@@ -1,1750 +1,1750 @@
-\section{General Switches}
-
-\begin{Introduction}{SWITCHES}
-Switches are set on or off using the commands \nameref{on} or
-\nameref{off}, respectively.
-The default setting of the switches described in this section is
-\nameref{off} unless stated otherwise. 
-\end{Introduction}
-
-\begin{Switch}{ALGINT}
-\index{integration}
-When the \name{algint} switch is on, the algebraic integration module (which
-must be loaded from the REDUCE library) is used for integration.
-
-\begin{Comments}
-Loading \name{algint} from the library automatically turns on the
-\name{algint} switch.  An error message will be given if \name{algint} is
-turned on when the \name{algint} has not been loaded from the library.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{ALLBRANCH}
-When \name{allbranch} is on, the operator \nameref{solve} selects all 
-branches of solutions. 
-When \name{allbranch} is off, it selects only the principal
-branches.  Default is \name{on}.
-
-\begin{Examples}
-
-solve(log(sin(x+3)),x);    &
-\begin{multilineoutput}{6cm}
-\{X=2*ARBINT(1)*PI - ASIN(1) - 3,
- X=2*ARBINT(1)*PI + ASIN(1) + PI - 3\}
-\end{multilineoutput}\\
-off allbranch; \\
-solve(log(sin(x+3)),x);    &
-                 {X=ASIN(1) - 3}
-\end{Examples}
-
-\begin{Comments}
-\nameref{arbint}(1) indicates an arbitrary integer, which is given a
-unique identifier by REDUCE, showing that there are infinitely many
-solutions of this type.  When \name{allbranch} is off, the single
-canonical solution is given.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{ALLFAC}
-\index{output}
-The \name{allfac} switch, when on, causes REDUCE to factor out automatically
-common products in the output of expressions.  Default is \name{on}.
-
-\begin{Examples}
-x + x*y**3 + x**2*cos(z);  &      X*(COS(Z)*X + Y^{3}  + 1) \\
-off allfac; \\
-x + x*y**3 + x**2*cos(z);  &      COS(Z)*X^{2} + X*Y^{3}  + X
-\end{Examples}
-
-\begin{Comments}
-The \name{allfac} switch has no effect when \name{pri} is off.  Although the
-switch setting stays as it was, printing behavior is as if it were off.
-\end{Comments}
-\end{Switch}
-
-
-% \begin{Switch}{ALLPREC}
-%
-% \end{Switch}
-%
-%
-\begin{Switch}{ARBVARS}
-\index{solve}
-When \name{arbvars} is on, the solutions of singular or underdetermined
-systems of equations are presented in terms of arbitrary complex variables
-(see \nameref{arbcomplex}). Otherwise, the solution is parametrized in
-terms of some of the input variables. Default is \name{on}.
-
-\begin{Examples}
-solve({2x + y,4x + 2y},{x,y});                          &
-                   \{\{x= - \rfrac{arbcomplex(1)}{2},y=arbcomplex(1)\}\} \\
-solve({sqrt(x)+ y**3-1},{x,y});				&
-		   \{\{y=arbcomplex(2),x=y^6  - 2*y^3  + 1\}\} \\
-off arbvars; \\
-solve({2x + y,4x + 2y},{x,y});                          &
-                   \{\{x= - \rfrac{y}{2}\}\} \\
-solve({sqrt(x)+ y**3-1},{x,y});				&
-		   \{\{x=y^6  - 2*y^3  + 1\}\} \\
-\end{Examples}
-\begin{Comments}
-
-With \name{arbvars} off, the return value \name{\{\{\}\}} means that the
-equations given to \nameref{solve} imply no relation among the input
-variables.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{BALANCED\_MOD}
-\index{modular}
-\nameref{modular} numbers are normally produced in the range [0,...\meta{n}), 
-where
-\meta{n} is the current modulus.  With \name{balanced\_mod} on, the range
-[-\meta{n}/2,\meta{n}/2] is used instead.
-
-\begin{Examples}
-setmod 7; & 1 \\
-on modular; \\
-4; & 4 \\
-on balanced_mod; \\
-4; & -3
-\end{Examples}
-\end{Switch}
-
-
-\begin{Switch}{BFSPACE}
-\index{output}\index{floating point}
-Floating point numbers are normally printed in a compact notation (either
-fixed point or in scientific notation if \nameref{SCIENTIFIC\_NOTATION}
-has been used).  In some (but not all) cases, it helps comprehensibility
-if spaces are inserted in the number at regular intervals.  The switch
-\name{bfspace}, if on, will cause a blank to be inserted in the number after
-every five characters.
