Universal mapping for free algebra. This corresponds to the algebraic substitution operation.

A variant of liftMap, each value is given by Sized.

Another variant of liftMap. This function relies on terms'; if you have more efficient implementation, it is encouraged to override this method.

Since 0.6.0.0

Arity of given polynomial.

Arity of given polynomial, using type proxy.

Non-dependent version of arity.

Inject coefficient into polynomial.

Inject coefficient into polynomial with result-type explicitly given.

monomials f returns the finite set of all monomials appearing in f.

monomials f returns the finite set of all terms appearing in f; Term is a finite map from monomials to non-zero coefficient.

'coeff m f' returns the coefficient of monomial m in polynomial f.

Calculates constant coefficient.

Inject monic monomial.

Inject coefficient with monomial.

Construct polynomial from the given finite mapping from monomials to coefficients.

Returns total degree.

var n returns a polynomial representing n-th variable.

Adjusting coefficients of each term.

m >|* f multiplies polynomial f by monomial m.

Flipped version of (>|*)

A variant of coeff' which takes OrderedMonomial instead of Monomial

The default implementation is not enough efficient. So it is strongly recomended to give explicit definition to terms.

Leading term with respect to its monomial ordering.

Leading monomial with respect to its monomial ordering.

Leading coefficient with respect to its monomial ordering.

Splitting leading term, returning a pair of the leading term and the new polynomial with the leading term subtracted.

The collection of all monomials in the given polynomial, with metadata of their ordering.

A variant of fromMonomial which takes OrderedMonomial as argument.

A variant of toPolynomial' which takes OrderedMonomial as argument.

A variant of polynomial' which takes OrderedMonomial as argument.

The default implementation combines mapKeys and polynomial', hence is not enough efficient. So it is strongly recomended to give explicit definition to polynomial.

A variant of (>|*) which takes OrderedMonomial as argument.

Flipped version of (>*)

diff n f partially diffrenciates n-th variable in the given polynomial f. The default implementation uses terms and polynomial and is really naive; please consider overrideing for efficiency.

Same as mapMonomial, but maping function is assumed to be strictly monotonic (i.e. a < b implies f a < f b).