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.

* : (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.

+ : (%, %) -> %

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.

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.

apply : (%, Integer, Integer) -> R

A(i, j) returns $A_i, j$

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

~= : (%, %) -> Boolean

from BasicType

CoercibleTo(OutputForm)

SetCategory

BasicType