## `Cat::UnivariatePolynomial` -- the category of univariate polynomials

#### Introduction

``Cat::UnivariatePolynomial`(R)` represents the category of univariate polynomials over `R`.

#### Generating the category

`Cat::UnivariatePolynomial(R)`

#### Parameters

`R` | - | A domain which must be from the category `Cat::CommutativeRing`.

#### Categories

if `R` has `Cat::Field` then
`Cat::EuclideanDomain`
`Cat::Polynomial(R)`

, `Cat::DifferentialRing`

#### Details

- A ``Cat::UnivariatePolynomial`(R)` is a univariate polynomial over the commutative ring `R`.

#### Method pdivide: pseudo-divide polynomials

- `pdivide(dom p, dom q)`
- - Must compute the pseudo-division of `p` and `q`.
  - Must return a sequence `(b, s, r)` of a ring element `b` and polynomials `s` and `r` such that `multcoeffs(p, b) = s * q + r` holds with `b = lcoeff(q)^(degree(p) - degree(q) + 1)`.

#### Method pquo: returns pseudo-quotient

- `pquo(dom p, dom q)`
- - Must return the pseudo-quotient of `p` and `q`, i.e. the second element `s` of the sequence returned by the method `"pdivide"`.

#### Method prem: returns pseudo-reminder

- `prem(dom p, dom q)`
- - Must return the pseudo-reminder of `p` and `q`, i.e. the third element `r` of the sequence returned by the method `"pdivide"`.

#### Changes

- Has been renamed. Used to be `Cat::UnivariatePolynomialCat`.

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