R interface to yacas computer algebra package

Description

Ryacas allows one to use the yacas computer algebra package entirely from within R.

Details

Please read the "Getting started" vignette.

Author(s)

Maintainer: Mikkel Meyer Andersen mikl@math.aau.dk [copyright holder]

Authors:

• Rob Goedman goedman@mac.com [copyright holder]

• Gabor Grothendieck ggrothendieck@gmail.com [copyright holder]

• Søren Højsgaard sorenh@math.aau.dk [copyright holder]

• Grzegorz Mazur teoretyk@gmail.com [copyright holder]

• Ayal Pinkus apinkus@xs4all.nl [copyright holder]

Other contributors:

• Nemanja Trifunovic (UTF-8 part of yacas (src/yacas/include/yacas/utf8*)) [copyright holder]

See Also

Useful links:

• https://github.com/r-cas/ryacas

• http://www.yacas.org

• Report bugs at https://github.com/r-cas/ryacas/issues

Pipe operator

Description

Pipe operator

Usage

lhs %>% rhs

Matrix multiplication

Description

Matrix multiplication

Usage

x %*% y

Arguments

Find the Hessian matrix of yac symbol

Description

Find the Hessian matrix of yac symbol

Usage

Hessian(expr, ...)

Arguments

Find the Jacobian matrix of yac symbol

Description

Find the Jacobian matrix of yac symbol

Usage

Jacobian(expr, ...)

Arguments

Math functions

Description

Math functions

Usage

## S3 method for class 'yac_symbol'
Math(x, ...)

Arguments

Math operators

Description

Math operators

Usage

## S3 method for class 'yac_symbol'
Ops(e1, e2)

Arguments

Extract or replace parts of an object

Description

Extract or replace parts of an object

Usage

## S3 replacement method for class 'yac_symbol'
x[i, j] <- value

Arguments

Extract or replace parts of an object

Description

Extract or replace parts of an object

Usage

## S3 method for class 'yac_symbol'
x[i, j]

Arguments

Extract parts of an object

Description

Extract parts of an object

Usage

## S3 method for class 'yac_symbol'
x[[i]]

Arguments

Convert yac symbol to character

Description

Convert yac symbol to character

Usage

## S3 method for class 'yac_symbol'
as.character(x, ...)

Arguments

Convert yacas object to R

Description

If x is a yacas command as string, convert to a character vector/matrix in R. If x is a yac_symbol (e.g. from ysym()), then convert it to a numeric object if there are no variables or a character type if there are variables.

Usage

as_r(x)

Arguments

Details

In yacas a vector is a list, and a matrix is a list of lists.

Convert R vector/matrix to yacas vector (list) or matrix (list of lists)

Description

Convert R vector/matrix to yacas vector (list) or matrix (list of lists)

Usage

as_y(x)

Arguments

Combine R Objects by Columns

Description

Combine R Objects by Columns

Usage

## S3 method for class 'yac_symbol'
cbind(..., deparse.level = 1)

Arguments

Find the derivative of yac symbol

Description

Find the derivative of yac symbol

Usage

## S3 method for class 'yac_symbol'
deriv(expr, ...)

Arguments

Matrix Determinant

Description

From base::det().

Usage

det(x, ...)

Arguments

Examples

(x <- matrix(1:4, ncol = 2))
det(x)
det(ysym(x))

Matrix diagonals

Description

From base::diag().

Usage

diag(x, ...)

Arguments

Matrix diagonals

Description

From base::diag().

Usage

diag(x) <- value

Arguments

Get width of yacas output

Description

Get width of yacas output

Usage

get_output_width()

Integration of Functions

Description

If f is a yac_symbol, yacas's Integrate() is used. Else, stats::integrate() is used.

Usage

integrate(f, ...)

Arguments

Details

Additional arguments:

• yac_symbol: var, lower, upper

• Else (stats::integrate()): lower, upper

Limits

Description

If first argument is a yac_symbol, yacas's Limit() is used.

Usage

lim(...)

