Expand research roadmap

[danielsuit]

Summary

• Replaced the placeholder upcoming-functions file with a detailed research and implementation roadmap.
• Added deeper expansion plans for every existing README topic, professional maturity requirements, 50 additional math areas, and professional_function_catalog.md with 8,600 candidate functions.
• Moved the roadmap API surface into code with mathfunctionize/upcoming.py, metadata registry helpers, and callable placeholders for planned functions.
• Wired planned placeholders into mathfunctionize.mathfunctionize without overwriting implemented functions.
• Implemented real functions in previously thin or incomplete areas:
  • Statistics: fixed variance, added standardDeviation, sample statistics, quartiles, IQR, percentile, z-score, covariance, and correlation.
  • Probability: fixed gammaPDF, added Bernoulli/binomial/Poisson/exponential helpers, expected value, conditional probability, and independence checks.
  • Complex numbers: added shared parsing/formatting, multiplication, division, modulus, argument, and polar conversion helpers.
  • Number theory: added gcd/lcm, extended gcd, modular exponentiation/inverse, factorization, sieve, totient, coprime, divisors, and perfect-number checks.
  • Linear algebra: added identity, trace, minors, cofactors, inverse, row echelon, rank, dot product, cross product, and vector norm.
• Added focused tests for the newly implemented gap functions and updated roadmap-placeholder tests so newly implemented gcd is validated as real code.

Verification

• python3 -m unittest discover -v passed: 86 tests.
• git diff --check passed.
• Import/runtime spot checks passed for implemented gap functions including gcd, binomialPMF, and complex_multiplication.
• Previous registry verification remains covered by tests: professional catalog has 86 topics and 8,600 candidate functions, with 100 per topic.

  

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