-\begin{Examples}
-on rounded; \\
-1.2345678;  & 1.2345678 \\
-on bfspace; \\
-1.2345678;  & 1.234 5678
-\end{Examples}
-\begin{Comments}
-\name{bfspace} is normally off.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{COMBINEEXPT}
-\index{exponent simplification}
-REDUCE is in general poor at surd simplification.  However, when the
-switch \name{combineexpt} is on, the system attempts to combine
-exponentials whenever possible.
-\begin{TEX}
-\begin{Examples}
-3^(1/2)*3^(1/3)*3^(1/6); & SQRT(3)*3^{\rfrac{1}{3}}*3^{\rfrac{1}{6}} \\
-on combineexpt; \\
-ws; & 1
-\end{Examples}
-\end{TEX}
-\begin{INFO}
-{\begin{Examples}
-3^(1/2)*3^(1/3)*3^(1/6); & SQRT(3)*3^{1/3}*3^{1/6} \\
-on combineexpt; \\
-ws; & 1
-\end{Examples}}
-\end{INFO}
-
-\end{Switch}
-
-
-\begin{Switch}{COMBINELOGS}
-\index{logarithm}
-In many cases it is desirable to expand product arguments of logarithms,
-or collect a sum of logarithms into a single logarithm.  Since these are
-inverse operations, it is not possible to provide rules for doing both at
-the same time and preserve the REDUCE concept of idempotent evaluation.
-As an alternative, REDUCE provides two switches \nameref{expandlogs} and
-\name{combinelogs} to carry out these operations.
-\begin{Examples}
-on expandlogs; \\
-log(x*y); & LOG(X) + LOG(Y) \\
-on combinelogs; \\
-ws; & LOG(X*Y)
-\end{Examples}
-
-\begin{Comments}
-At the present time, it is possible to have both switches on at once,
-which could lead to infinite recursion.  However, an expression is
-switched from one form to the other in this case.  Users should not rely
-on this behavior, since it may change in the next release.
-\end{Comments}
-
-\end{Switch}
-
-
-\begin{Switch}{COMP}
-\index{compiler}
-When \name{comp} is on, any succeeding function definitions are compiled
-into a faster-running form.  Default is \name{off}.
-
-\begin{Examples}
-\explanation{The following procedure finds Fibonacci numbers recursively.
-Create a new file ``refib" in your current directory with the following
-lines in it:} \\[6mm]
-\begin{multilineinput}
-procedure refib(n);
-   if fixp n and n >= 0 then
-     if n <= 1 then 1
-       else refib(n-1) + refib(n-2)
-    else rederr "nonnegative integer only";
-
-end;
-\end{multilineinput}\\
-\explanation{Now load REDUCE and run the following:}\\
-on time;                     &             Time: 100 ms \\
-
-in "refib"$                  &             Time: 0 ms \\
-
-                             &              REFIB \\
-
-                             &              Time: 260 ms \\
-
-                             &              Time: 20 ms \\
-
-refib(80);                   &             37889062373143906 \\
-
-                             &              Time: 14840 ms \\
-
-on comp;                     &             Time: 80 ms \\
-
-in "refib"$                  &             Time: 20 ms \\
-
-                             &              REFIB \\
-
-                              &             Time: 640 ms \\
-
-refib(80);                   &             37889062373143906 \\
-
-                               &            Time: 10940 ms
-\end{Examples}
-\begin{Comments}
-Note that the compiled procedure runs faster.  Your time messages will
-differ depending upon which system you have.  Compiled functions remain so
-for the duration of the REDUCE session, and are then lost.  They must be
-recompiled if wanted in another session.  With the switch \nameref{time} on
-as shown above, the CPU time used in executing the command is returned in
-milliseconds.  Be careful not to leave \name{comp} on unless you want it,
-as it makes the processing of procedures much slower.
-
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{COMPLEX}
-\index{complex}
-When the \name{complex} switch is on, full complex arithmetic is used in
-simplification, function evaluation, and factorization.  Default is \name{off}.
