An Interface to the Computer Algebra System 'REDUCE'

Description

'REDUCE' is a portable general-purpose computer algebra system supporting scalar, vector, matrix and tensor algebra, symbolic differential and integral calculus, arbitrary precision numerical calculations and output in 'LaTeX' format. 'REDUCE' is based on 'Lisp' and is available on the two dialects 'Portable Standard Lisp' ('PSL') and 'Codemist Standard Lisp' ('CSL'). The 'redcas' package provides an interface for executing arbitrary 'REDUCE' code interactively from 'R', returning output as character vectors. 'R' code and 'REDUCE' code can be interspersed. It also provides a specialized function for calling the 'REDUCE' feature for solving systems of equations, returning the output as an 'R' object designed for the purpose. A further specialized function uses 'REDUCE' features to generate 'LaTeX' output and post-processes this for direct use in 'LaTeX' documents, e.g. using 'Sweave'.

Details

The package allows you to start a REDUCE session (redStart), send one or more vectors of REDUCE commands to the session for execution and retrieve the output (redExec), render output as LaTeX (asltx), and shut down the session and optionally return the entire output file (redClose). Output is returned as a list of character vectors containing the command output, the commands and the combined comands and output. redcas can also directly call the REDUCE operator for solving algebraic equations (redSolve), returning a redcas.solve object.

Several other functions are available: redExpand is called by redExec for checking and preparing the input vector while redDropOut and redSplitOut are called by redExec to format the output. All three can be called independently of redExec.

REDUCE uses a different terminology to R. Some translations:

Author(s)

Martin Gregory [aut, cre]

Maintainer: Martin Gregory <mairtin.macghreagoir@gmail.com>

References

Details of the REDUCE system including extensive documentation is available at the REDUCE web site.

Examples

## start a session
id <- redStart()

## can only run code if session was successfully started
if (is.numeric(id)) {
   ## define vectors of REDUCE code for submission
   x1 <- "solve((x+1)^2, x);"
   x2 <- "b:=factorize(45056);"
   x3 <- c("operator v; ",
	   "la:=-m/(v(2)^2 + v(3)^2)^(1/2) ;")

   ## execute x1 and display on the output of the commands
   y1 <- redExec(id, x1)
   writeLines(y1$out)

   ## execute x2 and display first the output and then the commands
   y2 <- redExec(id, x2)
   writeLines(c(y2$out, y2$cmd))

   ## execute x3 and display the log (commands and output interspersed)
   writeLines(y3 <- redExec(id, x3, split=FALSE))

   ## close the session
   redClose(id)
   }

Convert REDUCE output to LaTeX

Description

sends the name of an array or expression to the REDUCE process for display either as is or as LaTeX using the FANCY switch. If the object is an array, each element is printed. The LaTeX produced by REDUCE is then post-processed to translate object names according to a map specified by the user, to convert array arguments to indices and, optionally, to enclose the result in a math environment specified by the user.

Usage

asltx(id, x, usermap, mathenv="", mode="fancy", notify=0, timeout=0, debug=FALSE)

Arguments

Details

asltx uses redExec to display the object x as desired by:

1. constructing a call to the REDUCE function asltx with appropriate quoting of the arguments;

2. executing this call using redExec and specifying split=TRUE;

3. applying a standard set of transformations to remove some non-LaTeX markup and perform some conversions on the result. See below;

4. applying a set of transformations specified by the usermap argument.

Features of REDUCE conversion to LaTeX

REDUCE provides three different methods for converting output to LaTeX, the packages TMPRINT, RLFI and TRI. redcas uses the TMPRINT package which was designed for use with the TeXmacs editor (hence TM) and triggers conversion using the fancy and fancy_tex switches. TMPRINT was chosen because it can be easily applied to fragments, supports using the \frac command, produces LaTeX output and is well supported. In contrast RLFI is designed to produce complete documents using LaTeX 2.09 syntax and does not support the \frac command. TRI produces plain TeX output.

