Matrix and vector `Sym` objects

In Ryacas0: Legacy 'Ryacas' (Interface to 'Yacas' Computer Algebra System)

knitr::opts_chunk$set(echo = TRUE)

library(Ryacas0)

Matrices

Define a character matrix (covariance matrix from a certain $AR(1)$):

N <- 3
L1 <- diag(1, 1 + N)
L1[cbind(1+(1:N), 1:N)] <- "-alpha"
L1s <- as.Sym(L1)
L1s

Now, this can be converted to a Sym object:

L1s <- as.Sym(L1)
L1s

Operations can be performed:

L1s + 4
tmp <- L1s^4
tmp
Simplify(tmp)

Or the concentration matrix $K=L L'$ can be found:

K1s <- Simplify(L1s * Transpose(L1s))
K1s

This can be converted to $\LaTeX$:

TeXForm(K1s)

Which look like this:

cat("\\[ K_1 = ", TeXForm(K1s), " \\]", sep = "")

Vectors

Similar can be done for vectors:

x <- paste0("x", 1:2)
xs <- as.Sym(x)
xs

And matrix-vector multiplication (or matrix-matrix multiplication):

A <- matrix(paste0(paste0("a", 1:2), rep(1:2, each = 2)), 2, 2)
As <- as.Sym(A)
As

As*xs
As*As

Eval

xs
Eval(xs, list(x1 = 2, x2 = 3))

As
Eval(As, list(a11 = 11, a12 = 12, a21 = 21, a22 = 22))

Disabling functionality

The functionality can be disabled as follows:

Ryacas_options("module_matvec_enabled")
As
Ryacas_options(module_matvec_enabled = FALSE)
As

Ryacas0 documentation built on Jan. 12, 2023, 5:11 p.m.