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]