TMPRINT supports

1. inserting \left and \right in nested parentheses, braces and brackets;

2. converting variables whose names are those of Greek letters to the corresponding LaTeX command. Capitalized names are mapped to the command for the capital. For example, psi is mapped to \psi while Psi is mapped to \Psi. There are two exceptions; epsilon and kappa are mapped to \varepsilon and \varkappa, respectively. If you need \epsilon or \kappa you can use the usermap argument;

3. the following names are mapped to special symbols:

   infinity		\infty		union		\cup
   partial!-df		\partial		member		\in
   empty!-set		\emptyset		and		\wedge
   not		\neg		or		\vee
   not		\neg		when		|
   leq		\leq		!*wcomma!*		,\,
   geq		\geq		replaceby		\Rightarrow
   neq		\neq		!~		\forall
   intersection		\cap

Standard transformations

Standard transformations done by asltx are as follows:

1. removal of markup used for interactive display in TeXmacs and which has no correspondence with LaTeX markup;

2. replacement of REDUCE assignments := and ~:=~ with a plain equals sign;

3. reversing the unwanted conversion of numeric suffix to index. The REDUCE FANCY option assumes that a numeric suffix to a variable is a subscript index even when the variable is an array, e.g. cs1(a,b) is converted to cs_{1}(a,b). asltx undoes this conversion.

4. removal of redundant mathrm commands;

5. removal of unnecessary trailing spaces from Greek capitals;

6. replacement of mathit{Q} with mathrm{Q} where Q is one of the Greek capitals A, B, E, Z, H, I, M, N, O, P. i.e. those which have the same form as a Latin capital. This transformation is required to have the same type for as the Greek-only capitals.

User transformations

The usermap argument allows renaming variables, converting arguments in REDUCE objects to indices and specifying whether indices are covariant or contravariant. If a LaTeX command is used in the map, four backslashes are required to get the single backslash for LaTeX because the mapping is done using regular expressions. For example suppose we have arrays s, g, kminus and kplus in REDUCE and want the following mapping to LaTeX

then the ident element of the list passed to usermap would be

ident=c("s"="\\\\Sigma", kminus="K^-", kplus="K^\\+")

Since we are not mapping g it does not need to appear here.

To illustrate mapping arguments to indices, assume that all four arrays in the example above are two dimensional and s has one subscript and one superscript, g and kminus have two subscripts and kplus has two superscripts then the index element will be

index=c("\\\\Sigma"="_^", "g"="__", "K^-"="__", "K^\\+"="^^")

Note that the name of the index elements must be the result of applying the ident mapping. The names are regular expressions so the character + must be escaped in the names.

Value

A list containing the following elements is returned:

tex

the transformed LaTeX output;

out

the output of the executed commands;

cmd

the executed commands

raw

the interspersed commands and output.

Author(s)

Martin Gregory

See Also

redExec for details of executing REDUCE code.

Examples

## start the session
s1 <- redStart()

## can only run code if session was successfully started
if (is.numeric(s1)) {
   ## create the arrays
   redcode <- c("array g(2,2), s(3,3), kplus(2,2), kminus(2,2) ;",
		"operator x;",
		"g(0,0) := -u^(-2);",
		"g(1,1) := (u*x(3))^2;",
		"g(2,2) := g(1,1) * (sin(x(1)))^2;",
		"s(0,0) := 0;",
		"s(1,1) := df((u*x(3))^2, x(3));",
		"s(2,2) := df(g(2,2), x(1));",
		"s(3,3) := u^2;",
		"kplus(0,0) := df(g(0,0), u);",
		"kplus(1,1) := df(g(1,1), u);",
		"kplus(2,2) := df(g(2,2), u) ;",
		"kminus(0,0) := df(g(2,2), u);",
		"kminus(1,1) := df(g(1,1), u);",
		"kminus(2,2) := df(g(0,0), u) ;",
		"on nero ;"
		)

   o2 <- redExec(s1, redcode)

   ## create LaTeX output 
   writeLines(c("", asltx(s1, "g", mathenv="")[["tex"]], ""))
   writeLines(c("", asltx(s1, "s", mathenv="")[["tex"]], ""))
   writeLines(c("", asltx(s1, "kplus", mathenv="")[["tex"]], ""))
   writeLines(c("", asltx(s1, "kminus", mathenv="")[["tex"]], ""))

   ## close the session
   redClose(s1)
}

Print a redcas.solve object

Description

print.redcas.solve is a print method for function print in package base

Usage

print(x, ...) 

Arguments

Details

print.redcas.solve displays the equations, solutions if any and the list of unknowns and switches. The solutions displayed are those returned from REDUCE without any transformation to R objects.

