AngouriMath

Navigation

Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug Donate Contacts

← Back to list of members

DivideExact

 Method with 2 overloads

• DivideExact​(AngouriMath.​Functions.​MultivariatePolynomial,​System.​Boolean@,​System.​Int32)

  Summary

  The same division, saying why there is no quotient. settled is false where the division ran out of room rather than finishing:
  the term count grew past maxTerms, a monomial went past
  MaxDegree, or the loop reached its step limit.
  

  Remarks

  A caller that reads a null as "does not divide" is right only where
  the division was settled. Where it was not, the same null means "no
  answer", and a caller drawing a mathematical conclusion from it — that a polynomial is
  irreducible, say — would be stating exhaustion as a fact.
  

• DivideExact​(AngouriMath.​Functions.​MultivariatePolynomial,​System.​Int32)

  Summary

  divisor divided out, or null when it does
  not divide exactly.
  

  Remarks

  The leading term in lexicographic order is cancelled at each step, which lowers
  it strictly, so the loop terminates; when the divisor really divides, its
  leading term divides the leading term of what is left every time, and what
  remains at the end is zero. Anything else — a leading term that will not divide,
  or a remainder that never reaches zero — is the answer that it does not divide.
  That is the check the caller relies on: nothing is cancelled that has not been
  divided out and seen to leave nothing behind.