An expert system for solving Maths problems.

Currently the system:

• [X] Parses simple expressions
  • [X] The Four Six basic Functions
  • [X] Parentheses
  • [X] Common operators
    • Logs, Trig, Exponents
• [X] Outputs in LaTeX
• [X] Performs Constant Reduction
  • [X] Identity Elements
  • [X] Zero Elements
  • [X] Calculable Values
• [X] Parses Complex Expressions (LaTeX Like Language)
  • [X] Local Bindings
  • [X] Substitutions
  • [X] Ranged Operators (Summation)
• [X] Parses implied binding scopes
  • Parentage’s are often implied in summation notation
  • This is the first step in parsing Einstein Tensor Notation
• [ ] Unnests Separable bindings
• [ ] Performs Bounded Operations
• [-] Handles all algebraic numbers
  • [-] Special Constants
    • [X] The Common Ones
    • [ ] The Uncommon Ones
  • [ ] Arbitrary precision numbers
  • [ ] Rationals and Radicals
  • [ ] Power Towers
• [ ] Factor Polynomials
  • Have a special function called Roots that takes a polynomial and returns the algebraic roots
  • [ ] Have special cases for the Quadratic, Cubic, and Quartic formulæ
  • [ ] Use the Rational Root Theorem to find simple cases
  • [ ] Use Newton’s method to guess values and then try local algebraic numbers
    • This will look for symbolic roots near the point
    • In the worst case, this can “factor” a polynomial with a number that is only approximately known, which is good enough for some later methods to check validity.
      • The “number” can be compared with algebraic numbers as long as the polynomial has finite roots within the neighborhood.
• [ ] Rationalizes Denominators
  • Only when it makes things look better?
  • Will need a “score” for how pretty a result is to perform advanced simplification
  • This same part will also be used moving complex numbers to the numerator
• [-] Explores Integration Techniques
  • [X] Dynamic Binding Scopes
  • [ ] Symbolic Differentiation
  • [ ] Tree search though substations with a simplicity metric
    • [ ] U-Substitution
    • [ ] By Parts
    • [ ] Laplace
    • [ ] Half Tangent
    • [ ] Complexifying