Arguments

Details

Arguments:

• yac_symbol: f, var, val, from_left, from_right

Lower and upper triangular part of a matrix

Description

Lower and upper triangular part of a matrix

Usage

lower.tri(x, diag = FALSE)

Arguments

Matrix product of two matrices

Description

Matrix product of two matrices

Usage

matrix_product(x, y)

Arguments

Matrix Power

Description

Matrix Power

Usage

pow(x, n, ...)

## Default S3 method:
pow(x, n, ...)

Arguments

Examples

(x <- matrix(c(1, 2, 2, 3), ncol = 2))
pow(x, 2)
pow(ysym(x), 2)

Product of Vector Elements

Description

Product of Vector Elements

Usage

## S3 method for class 'yac_symbol'
prod(expr, ..., na.rm = FALSE)

Arguments

Combine R Objects by Rows

Description

Combine R Objects by Rows

Usage

## S3 method for class 'yac_symbol'
rbind(..., deparse.level = 1)

Arguments

Set width of yacas output

Description

Set width of yacas output

Usage

set_output_width(w)

Arguments

Simplify expression

Description

Simplify expression

Usage

simplify(x, timeout = 2)

Arguments

Solve a system of equations

Description

This generic function solves the equation $a x = b$ for $x$.

Usage

## S3 method for class 'yac_symbol'
solve(a, b, ...)

Arguments

Details

When a is a matrix and b not provided, this finds the inverse of a. When a is a matrix and a vector b is provided, the linear system of equations is solved.

Note that solving non-linear equations:

• solve(a, b): find roots of a for variable b, i.e. yacas Solve(a == 0, b)

• solve(a, b, v): find solutions to a == b for variable v, i.e. yacas Solve(a == b, v)

This also works for a system of equations (when a is a vector)

Examples

A <- outer(0:3, 1:4, "-") + diag(2:5)
a <- 1:4
B <- ysym(A)
b <- ysym(a)
solve(A)
solve(B)
solve(A, a)
solve(B, b)

poly <- ysym("x^2 - x - 6")
solve(poly, "x")    # Solve(poly == 0, x)
solve(poly, 3, "x") # Solve(poly == 3, x)

Summation

Description

If only expr given: sum elements.

Usage

## S3 method for class 'yac_symbol'
sum(expr, var, lower, upper, ..., na.rm = FALSE)

Arguments

Details

Else: sums expr by letting var taking values from lower to upper (potentially Inf)

t

Description

t

Usage

## S3 method for class 'yac_symbol'
t(x)

Arguments

Export object to TeX

Description

Export object to TeX

Usage

tex(x)

Arguments

Matrix Trace

Description

The trace of a square matrix is the sum of the diagonal elements.

Usage

tr(x, ...)

## Default S3 method:
tr(x, ...)

Arguments

Examples

(x <- matrix(1:4, ncol = 2))
tr(x)
tr(ysym(x))

Lower and upper triangular part of a matrix

Description

Lower and upper triangular part of a matrix

Usage

upper.tri(x, diag = FALSE)

Arguments

Vectorize

Description

Vectorize

Usage

vec(x, ...)

## Default S3 method:
vec(x, ...)

Arguments

Examples

(x <- matrix(1:9, ncol = 3))
vec(x)
vec(ysym(x))

Half-Vectorize

Description

Half-Vectorize

Usage

vech(x, ...)

## Default S3 method:
vech(x, ...)

Arguments

Examples

A <- mtcars[, c(1, 3, 4, 5, 6, 7)]
x <- cov(A)
vech(x)
vech(ysym(x))

Give a variable a value

Description

Give a variable a value

Usage

with_value(x, var, val)

Arguments

Evaluate a yacas expression

Description

Evaluate a yacas expression by replacing variables with values as for the given list.

Usage

y_eval(expr, ..., as.r = FALSE)

Arguments

Examples

# Evaluate as yacas object
eq <- ysym("2*y+x^2+2*x-3")
y_eval(eq, x=3, y=2)

# Evaluate as R expression:
y_eval(eq, x=3, y=2, as.r=TRUE)
# This allows to use vectors:
y_eval(eq, x=1:10, y=2, as.r=TRUE)
# and to plot functions:
curve(y_eval(eq, x=x, y=2, as.r=TRUE), xlim=c(0,10))

Prepare simple yacas call

Description

Prepare simple yacas call

Usage

y_fn(x, fn, ...)

