then must check that their images can be divided. I cannot reuse the implementation of FractionFieldImpl::InducedHomImpl::myApply because there is no equivalent of RefNum and RefDen in RingQQImpl.

Bugs, Shortcomings and other ideas

This code is probably not exception safe; I do not know what the mpq_* 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 mpq_t value might be needed.

How to check that induced homomorphisms are vaguely sensible?? e.g. given ZZ->ZZ[x] ker=0, but cannot induce QQ->ZZ[x]; so it is not sufficient simply to check that the kernel is zero.