The layout depends on the length of the individual solution values and the width option. If there is sufficient space, the solutions for each unknown are printed in separate columns on the same line, for example with a width of 80, the output of the example below will be:

Equations:
  x+y+z = 0
  x^2 + y^2 + z^2 = 9
  x^2 + y^2 = z^2

Number of solutions: 4

Solutions:
               x               y               z
   2.12132034356               0  -2.12132034356
  -2.12132034356               0   2.12132034356
               0   2.12132034356  -2.12132034356
               0  -2.12132034356   2.12132034356

Unknowns: x,y,z
Switches:  rounded

If all values for a solution with not fit on a line, they are printed below each other. With a width of 30, the solutions section would be

Solution 1:
x:    2.12132034356
y:                0
z:   -2.12132034356

Solution 2:
x:   -2.12132034356
y:                0
z:    2.12132034356

Solution 3:
x:                0
y:    2.12132034356
z:   -2.12132034356

Solution 4:
x:                0
y:   -2.12132034356
z:    2.12132034356

Value

print.redcas.solve is called for its side-effect and returns NULL.

Examples

## start the session
r0 <- redStart()

## can only run code if session was successfully started
if (is.numeric(r0)) {
   rsobj <- redSolve(id=r0,
		     eqns=c("x+y+z = 0", "x^2 + y^2 + z^2 = 9", "x^2 + y^2 = z^2"),
		     unknowns=c("x", "y", "z"),
		     switch=c("on rounded;") )
   print(rsobj)
   redClose(r0)
}

function to close a REDUCE session and optionally save the log file

Description

redClose closes the connection to the REDUCE session thereby ending the session. If requested the log file is copied from the temporary location to one specified by the log argument.

Usage

redClose(id, log)

Arguments

Details

The session log returned by redClose includes the submit block markers set by redExec.

In addition to closing the connection, redClose removes the session's entry from the session registry.

Value

redClose returns TRUE if the session is closed, FALSE if it does not exist.

Author(s)

martin gregory

See Also

redStart for creating a REDUCE session and showSessions to display the session registry.

Examples

## Open a CSL session:
s1 <- redStart()
## can only run code if session was successfully started
if (is.numeric(s1)) {
   ## show session details:
   print(showSessions())
   ## close session:
   redClose(s1)
}

Retrieve the directory containing the REDUCE code which is part of redcas.

Description

redCodeDir retrieves the full path to the directory containing the REDUCE code which is part of redcas.

Usage

redCodeDir()

Details

In addition to returning the REDUCE code directory, redCodedir assigns three environment variables:

REDCODEDIR

the full path to the directory containing the REDUCE code which is the reduce sub-directory of the redcas package;

REDCAS_CODE_PATH

the full path to the program redcas.red which defines REDUCE procedures used by redcas;

TMPRINT_PSL_PATH

the full path to the program tmprint-psl.red which makes a modified version of the REDUCE package TMPRINT which implements LaTeX rendering for the PSL dialect. The change is minor and is designed to ensure that the TeXmacs markup is identical to that of CSL.

You can use the two programs directly in REDUCE. You need only load redcas.red as it loads tmprint-psl.red if executing in PSL. In order to have tmprint-psl.red loaded, you must assign the environment variable TMPRINT_PSL_PATH before starting REDUCE.

Value

redCodeDir returns the full path to the directory containing the REDUCE code which is part of redcas.

Author(s)

martin gregory

Examples

redCodeDir()
Sys.getenv("REDCAS_CODE_PATH")
Sys.getenv("TMPRINT_PSL_PATH")

Removes certain elements from the REDUCE output.

Description

Removes blank lines or the submit block end marker from the REDUCE output.

Usage

redDropOut(x, what)

Arguments

Details

redDropOut is called by redExec if the option drop.blank.lines is TRUE, so you generally do not need to call it explicity. If you have forgotten to set the option, you can use this function to remove blank lines.

The purpose of what='marker' is to remove the end of block marker described in the details section of redExec. This may be useful if you need to process a REDUCE transcript not produced by redcas.

When removing blank lines and the output is not LaTeX or the switch NAT is on, output may be difficult to read and difficult to parse.

Value

The input vector with the corresponding elements removed.

Author(s)

Martin Gregory

See Also

redExec

Examples

x <- c("first", "", "last")
## this will return elements 1 and 3:
redDropOut(x, "blank")

execute REDUCE commands from R

Description

sends a vector of commands to the REDUCE process for execution and retrieves and formats the output.

