coerce: Coercion

In jordan: A Suite of Routines for Working with Jordan Algebras

Coercion

Description

Various coercions needed in the package

Usage

as.jordan(x,class)
vec_to_rsm1(x)
vec_to_chm1(x)
vec_to_qhm1(x)
vec_to_albert1(x)
rsm1_to_vec(M)
chm1_to_vec(M)
qhm1_to_vec(M)
albert1_to_vec(H)
as.real_symmetric_matrix(x,d,single=FALSE)
as.complex_herm_matrix(x,d,single=FALSE)
as.quaternion_herm_matrix(x,d,single=FALSE)
as.albert(x,single=FALSE)
numeric_to_real_symmetric_matrix(x,d)
numeric_to_complex_herm_matrix(x,d)
numeric_to_quaternion_herm_matrix(x,d)
numeric_to_albert(e1)
as.list(x,...)
matrix1_to_jordan(x)

Arguments

x, e1	Numeric vector of independent entries
M, H	A matrix
d	Dimensionality of algebra
single	Boolean, indicating whether a single value is to be returned
class	Class of object
...	Further arguments, currently ignored

Details

The numeral “1” in a function name means that it operates on, or returns, a single element, usually a matrix. Thus function as.1matrix() is used to convert a jordan object to a list of matrices. Length one jordan objects are converted to a matrix.

Functions vec_to_rsm1() et seq convert a numeric vector to a (symmetric, complex, quaternion, octonion) matrix, that is, elements of a matrix-based Jordan algebra.

Functions rsm1_to_vec() convert a (symmetric, complex, quaternion, octonion) matrix to a numeric vector of independent components. The upper triangular components are used; no checking for symmetry is performed (the lower triangular components, and non-real components of the diagonal, are discarded).

Functions as.real_symmetric_matrix(), as.complex_herm_matrix(), as.quaternion_herm_matrix() and as.albert() take a numeric matrix and return a (matrix-based) Jordan object.

Functions numeric_to_real_symmetric_matrix() have not been coded up yet.

Function matrix1_to_jordan() takes a matrix and returns a length-1 (matrix based) Jordan vector. It uses the class of the entries (real, complex, quaternion, octonion) to decide which type of Jordan to return.

Value

Return a coerced value.

Author(s)

Robin K. S. Hankin

Examples

vec_to_chm1(1:16)  # Hermitian matrix

as.1matrix(rchm())

as.complex_herm_matrix(matrix(runif(75),ncol=3))

matrix1_to_jordan(cprod(matrix(rnorm(35),7,5)))
matrix1_to_jordan(matrix(c(1,1+1i,1-1i,3),2,2))
matrix1_to_jordan(Oil + matrix(1,3,3))

jordan documentation built on July 4, 2024, 5:06 p.m.