I want to build a CAS that includes the following features (though not necessary all at the same time)

• Operations
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Exponentiation
    • Handle roots as exponentiation by a fraction
  • Trigonometric functions
  • Logarithims
• Numbers
  
  • Floating points
  • Native/intelligent handling of ratios/fractions
  • Multiples of pi
  • uint8_t, uint16_t, etc. programmer math with BIN, HEX representation
  • Complex numbers in a+bi and ae^bi form
  • Matrices
  • Vectors
  • Quanternions
• Features
  • Calculation with units
    • Automatic conversion between unit types including Freedom system
  • Algebra
    • Solving for variables
    • Substituting variables
  • Calculus
    • Basic integration/differentiation according to tables