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TODO.md

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TODO list

General

  • Finish SetPy and subclasses
    • Create tests for SetPy and subclasses

Future features

  • Matrices
    • Eigenvectors and eigenvalues
    • Diagonalization
    • Sparse and dense matrices
  • Functions
    • Intelligent function equality test (identities)
    • Find roots and fixed points
    • Limits
    • Integration (symbolic and definite)
    • Find max and min values
    • Taylor and Maclaurin series
    • Multivariate functions
  • Discrete math
    • Graphs
      • Directed and undirected
      • Test for acyclicity
      • Minimum spanning trees
      • Searches and shortest paths
      • Relation to digraph conversion and vice versa
    • Sets
      • Power sets and partitions
    • Relations
      • Produce range from domain and codomain
      • Tests for totality, function, surjectivity and injectivity
      • Composition and combination
      • Conversion from total functions on real numbers to Functions
    • Logical statements
      • Parse strings of logical statements
      • Generate truth tables
      • Generate proofs and counter examples
    • Automata and Languages
      • Finite State Automata
        • Nondeterministic and deterministic
      • Pushdown Automata
      • Grammars
      • Conversion between automata types, minimization, equality tests
  • Abstract algebra
    • Groups (finite)
      • Test if set is group under operator
      • Find identity and inverses of elements
      • Find subgroups
      • Test if two groups are isomorphic
    • Permutations (finite)
      • Test if function is permutation on a finite set
      • Decompose permutation into disjoint cycles
      • Find if permutation is even or odd
      • Compose permutations
      • Find order of permutation
  • Number theory
    • Greatest common divisor / lowest common multiple
      • Euclid's algorithm
    • Modular arithmetic
    • Coprime and prime tests
  • Sequences
    • Infinite sums
      • Tests for convergence and divergence
  • Geometric shapes
    • Circles and ellipses
    • Arbitrary polygons
    • Area, perimeter
    • Solving for angles
    • Finding symmetries
  • Random variables
    • Discrete and continuous
    • Expected value, variance, median and mode
    • Arithmetic on variables
  • Distributions
    • Binomial, Gaussian, Chi squared, etc.
  • Graphics and plotting support
    • Plotting functions
    • Drawing shapes
    • Drawing distributions
    • Drawing graphs
    • Venn diagrams of sets