PolyRing

• Examples

• User documentation for PolyRing
  • Pseudo-constructors
  • Queries and views
  • Operations on a PolyRing
  • Homomorphisms
• Maintainer documentation for PolyRing
• Bugs, Shortcomings and other ideas

Examples

• ex-PolyRing1.C
• ex-PolyRing2.C
• ex-PolyIterator1.C
• ex-PolyIterator2.C
• ex-PolyInput1.C
• ex-factor1.C

User documentation for PolyRing

PolyRing is an abstract class (inheriting from ring) representing rings of polynomials with coefficients in a commutative ring R.

The polynomials may be (dense) univariate or (sparse) multivariate.

See RingElem PolyRing for operations on its elements, but only a few operations are available at this level of abstraction: see RingElem SparsePolyRing or RingElem DenseUPolyRing for more operations on polynomials of SparsePolyRing or DenseUPolyRing.

Pseudo-constructors

There are several functions to create polynomial rings: see

• SparsePolyRing constructors for the sparse implementation and
• DenseUPolyRing constructors for the dense (univariate) implementation.

• PolyRing(R) -- sort of downcast the ring R to a poly ring; will throw an ErrorInfo object with code ERR::NotPolyRing if needed.

Queries and views

Let R be an object of type ring.

• IsPolyRing(R) -- true if R is actually PolyRing
• PolyRingPtr(R) -- pointer to impl of R (for calling mem fns); will throw an ErrorInfo object with code ERR::NotPolyRing if needed

Operations on a PolyRing

In addition to the standard ring operations, a PolyRing may be used in other functions.

Let P be an object of type PolyRing.

• NumIndets(P) -- the number of indeterminates in P
• CoeffRing(P) -- the ring of coefficients of P
• indets(P) -- a const std::vector of RingElems whose i-th element is the i-th indeterminate in P
• indets(P, str) -- a std::vector of RingElems with all indeterminates in P whose head is the string str
• indet(P,i) -- the i-th indet of P as a RingElem
• IndetPower(P,i,n) -- the n-th power of the i-th indet of P as a RingElem

Homomorphisms

Let P be an object of type PolyRing. Let R be an object of type ring.

CoeffEmbeddingHom(P)

-- the homomorphism which maps CoeffRing(P) into P

PolyRingHom(P, R, CoeffHom, IndetImages)

-- the homomorphism from P to R which maps the coeffs using CoeffHom, and maps the k-th indet into IndetImages[k]

EvalHom(P, IndetImages)

-- the evaluation homomorphism from P to CoeffRing(P) which is the identity on the coeffs, and maps the kth indet into IndetImages[k]

PolyAlgebraHom(P, R, IndetImages)

-- this is the identity on coeffs, and maps the k-th indet into IndetImages[k]

Maintainer documentation for PolyRing

The hard part has been deciding which member functions should be in PolyRingBase and which should be in less abstract classes. If you want to modify the code here, you should probably also look at SparsePolyRing and DUPolyRing before messing with the code!

The implementations in PolyRing.C are all very simple: they just conduct some sanity checks on the function arguments before passing them to the PolyRing member function which will actually do the work.

Bugs, Shortcomings and other ideas

What precisely should the fancy version of deriv do? What are permitted values for the second arg? Must coeff=1? What if the second arg does not have precisely one term?

The range of member functions on RawValues is rather a hotch-potch. Hopefully, experience and use of the code will bring some better order to the chaos.

Verify the true need for myRemoveBigContent, myMulByCoeff, myDivByCoeff. If the coeff ring has zero divisors then myMulByCoeff could change the structure of the poly!

Maintainer doc is largely absent.