Usage

redExec(id, x, split = TRUE, drop.blank.lines = FALSE, notify=0, timeout=0)

Arguments

Details

Before submitting the vector x, redExec modifies it as follows:

• inserts a ";" terminator at the start of x. This is required to ensure that the first command in the next submit block has a number. Numbers are required to distinguish commands from command output;

• replaces any file names in x with their contents. This means that the contents of the files are executed directly and not via an IN or IN_TEX command. Files are specified by preceding the filename with file:. A terminator is not required and, if present, is ignored;

• appends a command to x in order to set an end of block marker. This is required so that redExec can wait until all the commands submitted have been executed. This is especially important for commands which run for a long time.

When reading the output from the submitted commands, redExec removes the end of block command and the marker it sets.

Care must be taken when using the drop.blank.lines option. In particular, if using the REDUCE NAT switch, which is the default, and output is not formatted for LaTeX, it may be difficult to read the output.

If REDUCE prompts for input during a sumbit block, redExec will write an informative message, return the output and close the session, writing the log to the current directory. This most likely happens if you use a variable as an operator but did not declare it as such. One way to avoid this is to turn off the switch INT which causes REDUCE to declare any undeclared operators it encounters. If you do this, be sure to turn on INT before you call redClose as otherwise the REDUCE session will hang. You should use the code on int;;. Note that both semicolons are required. Since REDUCE is run via a pipe, INT is on by default.

If the last statement (element of x) is missing a terminator (semi-colon or dollar sign) redExec checks whether the last non-blank, non-comment element of the input vector has a terminator. If not it stops with an appropriate message and returns FALSE. This reduces the likelihood that redExec fails to return.

Value

Like R, the REDUCE log contains both commands and outputs. If split is TRUE a list containing the following elements is returned:

out

the output of the executed commands;

cmd

the executed commands

raw

the interspersed commands and output.

If split is FALSE, redExec returns a character vector with the output from the REDUCE commands.

Author(s)

Martin Gregory

See Also

redStart for starting a REDUCE session, redSplitOut and redDropOut for post-processing the output if the split or drop.blank.lines are not used.

Examples

s1 <- redStart()

## can only run code if session was successfully started
if (is.numeric(s1)) {
   ## submit with neither split nor drop.blank.lines
   x1 <- c("solve((x+1)^2, x);",
	   "b:=factorize(45056);",
	   "operator v; ",
	   "la:=-m/(v(2)^2 + v(3)^2)^(1/2) ;")
   writeLines("## submit with neither split nor drop.blank.lines")
   writeLines(y1 <- redExec(s1, x1, split=FALSE))

   ## submit with split=TRUE and drop.blank.lines=TRUE
   writeLines("\n## submit with split=TRUE and drop.blank.lines=TRUE")
   writeLines(redExec(s1, x1, drop.blank.lines=TRUE)[["out"]])

   ## submit with file name in input
   tfile <- tempfile('reduce')
   writeLines(c(paste0('write "code from ', tfile, '";'),
		"b:=factorize(54056);"),
	      tfile)
   x3 <- c("la:=-m/(v(2)^2 + v(3)^2)^(1/2) ;",
	   paste0("file:",tfile))
   y3 <- redExec(s1, x3, split=TRUE)
   writeLines("\n## submit with file name in input")
   writeLines("## commands")
   writeLines(y3$cmd)
   writeLines("\n## output")
   writeLines(y3$out)
   redClose(s1)
}

Insert the content of a file into a vector

Description

A vector of REDUCE commands may contain the name of a file containing REDUCE commands. redExpand returns a vector containing the commands up to the element containing the file name, the contents of the file and the elements following the file name. Multiple files may be specified in the input vector.

Usage

redExpand(x)

Arguments

Details

redExpand is called by redExec before submitting commands so it is generally not necessary to call it explicitly. It can be used if you wish do the expansion yourself. If the input vector elements x_j, x_k, where j < k, are file references, then the output vector will consist of

• x₁...x_j-1

• the contents of x_j

• x_j+1...x_k-1

• the contents of x_k

• x_k+1...x_n

Value

a character vector containing the commands to submit with any file names replaced by their contents.