-
-\begin{Examples}
-
-factorize(a**2 + b**2);      &    \{A^{2}  + B^{2} \} \\
-on complex; \\
-
-factorize(a**2 + b**2);      &    \{A - I*B,A + I*B\} \\
-
-(x**2 + y**2)/(x + i*y);     &    X - I*Y \\
-
-on rounded;             &
-
-    *** Domain mode COMPLEX changed to COMPLEX\_FLOAT \\
-
-sqrt(-17);                   &    4.12310562562*I \\
-
-log(7*i);                    &    1.94591014906 + 1.57079632679*I
-\end{Examples}
-
-\begin{Comments}
-Complex floating-point can be done by turning on \nameref{rounded} in
-addition to \name{complex}.  With \name{complex} off however, REDUCE knows
-that \IFTEX{$i$}{i} is the square root of \IFTEX{$-1$}{-1} but will not
-carry out more complicated complex operations.  If you want complex
-denominators cleared by multiplication by their conjugates, turn on the
-switch \nameref{rationalize}.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{CREF}
-\index{cross reference}
-The switch \name{cref} invokes the CREF cross-reference program that
-processes a set of procedure definitions to produce a summary of their
-entry points, undefined procedures, non-local variables and so on.  The
-program will also check that procedures are called with a consistent
-number of arguments, and print a diagnostic message otherwise.
-
-The output is alphabetized on the first seven characters of each function
-name.
-
-To invoke the cross-reference program, \name{cref} is first turned on.
-This causes the program to load and the cross-referencing process to
-begin.  After all the required definitions are loaded, turning \name{cref}
-off will cause a cross-reference listing to be produced.
-
-\begin{Comments}
-
-Algebraic procedures in REDUCE are treated as if they were symbolic, so
-that algebraic constructs will actually appear as calls to symbolic
-functions, such as \name{aeval}.
-\end{Comments}
-
-\end{Switch}
-
-
-\begin{Switch}{CRAMER}
-\index{matrix}\index{linear system}\index{solve}
-When the \name{cramer} switch is on, \nameref{matrix} inversion 
-and linear equation
-solving (operator \nameref{solve}) is done by Cramer's rule, through exterior
-multiplication. Default is \name{off}.
-
-\begin{Examples}
-on time;                     &             Time: 80 ms \\
-off output;                  &             Time: 100 ms \\[4mm]
-\begin{multilineinput}
-mm := mat((a,b,c,d,f),(a,a,c,f,b),(b,c,a,c,d), (c,c,a,b,f),
-          (d,a,d,e,f));
-\end{multilineinput} &             Time: 300 ms \\
-inverse := 1/mm;             &             Time: 18460 ms \\
-on cramer;                   &             Time: 80 ms \\
-cramersinv := 1/mm;          &             Time: 9260 ms
-\end{Examples}
-
-\begin{Comments}
-Your time readings will vary depending on the REDUCE version you use.
-After you invert the matrix, turn on \nameref{output} and ask for one of
-the elements of the inverse matrix, such as \name{cramersinv(3,2)}, so that
-you can see the size of the expressions produced.
-
-Inversion of matrices and the solution of linear equations with dense
-symbolic entries in many variables is generally considerably faster with
-\name{cramer} on.  However, inversion of numeric-valued matrices is
-slower.  Consider the matrices you're inverting before deciding whether to
-turn \name{cramer} on or off.  A substantial portion of the time in matrix
-inversion is given to formatting the results for printing.  To save this
-time, turn \name{output} off, as shown in this example or terminate the
-expression with a dollar sign instead of a semicolon.  The results are
-still available to you in the workspace associated with your prompt
-number, or you can assign them to an identifier for further use.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{DEFN}
-\index{lisp}
-When the switch \name{defn} is on, the Standard Lisp equivalent of the
-input statement or procedure is printed, but not evaluated.  Default is
-\name{off}.
