deep-rooted vs invariant

deep-rooted

adj
  • Firmly established in thought or behaviour and difficult to change. 

  • Having deep roots; (of a non-living object) deeply and firmly embedded (in the ground, etc.). 

invariant

noun
  • An invariant quantity, function etc. 

adj
  • Neither covariant nor contravariant. 

  • not varying; constant 

  • Unaffected by a specified operation (especially by a transformation) 

How often have the words deep-rooted and invariant occurred in a corpus of books? (source: Google Ngram Viewer )