Author(s)

Martin Gregory

See Also

redExec

function to solve a system of equations using the REDUCE solve operator

Description

redSolve generates code for the REDUCE solve operator, executes it and converts the result to appropriate R objects if possible.

Usage

redSolve(id, eqns, unknowns, switches)

Arguments

Details

solve is a REDUCE operator for solving one or more simultaneous algebraic equations in one or more variables, both linear and non-linear. Equations may contain arbitrary constants which is why it is necessary to specify the unknowns. For example, given a quadratic equation with constants a, b and c:

16: solve(a*x^2 + b*x + c, x);
  
                     2
    sqrt( - 4*a*c + b ) - b
{x=-------------------------,
              2*a

                         2
     - (sqrt( - 4*a*c + b ) + b)
 x=------------------------------}
                2*a

The standard solution is returned as a REDUCE list. We can change the order of the expression to get the usual form by using the korder declaration before calling solve:

17: korder b, a;
18: solve(a*x^2 + b*x + c, x);

          2
    sqrt(b  - 4*a*c) - b
{x=----------------------,
            2*a

              2
     - (sqrt(b  - 4*a*c) + b)
 x=---------------------------}
               2*a

If the solve operator could not find an explicit solution, it may still be able to find one in terms of an equation for the unknown. Such a solution is identified by specifying the subsidiary equation as the argument of the operator root_of. If there are several unknowns, each solution will be a list of equations for the unknowns. For example,

  solve(x^7 - x^6 + x^2 = 1, x) ;
  {x=root_of(x_**6  + x_ + 1,x_,tag_1),x=1}

Note that redSolve turns off the NAT switch as otherwise the results will not be parsed correctly. redSolve will ensure that NAT is off for the duration of its execution. Turning on the NAT switch using the switches parameter results in an error.

There are several switches related to solve, in particular cramer, multiplicities, fullroots, trigform and varopt. See the REDUCE manual section 7.17 for details of these and of the methods used for solving equations.

Value

redSolve returns an object of class "redcas.solve" which contains the following elements:

solutions

a list of the solutions as returned by REDUCE. Each solution is a character vector.

rsolutions

a list of the solutions, where possible converted to appropriate R objects. Because each element of a solution may be of a different type (real, complex, string), each solution is a list rather than a vector.

nsolutions

numeric. The number of solutions.

rc

numeric. The return code. 0 is success, 1 failure

root_of

a complex vector identifying which solutions are presented in terms of the REDUCE root_of operator. A solution may expressed one or more unknowns in terms of the roots of another equation. In this case the other equation is enclosed in root_of(). This slot is a complex vector with the real part identifying the solution containing root_of() and the imaginary part the index of the unknown in that solution. This item is intended for use in a future release.

eqns

the vector of equations passed to redSolve

unknowns

the vector of unknowns passed to redSolve

switches

the vector of switches passed to redSolve

The redcas.solve object may be printed using the print method.

Author(s)

martin gregory

See Also

print to print a redcas.solve object, REDUCE manual section 7.17 for details of the REDUCE solve operator and redStart for creating a REDUCE session.

Examples

## Open a CSL session:
s1 <- redStart()

## can only run code if session was successfully started
if (is.numeric(s1)) {
   sol <- redSolve(s1, eqns=c("x+3y=7", "y-x=1"), unknowns=c("x", "y"))
   print(sol)

   ## close session:
   redClose(s1)
}

convert the vector returned by redExec into commands and command output.

Description

REDUCE output contains both the commands issued and the output from the commands. Since the output is of interest, redSplitOut separates the input vector into a list containing vectors of output, commands and the input to redSplitOut.

Usage

redSplitOut(x)

Arguments

Details

Although it is possible to use the REDUCE switch ECHO to prevent display of commands, this does not prevent display of the sequence numbers for the commands. redSplitOut can be called by redExec to separate the output from the commands. It can also be used after the call if the split option was not used or on an arbitrary output file from REDUCE, for example the full output which can be retrieved by redClose.

Value

A list containing three elements:

Author(s)

Martin Gregory

See Also

redExec

Examples

result <- c("5: ",
            "{x=-1}",
            "",
            "6: ",
            "b := {{2,12},{11,1}}",
            "",
            "7: ",
            "8: ",
            "               - m",
            "la := ---------------------",
            "                2       2",
            "       sqrt(v(3)  + v(2) )",
            "",
            "9: ",
            "",
            "10: ")
split <- redSplitOut(result)
writeLines(split$out)

function to start a REDUCE session

Description

Starts a REDUCE session using a pipe connection sending the output (log) to a temporary file.