-
-\begin{Examples}
-
-on defn; \\
-
-17/3;                        &         (AEVAL (LIST 'QUOTIENT 17 3)) \\
-
-df(sin(x),x,2);          
-         &         (AEVAL (LIST 'DF (LIST 'SIN 'X) 'X 2)) \\
-\begin{multilineinput}
-procedure coshval(a);
-   begin scalar g;
-      g := (exp(a) + exp(-a))/2;
-      return g
-   end;
-\end{multilineinput} &
-\begin{multilineoutput}{7cm}
-(AEVAL 
-  (PROGN 
-    (FLAG '(COSHVAL) 'OPFN) 
-    (DE COSHVAL (A) 
-      (PROG (G) 
-        (SETQ G 
-          (AEVAL 
-             (LIST 
-                'QUOTIENT 
-                (LIST 
-                   'PLUS 
-                   (LIST 'EXP A) 
-                   (LIST 'EXP (LIST 'MINUS A))) 
-                2))) 
-       (RETURN G)))) ) 
-\end{multilineoutput} \\
-
-coshval(1);                 &       (AEVAL (LIST 'COSHVAL 1)) \\
-
-off defn; \\
-
-coshval(1);                 &   Declare COSHVAL operator? (Y or N) \\
-
-n \\
-\begin{multilineinput}
-procedure coshval(a);
-   begin scalar g;
-      g := (exp(a) + exp(-a))/2;
-      return g
-   end;
-\end{multilineinput} &       COSHVAL \\
-
-on rounded; \\
-
-coshval(1);                 &       1.54308063482
-\end{Examples}
-
-\begin{Comments}
-The above function \name{coshval} finds the hyperbolic cosine (cosh) of its
-argument.  When \name{defn} is on, you can see the Standard Lisp equivalent
-of the function, but it is not entered into the system as shown by the
-message \name{Declare COSHVAL operator?}.  It must be reentered with
-\name{defn} off to be recognized.  This procedure is used as an example; a
-more efficient procedure would eliminate the unnecessary local variable
-with
-\begin{verbatim}
-      procedure coshval(a);
-         (exp(a) + exp(-a))/2;
-\end{verbatim}
-
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{DEMO}
-\index{interactive}\index{output}
-The \name{demo} switch is used for interactive files, causing the system
-to pause after each command in the file until you type a \key{Return}.
-Default is \name{off}.
-
-\begin{Comments}
-The switch \name{demo} has no effect on top level interactive
-statements.  Use it when you want to slow down operations in a file so
-you can see what is happening.
-
-You can either include the \name{on demo} command in the file, or enter
-it from the top level before bringing in any file.  Unlike the
-\nameref{pause} command, \name{on demo} does not permit you to interrupt
-the file for questions of your own.
-
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{DFPRINT}
-\index{output}\index{derivative}
-When \name{dfprint} is on, expressions in the differentiation operator
-\nameref{df} are printed in a more ``natural'' notation, with the
-differentiation variables appearing as subscripts.  In addition, if the
-switch \nameref{noarg} is on (the default), the arguments of the
-differentiated operator are suppressed.
-
-\begin{Examples}
-operator f; \\
-df(f x,x); & DF(F(X),X); \\
-on dfprint; \\
-ws;  & F_{X} \\
-df(f(x,y),x,y); & F_{X}_{,}_{Y} \\
-off noarg; \\
-ws; & F(X,Y)_{X}
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{DIV}
-\index{output}
-When \name{div} is on, the system divides any simple factors found in
-the denominator of an expression into the numerator.  Default is \name{off}.
-
-\begin{Examples}
-
-on div; \\
-
-a := x**2/y**2;             &      A := X^{2} *Y^{-2} \\
-
-b := a/(3*z);               &      B := \rfrac{1}{3}*X^{2} *Y^{-2}  *Z^{-1} \\
-
-off div; \\
-
-a;                           &    \rfrac{X^{2}}{Y^{2}}\\
-
-b;                           &   \rfrac{X^{2}}{3*Y^{2} *Z}
-                                       
-\end{Examples}
-
-\begin{Comments}
-The \name{div} switch only has effect when the \nameref{pri} switch is on.
-When \name{pri} is off, regardless of the setting of \name{div}, the
-printing behavior is as if \name{div} were off.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{ECHO}
-\index{output}
-The \name{echo} switch is normally off for top-level entry, and on when files
-are brought in.  If \name{echo} is turned on at the top level, your input
-statements are echoed to the screen (thus appearing twice).  Default
-\name{off} (but note default \name{on} for files).
-
-\begin{Comments}
-If you want to display certain portions of a file and not others, use the
-commands \name{off echo} and \name{on echo} inside the file.  If you want
-no display of the file, use the input command
-
-	\name{in} {\em filename}\name{\$}
-
-rather than using the semicolon delimiter.
-
-Be careful when you use commands within a file to generate another file.
