# IncidenceAlgebra(R, S)¶

A domain for incidence matrices of finite posets.

*: (%, %) -> %
x * y is the product of the matrices x and y. Error: if the dimensions are incompatible.
*: (%, R) -> %
r*x is the left scalar multiple of the scalar r and the matrix x.
*: (Permutation Integer, %) -> %
\pi * A permutes the indices and the matrix according to the permutation \pi.
*: (R, %) -> %
r*x is the left scalar multiple of the scalar r and the matrix x.
+: (%, %) -> %
x + y is the sum of the matrices x and y. Error: if the dimensions are incompatible.
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
x ^ n computes a non-negative integral power of the matrix x. Error: if the matrix is not square.
~=: (%, %) -> Boolean
from BasicType
apply: (%, Integer, Integer) -> R
A(i, j) returns $A_{i, j}$
apply: (%, S, S) -> R
A(s, t) returns $A_{i, j}$, where $i$, $j$ are the positions of $s$ and $t$ in the index list.
coerce: % -> OutputForm
from CoercibleTo OutputForm
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
incidenceAlgebra: (Matrix R, List S) -> %
incidenceAlgebra(A, ss) constructs an adjacency matrix with with indices ss and Matrix A
incidenceAlgebra: (Matrix R, OneDimensionalArray S) -> %
incidenceAlgebra(A, ss) constructs an adjacency matrix with with indices ss and Matrix A
indices: % -> OneDimensionalArray S
indices(A) returns the indices of the incidence matrix A
latex: % -> String
from SetCategory
matrix: % -> Matrix R
matrix(A) returns the underlying matrix of the incidence matrix A

BasicType

SetCategory