Usage

redStart(dialect = "csl", dirpath, options, echo=FALSE)

Arguments

Details

redcas finds the REDUCE executables in two different ways. The first is the explicit specification of the path using the dirpath argument passed to the redStart function. If this does not contain the REDUCE executable, redStart stops executing on the assumption that a specific version was intended.

The second method is used if dirpath is not specified. This determines the path at package load time by searching the following three locations in turn until the executable is found:

• the environment variable REDUCE_EXEC exists and contains the path to a directory containing an executable;

• the R option reduce_exec exists and contains the path to a directory containing the executable;

• the REDUCE executable is found in a directory named in the environment variable PATH.

This approach provides the flexibility to have a default version while being able to call different versions explicitly.

While it is possible to start a second REDUCE session without closing the first, garbage collection closes its connection. A future release will fix this issue.

redStart carries out the following actions:

• creates the REDUCE session using a pipe connection and sending the REDUCE output to a temporary file (in REDUCE terminology referred to as a log);

• registers the session, acquiring a session identifier

• calls redExec to load the REDUCE functions which are part of the package and to set the ECHO switch if requested.

• returns the session identifier.

Value

The session identifier which is an integer >0 if the session started successfully. If the session could not be started, redStart terminates using stop. If no REDUCE executable was found returns FALSE.

Author(s)

martin gregory

See Also

showSessions to list active sessions and redClose for closing a session.

Examples

## Open a CSL session:
id1 <- redStart()
## can only run code if session was successfully started
if (is.numeric(id1)) {
   ## show session details:
   print(showSessions())
   ## close session:
   redClose(id1)
}

Class "redcas.solve"

Description

Contains the inputs and outputs of a call to the function redSolve which executes the REDUCE solve operator to determine solutions to a system of algebraic equations.

Usage

redcas.solve(...)

Arguments

Objects from the Class

Objects are created by calls to the function redSolve and can be used as input to the print method.

Slots

.Data:

Object of class "list" containing the actual data.

solutions:

Object of class "list" containing a character vector for each solution of the system of equations. The character vectors have a named element for each unknown with the name being the unknown and the value being the value of the unknown for the solution. This is essentially a copy of the list returned by the REDUCE solve operator.

rsolutions:

Object of class "list" containing a list for each solution converted to appropriate R types where possible. A vector will not suffice because the values of the unknowns may be of different types: integer, real, complex or expression. Explicit real and complex numbers are always converted. If the REDUCE switch ROUNDED is off, real and complex numbers may be expressions and may result in errors or NaN if conversion were attempted.

nsolutions:

Object of class "numeric". The number of solutions

rc:

Object of class "numeric". Return code from the redSolve call: 0 is success and 1 failure.

root_of:

Object of class "complex". A solution may express one or more unknowns in terms of the roots of another equation. In this case the other equation is enclosed in root_of(). This slot is a complex vector with the real part identifying the solution contain root_of() and the imaginary part the index of the unknown in that solution.

eqns:

Object of class "character". The system of equations provided to redSolve

unknowns:

Object of class "character". The unknowns provided to redSolve

switches:

Object of class "character". Any REDUCE switches set prior to executing the REDUCE solve function.

Extends

Class "list", from data part. Class "vector", by class "list", distance 2.

Methods

A print method, print, is defined.

Author(s)

Martin Gregory

See Also

redSolve is currently the only function using this class.

Examples

showClass("redcas.solve")

function to list details for currently active REDUCE sessions.

Description

For each active REDUCE session returns the full path to the REDUCE executable and the temporary log file, the connection identifier, the number of code blocks executed and the number of lines read from the log so far.

Usage

showSessions(id)

Arguments

Value

A data frame with the following columns:

Author(s)

martin gregory

See Also

redStart for creating a REDUCE session and redClose for closing a session.

Examples

## Open a PSL session:
id1 <- redStart('psl')
## can only run code if session was successfully started
if (is.numeric(id1)) {
   ## show session details:
   print(showSessions(id1))

   ## retrieve the entire transcript up to now
   writeLines(readLines(showSessions(id1)[,'logname'], warn=FALSE))

   ## close session:
   redClose(id1)
}