R interface to yacas computer algebra package

Description

Ryacas0 allows one to use the yacas computer algebra package entirely from within R. It takes an R expression, an R one line function or a yacas string and returns an R expression or a variety of other formats. It can be used for symbolic mathematics, exact arithmetic, ASCII pretty printing and R to TeX conversions. The main command is yacas and ?yacas provides some information on installation and startup.

Details

The following are sources of information on "Ryacas0":

Note

There is a note in the help file of the yacas command that discusses a number of installation and startup issues.

Examples

print(yacas(expression(integrate(1/x, x))))
print(yacas("Integrate(x)1/x"))
x <- Sym("x"); Integrate(1/x, x)
acos(Sym("1/2"))

Evaluate a yacas expression.

Description

Evaluate a yacas expression.

Usage

Eval(x, env = parent.frame(), ...)

Arguments

Examples

Eval(yacas(expression(x*x)), list(x=2))

# same
x <- 2
Eval(yacas(expression(x*x)))

Set or get options for the Ryacas package

Description

Set or get options for the Ryacas package

Usage

Ryacas_options(...)

Arguments

Supported options

The following options are supported

• module_matvec_enabled (default TRUE): Print yacas List()'s as vectors and List(List(), ...)'s as matrices.

• prettyform_default (default FALSE): Print yacas as PrettyForm() as default.

Sym

Description

The Symbol interface to yacas.

Usage

Sym(...) 
Expr(x)

Arguments

Details

An object of class "Sym" is internally a yacas character string. An object of class "Expr" is internally an R expression. One can combine such objects using the Math and Ops R operators (see help(Math) and help(Ops) for a list). Also there are methods for a number of R generics: as.character.Sym, as.expression.Sym, determinant.Sym, deriv.Sym and print.Sym and yacas-oriented functions: Clear, Conjugate, Expand, Factor, Factorial, I, Identity, Infinity, Integrate, Inverse, InverseTaylor, Limit, List, N, Newton, Pi, Precision, PrettyForm, PrettyPrinter, Set, Simplify, Solve, Subst, Taylor, TeXForm, Transpose, Ver and "%Where%" all of which have the same meaning as the corresponding yacas commands. Try vignette("Rycas-Sym") for many examples.

Get Sym objects with getSyms().

Value

Sym returns a "Sym" object and Expr returns an "Expr" object.

Note

Currently the only Expr methods implemented are as.character.Expr, deriv.Expr, Math.Expr, Ops.Expr and print.Expr.

See Also

as.Sym.matrix()

Examples

x <- Sym("x")
x*x
Integrate(x*x, x)
Sym("%") %Where% list(x = 10)

acos(Sym("1/2"))

y <- Exprq(x)
y*y
deriv(y*y, y)
Exprq(acos(1/2))

Convert character vector to yacas object

Description

Simple and raw conversion to yacas

Usage

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

Arguments

Examples

x <- c("a", "2", "4", "c", "d", "6")
x
y <- as.Sym(x)
y
Eval(y, list(a = 3, c = 3, d = 3))

Convert character matrix to yacas object

Description

Simple and raw conversion to yacas

Usage

## S3 method for class 'matrix'
as.Sym(x, ...)

Arguments

Examples

x <- matrix(c("a", "2", "4", "c", "d", "6"), 3, 2)
x
y <- as.Sym(x)
y
Eval(y, list(a = 3, c = 3, d = 3))

Get body of function as an expression.

Description

Get body of function as an expression.

Usage

bodyAsExpression(x)

Arguments

Details

This function is similar to the R body function except that function returns a call object whereas this one returns an expression usable in Ryacas calculations.

Value

An expression.

See Also

body

Examples

# construct an R function for the Burr probability density
# function (PDF) given the Burr cumulative distribution function (CDF)
BurrCDF <- function(x, c = 1, k = 1) 1-(1+x^c)^-k

# transfer CDF to yacas
yacas(BurrCDF)

# create a template for the PDF from the CDF
BurrPDF <- BurrCDF

# differentiate CDF and place resulting expression in body
body(BurrPDF) <- yacas(expression(deriv(BurrCDF(x,c,k))))[[1]]

# test out PDF
BurrPDF(1)

List Sym() objects

Description

Lists all Sym() objects in the global environment (.GlobalEnv)

Usage

getSyms(all.names = FALSE)

Arguments

Examples

getSyms()
xs <- Sym("x")
getSyms()

Get width of yacas output

Description

Get width of yacas output

Usage

get_output_width()

Root function

Description

The $y$'th root of $x$, i.e. $x^(1/y)$.

