Nice to have:

- Permutations -- composition (trivial; use sort and map-with)
- Analysis:
  - error function, cosine integral, sine integral, fresnel functions
  - logarithm integral, zeta function
  - airy wave function
  - hypergeometric functions
  - elliptic functions
  - numerical integration
  - numerical differentiation
  - infinite limits, sums, products (all done using a limit combinator)
  - finding roots with Newton's method
  - solving ODEs with Runge-Kutta
  - matrices: singular value decomposition, eigenvalues, LU decomposition,
    polar decomposition
  - square root of a matrix, e^matrix
  - finding roots of polynomials
- Algebra:
  - p^
  - p^mod for polynomials
  - pmod-inv for polynomials
  - matrices: row reduction, integer row reduction, matrix inverse,
    determinant
  - probablistic primality tests
  - polynomials over finite fields
  - elliptic curves: group of points, over Q and finite fields
  - elliptic curve factorization of integers
  - interval arithmetic
  - combinatorics: stirling numbers
  - factoring polynomials over finite fields
  - minimal and characteristic polynomials of algebraic numbers
  - norm and trace of algebraic numbers
  - minimal and characteristic polynomials of matrices
- Logic:
  - tautology checker
  - CNF, DNF
  - natural deduction proof checker
- Statistics:
  - linear regression
- Geometry:
  - regions
  - rectangles, ellipses, lines
  - unions, intersections, complements of regions
  - shortest distance between two regions
  - tangents
  - intersection testing
  - projections
- Symbolic algebra:
  - trigonometric identities
  - symbolic differentiation
  - differential forms
  - wedge product
  - power series
- Graphics:
  - 2D, 3D plots
  - y=f(x), implicit, parametric
  - "4D" animated 3D plots
  - prettyprinting of symbolic expressions