amoeba

1.0.0

Nelder-Mead multi-dimentional minimization, aka the amoeba method

bigpi

1.0.0

Calculate several digits of pi

brent

1.0.0

Brent's method in J

contfrac

1.0.0

Continued fraction utilities

det

1.0.0

Definitions for determinants

fermat

1.0.0

Fermat factorization

gamesolver

1.0.0

Find optimal mixed strategies for 2-person games

gcd

1.0.0

Calculate GCD

integer

1.0.0

Various integer definitions

integrat

1.0.0

Various methods for numeric integration

jacobi

1.0.0

Jacobi's method for eigenvalues and vectors

legendre

1.0.0

Legendre symbol and quadratic residues

linear

1.0.0

Solve linear equations

makemat

1.0.0

Make various matrices

matfacto

1.0.0

Matrix factorization

mathutil

1.0.0

Math utilities

matutil

1.0.0

Matrix utilities

mean

1.0.0

Various means

numbers

1.0.0

Various number definitions

pollard

1.0.0

Pollard factorizations

poly

1.0.0

Polynomial functions

primutil

1.0.0

Primes - prime testing programs

quatern

1.0.0

Definitions for quaternions

rsa

1.0.0

RSA encryption

simplex

1.0.0

Simplex method

simplexnr

1.0.0

Simplex method

spline

1.0.0

Spline utilities

svd

1.0.0

Singular value decomposition

amoeba

c

Nelder-Mead multi-dimentional minimization

bigpi

v

Calculate pi to different levels of of precision

brent

a

Adverb to solve f(x) = y0 by Brent's method.

contfrac

v

create continued fraction

contfracx

v

expand continued fraction

det

v

Determinants of a matrix by recursive expansion of minors

detm

v

Determinants of square matrix by Gauss elimination

fermatfactor

v

Find factor of n near square root of n using Fermat's method

solvegame

v

Find optimal mixed strategies for 2-person games

gcd

v

Greatest common denominator

inta

v

Augmented integers

inte

v

Extended integers

ints

v

Symmetric integers

intm

v

Minus integers

intn

v

Normal integers

intr

v

Reflexive integers

jint

v

Complex integers

jints

c

symmetric ints

integrate

c

Numeric integration by Aitken extrapolation on Gauss integrals

simpson

c

Numeric integration by Simpson's method

adapt

c

Numeric integration by adaptive quadrature

jacobi

v

Calculate eigenvalues and vectors using Jacobi's method

quadres

v

Quadratic residues of p

quadrec

v

Quadratic reciprocity

legendre

v

Legendre symbol (n/p) for integer n, odd prime p

gauss_elimination

v

Gauss elimination (partial pivoting)

gauss_jordan

v

Gauss-Jordan elimination (full pivoting)

gauss_seidel

v

Solves Ax=B for matrix A, vector B

jacobi_iteration

v

Solves Ax=B for matrix A, vector B

bandmat

v

Band matrix in position x from diagonal y

cidmat

v

Counter identity matrix of size y

diagmat

v

Diagonal matrix with y on diagonal

hilbertmat

v

Hilbert matrix of size y

ltmat

v

Lower triangular matrix (of 1's) of size y

utmat

v

Upper triangular matrix (of 1's) of size y

choleski

v

Choleski decomposition of matrix y

lud

v

LU decomposition of matrix y

qrd

v

QR decomposition of matrix y

det

v

Determinant of matrix y

mp

v

Matrix product of x and y

powermod

a

x (n powermod) y computes n|x^y

randomint

v

Random integer in range 0, <: 10^y

randomintd

v

Random integer with y digits

timesmod

a

x (n timesmod) y computes n|x*y

diag

v

Diagonal of matrix

invsut

v

Invert square upper-triangular matrix

minors

v

minors of matrix

band

v

b band M - zero all but x bands of matrix y

cond

v

Condition number of matrix

pivot

v

Pivot at row, column

coldrop

v

Drop cols from M

coltake

v

Take cols from M

rowdrop

v

Drop rows from M

rowtake

v

Take rows from M

rowswap

v

Swap rows i and j

rowscale

v

Multiply row i by n

rowshear

v

Multiply row j by n and add to row i

arithmean

v

Arithmetic mean of y

geomean

v

Geometric mean of y

harmean

v

Harmonic mean of y

commonmean

v

Common mean of y

bell

v

Number of ways of partitioning y things into subsets

bernoulli

v

Bernoulli numbers from 0 to y

catalan

v

Catalan numbers

cycles

v

Table of Stirling cycle numbers (S1)

cycle

v

Number of ways of partitioning n items into k cycles

eulers

v

Table of Eulerian numbers

euler

v

Number of permutations of size n with k ascents

fermat

v

Fermat numbers

fibonacci

v

first y+1 Fibonacci numbers

lucas

v

first y+1 Lucas numbers

fibbinet

v

Calculates nth Fibonacci number using Binet formula

subsets

v

Table of Stirling subset numbers (S2)

subset

v

Number of ways of partitioning n items into k sets

tangent

v

tangent numbers from 0 to y

pollardrho

v

Pollard rho factorization

pollardpm1

v

Pollard p-1 factorizaton

chebyshev_tp

v

Evaluate Chebyshev T polynomial of order n at x

chebyshev_up

v

Evaluate Chebyshev U polynomial of order n at x

chebyshev_tpc

v

Returns coefficients of Chebyshev T polynomial of order n

chebyshev_upc

v

Returns coefficients of Chebyshev U polynomial of order n

legendre_pc

v

Returns coefficients of legendre polynomial of order n

prevprime

v

Previous prime number to y

nextprime

v

Next prime number after y

primeq

v

Test for prime

primesto

v

Primes up to y

carmichaelq

v

Test composite for Carmichael number

inversep

v

Inverse mod p

mersenneq

v

Test if prime p generates a mersenne prime

primepowersto

v

Generate prime powers up to y

smallprimefactors

v

Get small primefactors from number

qncon

v

Conjugate

qnmul

v

Multiplication

qnrec

v

Reciprocal

qndivl

v

Division (left quotient)

qndivr

v

Division (right quotient)

qndivml

v

Division (using matrix divide, left quotient)

qndivmr

v

Division (using matrix divide, right quotient)

qnpolar

v

Convert to/from polar form

simplex

v

Simplex method

simplexnr

v

Run simplex method

cubicspline

v

Calculate cubic spline

interspline

v

Interpolate spline

freespline

v

Calculate spline

aprxspline

v

Approximate by spline

svd

v

Singular value decomposition of matrix y