Matrix Cofactors

Dot product

Cross product

Matrix product

Computes AB

Matrix-vector product

Computes MV where V is represented as a 1D list of numbers

Matrix power

Quaternion product

Computes PQ for quaternion arrays P and Q.

Semi-pervasive; the last axis of the inputs must be of length 4, and will be interpreted as the input quaternions’ real, i, j, and k.

# Computes (1+2i+3j+4k)(1+3i+5j+7k) and (2+4i+6j+8k)(5+6i+7j+8k)
Qqp [1_2_3_4 2_4_6_8] [1_3_5_7 5_6_7_8]
## ╭─
## ╷  ¯48  6  6 12
##   ¯120 24 60 48
##                 ╯

Create 3D rotation quaternions.

Expects an angle array θ and a unit vector axis array U.

Semi-pervasive; the unit vector array must have one extra trailing axis compared to the angle array, and that axis must be length 3.

For each angle-vector pair, computes cos(θ/2) + Usin(θ/2).

# Creates two rotation quaternions:
# - η radians about 0_0_1
# - π radians about 3/5_4/5_0
RQuat η_π [0_0_1 3/5_4/5_0]

To use rotation quaternions created by RQuat to rotate 3D vectors, see QRot.

Rotate a 3D vector array using a quaternion array.

To create rotation quaternions to use with QRot, see RQuat.

Expects a quaternion array Q and a 3D vector array V.

Semi-pervasive; the input arrays should have matching shapes aside from the final axis, which should be of lengths 4 and 3 respectively.

For each quaternion-vector pair, computes Q * V * Q’.

RQuat η 0_0_1        # Create a rotation by η radians about 0_0_1
QRot ¤⊙[3_2_0 1_3_2] # Use the quaternion to rotate 3_2_0 and 1_3_2

QRot can be used with ⍜ to undo the rotations afterward.

Greatest common divisor

Ignores sign

Least common multiple

Ignores sign

Encode an array of numbers into digits of a given base

Analogous to ⋯ for base 2; the least significant digit is first.

Base allows multiple bases as input.

# Encodes 6 in base 2, 7 in base 3, 8 in base 4, and 9 in base 5.
Base [2_3 4_5] [6_7 8_9]
## ╭─
## ╷ 0 1 1
## ╷ 1 2 0
##
##   0 2 0
##   4 1 0
##         ╯

You can use ⌝Base to decode from a base/bases.

# Decodes 6 in base 2, 7 in base 3, 8 in base 4, and 9 in base 5.
⌝Base [2_3 4_5] [[0_1_1 1_2_0] [0_2_0 4_1_0]]
## ╭─
## ╷ 6 7
##   8 9
##       ╯

Inverse of N modulo M (M if nonexistent)

Multiplicative order of N modulo M

Convert a number X to a continued fraction to N terms.

Use °CFrac to convert to a number from a continued fraction.

Box-Muller transform

Converts uniformly distributed pairs of input values to standard normally distributed pairs of output values

Generate a 2 dimensional square Gaussian kernel

Geometric distribution

Probability of X failures before the first success of repeated trials with success probability p

Cumulative geometric distribution

Probability of X or fewer failures before the first success of repeated trials with success probability p

Poisson distribution

Probability of X occurrences of an unlikely event over many trials with expected value λ

Cumulative Poisson distribution

Probability of X or fewer occurrences of an unlikely event over many trials with expected value λ