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