Usage

root(x, y)

Arguments

Value

The root y'th root of x

Set width of yacas output

Description

Set width of yacas output

Usage

set_output_width(w)

Arguments

Removes part of expression containing variable

Description

Yacas' Solve(eq, x) can return e.g. x == expr and ⁠{x == expr1, x == expr2, ...}⁠. Some usages are easier if the initial ⁠x == ⁠ part is removed. This is the purpose of this function.

Usage

stripvar(expr, var)

Arguments

Value

Expression with left-hand side removed

yacas interface – silent version

Description

Similar to yacas() but silent. This can be useful when working with yacas directly.

Usage

syacas(x, ...)

Arguments

See Also

yacas

Get Yacas variables

Description

Get Yacas variables

Usage

y_ls()

Value

Vector of variables defined in yacas

yacas interface

Description

Interface to the yacas computer algebra system.

Usage

yacas(x, ...)
## S3 method for class 'character'
yacas(x, verbose = FALSE, method, 
    retclass = c("expression", "character", "unquote"), 
    addSemi = TRUE, ...)

Arguments

Details

The user supplies an R expression, an R function name corresponding to a function with a single line body, a formula or a yacas input string. In the case of a formula it is regarded as an expression represented by the right hand side of the formula while the left hand side, if any, is ignored.

Note the silent version syacas().

Value

An R object of class "yacas" is returned. If PrettyPrinter("OMForm") is in effect, which it is by default, then the first component is an R expression and the OMForm component contains OpenMath XML code. In other cases the first component is NULL and the YacasForm or PrettyForm components have display information.

Generally an expression. Refer to details.

Note

Windows Installation. On Windows one can install Ryacas by issuing the commands:

or by using the Packages | Install package(s) menu in place of the first command. The second command downloads scripts.dat and yacas.exe from the internet and installs them into R_HOME/library/Ryacas/yacdir where R_HOME is the location of your R installation.

Normally the default locations of yacas, its initialization file and the scripts file are sufficient but, if necessary, they can be overridden via the environment variables: YACAS_HOME, YACAS_INIT and YACAS_SCRIPTS. The YACAS_INVOKE_STRING environment variable discussed in the next section overrides all three of these.

All OS Installation. The YACAS_INVOKE_STRING environment variable can be used to override the invocation string for yacas. Normally it is not used. If it does need to be used then a typical use might be:

yacmode. There is also a utility yacmode which is called without arguments and just turns R into a terminal into yacas until one quits out of it (and back to R) by entering stop, end, quit, exit or e.

Startup. yacas starts up when yacasStart() is called or the first time yacas is called. yacas is shut down when yacasStop() is called or when the package is detached using the detach() R command. On Windows, when yacas is shut down, the yacas process is terminated on Windows XP Pro but not on other versions of Windows. In those cases there will be a dangling process that the user must terminate manually.

Translation. The translation process occurs in several steps. If the input to the yacas function is an expression then it is translated to a valid yacas character string (otherwise, it is sent to yacas unprocessed). Yacas then processes the string and if retclass="expression" it is translated back to an R expression (otherwise it is sent back unprocessed). Examples of translations are:

References

http://www.yacas.org/

Examples

yacas(expression(Factor(x^2-1)))
exp1 <- expression(x^2 + 2 * x^2)
exp2 <- expression(2 * exp0)
exp3 <- expression(6 * pi * x)
exp4 <- expression((exp1 * (1 - sin(exp3))) / exp2)
print(yacas(exp4))

print(yacas("Version()")) # yacas version

# see demo("Ryacas-Function")

Yacas translations

Description

Translations from R to the yacas computer algebra system.

Note

The translation process occurs in several steps. If the input to the yacas function is an expression then it is translated to a valid yacas character string (otherwise, it is sent to yacas unprocessed). Yacas then processes the string and if retclass="expression" it is translated back to an R expression (otherwise it is sent back unprocessed). Currently supported translations are:

Note the Limit example in demo(Ryacas0) for adding translations on the fly.

The complete table under development.

Author(s)

Rob J Goedman

References

http://www.yacas.org/

Evaluate yacas expression

Description

This is a low-level function for evaluating yacas expression represented as string.

Usage

yacas_evaluate(expr)

Arguments

Value

Result of evaluating expr by yacas in OpenMath format and side-effects of the evaluation

Examples

yacas_evaluate("D(x)Sin(x^2)")

yacmode interface

Description

Interactive interface to the yacas

Usage

yacmode(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.

invisible NULL

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

http://www.yacas.org/

Examples

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

## End(Not run)