http://mathling.com/type/polynomial/quotient  library module

Imports

import module namespace util="http://mathling.com/core/utilities"
       at "../core/utilities.xqy"

import module namespace poly="http://mathling.com/type/polynomial"
       at "../types/polynomial.xqy"

import module namespace zpoly="http://mathling.com/type/polynomial/complex"
       at "../types/cpolynomial.xqy"

import module namespace errors="http://mathling.com/core/errors"
       at "../core/errors.xqy"

Functions

declare function this:quotient(
  $u as map(xs:string,item()*),
  $v as map(xs:string,item()*)
) as map(xs:string,item()*)
{
  if (util:kind($v)="polynomial" and poly:is-constant($v)) then (
    (: u / constant :)
    $u=>poly:times(1 div poly:as-real($v))
  ) else if (util:kind($v)="complex-polynomial" and zpoly:is-real($v)) then (
    this:quotient($u, zpoly:as-real-polynomial($v))
  ) else if (util:kind($u)="complex-polynomial" and zpoly:is-real($u)) then (
    this:quotient(zpoly:as-real-polynomial($u), $v)
  ) else (
    map {
      "kind": "polynomial-quotient",
      "u": $u,
      "v": $v
    }
  )
}

declare function this:u($poly as map(xs:string,item()*)) as map(xs:string,item()*)
{
  $poly("u")
}

declare function this:v($poly as map(xs:string,item()*)) as map(xs:string,item()*)
{
  $poly("v")
}

Original Source Code

xquery version "3.1";
(:~
 : One polynomial divided by another. The polynomial may be use real-values or
 : complex-valued coefficients. We attempt to simplify down where possible.
 :
 : Copyright© Mary Holstege 2023
 : CC-BY (https://creativecommons.org/licenses/by/4.0/)
 : @since May 2022
 : @custom:Status Bleeding edge
 :)
module namespace this="http://mathling.com/type/polynomial/quotient"; 

import module namespace errors="http://mathling.com/core/errors"
       at "../core/errors.xqy";
import module namespace util="http://mathling.com/core/utilities"
       at "../core/utilities.xqy";
import module namespace poly="http://mathling.com/type/polynomial"
       at "../types/polynomial.xqy";
import module namespace zpoly="http://mathling.com/type/polynomial/complex"
       at "../types/cpolynomial.xqy";

declare namespace map="http://www.w3.org/2005/xpath-functions/map";
declare namespace math="http://www.w3.org/2005/xpath-functions/math";

(:
 : quotient()
 : One polynomial divided by another: e.g. (2x³-x²+3)/(4x²-5x+1)
 : The polynomials may have either real or complex values.
 :
 : $u: one polynomial
 : $v: another polynomial
 :)
declare function this:quotient(
  $u as map(xs:string,item()*),
  $v as map(xs:string,item()*)
) as map(xs:string,item()*)
{
  if (util:kind($v)="polynomial" and poly:is-constant($v)) then (
    (: u / constant :)
    $u=>poly:times(1 div poly:as-real($v))
  ) else if (util:kind($v)="complex-polynomial" and zpoly:is-real($v)) then (
    this:quotient($u, zpoly:as-real-polynomial($v))
  ) else if (util:kind($u)="complex-polynomial" and zpoly:is-real($u)) then (
    this:quotient(zpoly:as-real-polynomial($u), $v)
  ) else (
    map {
      "kind": "polynomial-quotient",
      "u": $u,
      "v": $v
    }
  )
};

declare function this:u($poly as map(xs:string,item()*)) as map(xs:string,item()*)
{
  $poly("u")
};

declare function this:v($poly as map(xs:string,item()*)) as map(xs:string,item()*)
{
  $poly("v")
};