IncidenceAlgebra(R, S)

logic.spad line 287 [edit on github]

• R: Ring

• S: SetCategory

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

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

CoercibleTo OutputForm

SetCategory