Arguments

Examples

y_fn("x^2 - 1", "TeXForm")
yac_str(y_fn("x^2 - 1", "TeXForm"))

y_fn("x^2 - 1", "Factor")
yac_str(y_fn("x^2 - 1", "Factor"))

cmd <- "x^2 - 1 == 0" %>% y_fn("Solve", "x")
cmd
sol <- yac_str(cmd)
sol
yac_str(y_rmvars(sol))

Pretty print yacas strings

Description

Pretty print yacas strings

Usage

y_print(x)

Arguments

Examples

A <- diag(4)
Ayac <- as_y(A)
y_print(Ayac)

B <- A
B[2, 2] <- "-t"
Byac <- as_y(B)
Byac
y_print(Byac)

Remove/strip variable names

Description

This only builds a yacas command. You need to also call yac_str(), yac_expr() or similar. This is the reason that it does not call yacas: it depends on how you want it returned (string, expression).

Usage

y_rmvars(x)

Arguments

Examples

cmd <- "{x == 2, y == 4}"
yac_str(cmd)
yac_str(y_rmvars(cmd))

Run yacas command

Description

Run yacas command

Usage

yac(x, rettype = c("str", "expr", "silent"))

Arguments

Examples

yac("D(x) x^2 + 4*x")
yac("D(x) x^2 + 4*x", rettype = "str")
yac("D(x) x^2 + 4*x", rettype = "expr")
yac("D(x) x^2 + 4*x", rettype = "silent")

Assign yacas variable

Description

Assign yacas variable

Usage

yac_assign(value, x)

Arguments

yacas command line interface

Description

Interactive interface to the yacas

Usage

yac_cli(enable_history = TRUE)

Arguments

Details

The user types valid yacas input and presses return. Type 'quit' to return to R prompt.

Value

Output of yacas is returned.

Note

Note that command will use R history() and modify it by default. Yacas is given a limited amount of time to complete, otherwise ⁠\[1\] CommandLine(1) : User interrupted calculation⁠ is returned. E.g. Taylor(x,0,5) 1/(1+x) will work, but Taylor(x,0,12) 1/(1+x) is likely to take too long.

References

https://yacas.sourceforge.io/

Examples

## Not run: 
yac_cli()
 (x+y)^3-(x-y)^3
 Simplify(%)
 q

## End(Not run)

Run yacas command returning R expression

Description

Run yacas command returning R expression

Usage

yac_expr(x)

Arguments

Examples

yac_expr("D(x) x^2 + 4*x")
yac_expr("Limit(x, 1) (x^2 - 1)/(x - 1)")
yac_expr("Sum(n, 1, Infinity, (1/2)^n)")
yac_expr("Fibonacci(10)")
yac_expr("Sum(n, 1, 10, Fibonacci(n))")

Run yacas command silently

Description

Run yacas command silently

Usage

yac_silent(x)

Arguments

Run yacas command returning string/character

Description

Run yacas command returning string/character

Usage

yac_str(x)

Arguments

Examples

yac_str("D(x) x^2 + 4*x")
yac_str("Limit(x, 1) (x^2 - 1)/(x - 1)")
yac_str("Sum(n, 1, Infinity, (1/2)^n)")
yac_str("Fibonacci(10)")
yac_str("Sum(n, 1, 10, Fibonacci(n))")
yac_str("TeXForm(x^2 - 1)")

Make a yacas symbol

Description

This is an alias for ysym(). See description there.

Usage

yac_symbol(x)

Arguments

Value

A yac_symbol

Make a yacas symbol

Description

Note that this results in multiple calls to yacas and the performance may be slower than manually using e.g. yac_str().

Usage

ysym(x)

Arguments

Value

A yac_symbol

List defined yac_symbols

Description

List defined yac_symbols

Usage

ysym_ls(print_details = FALSE)

Arguments