Not all elementary functions can be expressed with exp-minus-log

https://www.stylewarning.com/posts/not-all-elementary/

Article

  • Critiques a paper claiming all elementary functions reduce to exp-minus-log (EML)
  • Points out EML can’t express polynomial roots like √x, which are classically elementary
  • Argues the paper uses a narrower-than-standard definition of “elementary function”

Discussion

  • Original paper authors acknowledged the limitation; debate is definitional, not mathematical
  • Commenters split: some call it goal-post-moving, others say it’s a valid scoping critique
  • Connection to Risch algorithm and symbolic integration brought up
  • Practical EML implementation linked; trig functions failing due to mirrored-case issues

Discuss on HN


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Added Apr 15, 2026
Modified Apr 15, 2026