irreducible vs unreconcilable

irreducible

adj
  • Not able to be reduced or lessened. 

  • Impossible to divide further into representations of lower dimension by means of any similarity transformation. 

  • Unable to be factorized into polynomials of lower degree, as (x² + 1). 

  • Not able to be brought to a simpler or reduced form. 

  • Unable to be factored into smaller integers; prime. 

  • Whose numerator and denominator share no common factor greater than 1. 

  • that its only divisors are units and associates. 

  • Not containing a sphere of codimension 1 that is not the boundary of a ball. 

noun
  • Such a polynomial 

unreconcilable

adj
  • Irreconcilable. 

noun
  • A person or thing that cannot be reconciled. 

How often have the words irreducible and unreconcilable occurred in a corpus of books? (source: Google Ngram Viewer )