-Since \name{echo} is on for files, the output file echoes input statements
-(unlike its behavior from the top level).  You should explicitly turn off
-\name{echo} when writing output, and turn it back on when you're done.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{ERRCONT}
-\index{error handling}
-When the \name{errcont} switch is on, error conditions do not stop file
-execution.  Error messages will be printed whether \name{errcont} is on or
-off.
-
-Default is \name{off}.
-
-\begin{Comments}
-\begin{TEX}
-The table below shows REDUCE behavior under the settings of \name{errcont} and
-\name{int} :
-
-  \begin{center}
-  \begin{tabular}{|l|l|p{9.5cm}|}
-\hline
-\multicolumn{3}{|c|}{Behavior in Case of Error in Files}\\
-\hline
-\multicolumn{1}{|c|}{errcont} &
-  \multicolumn{1}{c|}{int} &
-    \multicolumn{1}{c|}{Behavior when errors in files are encountered}\\
-\hline
-off & off &
-Message is printed and parsing continues, but no further statements are 
-executed; no commands from keyboard accepted except \verb|bye| or
-\verb|end| \\
-off & on &
-Message is printed, and you are asked if you wish to continue.  (This is the
-default behavior) \\
-on & off &
-Message is printed, and file continues to execute without pause \\
-on & on &
-Message is printed, and file continues to execute without pause\\
-\hline
-  \end{tabular}
-  \end{center}
-\end{TEX}
-\begin{INFO}
-The following describes what happens when an error occurs in a file under
-each setting of \name{errcont} and \name{int}:
-
-Both off:  Message is printed and parsing continues, but no further
-statements are executed; no commands from keyboard accepted except bye or
-end;
-
-\name{errcont} off, \name{int} on:  Message is printed, and you are asked
-if you wish to continue. (This is the default behavior);
-
-\name{errcont} on, \name{int} off:  Message is printed, and file continues
-to execute without pause;
-
-Both on: Message is printed, and file continues to execute without pause.
-\end{INFO}
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{EVALLHSEQP}
-\index{equation}
-Under normal circumstances, the right-hand-side of an \nameref{equation}
-is evaluated but not the left-hand-side.  This also applies to any
-substitutions made by the \nameref{sub} operator.  If both sides are to be
-evaluated, the switch \name{evallhseqp} should be turned on.
-
-\end{Switch}
-
-
-\begin{Switch}{EXP}
-\index{simplification}
-When the \name{exp} switch is on, powers and products of expressions are
-expanded.  Default is \name{on}.
-
-\begin{Examples}
-(x+1)**3;                    &     X^{3} + 3*X^{2} + 3*X + 1 \\
-(a + b*i)*(c + d*i);         &     A*C + A*D*I + B*C*I - B*D \\
-off exp; \\
-(x+1)**3;                    &     (X + 1)^{3} \\
-(a + b*i)*(c + d*i);         &       (A + B*I)*(C + D*I) \\
-length((x+1)**2/(y+1));      &     2
-\end{Examples}
-
-\begin{Comments}
-Note that REDUCE knows that \IFTEX{$i^2 = -1$}{i^2 = -1}.
-When \name{exp} is off, equivalent expressions may not simplify to the same
-form, although zero expressions still simplify to zero.  Several operators
-that expect a polynomial argument behave differently when \name{exp} is
-off, such as \nameref{length}.  Be cautious about leaving \name{exp} off.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{EXPANDLOGS}
-\index{logarithm}
-In many cases it is desirable to expand product arguments of logarithms,
-or collect a sum of logarithms into a single logarithm.  Since these are
-inverse operations, it is not possible to provide rules for doing both at
-the same time and preserve the REDUCE concept of idempotent evaluation.
-As an alternative, REDUCE provides two switches \name{expandlogs} and
-\nameref{combinelogs} to carry out these operations.  Both are off by default.
-\begin{Examples}
-on expandlogs; \\
-log(x*y); & LOG(X) + LOG(Y) \\
-on combinelogs; \\
-ws; & LOG(X*Y)
-\end{Examples}
-
-\begin{Comments}
-At the present time, it is possible to have both switches on at once,
-which could lead to infinite recursion.  However, an expression is
-switched from one form to the other in this case.  Users should not rely
-on this behavior, since it may change in the next release.
-\end{Comments}
-
-\end{Switch}
-
-
-\begin{Switch}{EZGCD}
-\index{greatest common divisor}\index{polynomial}
-When \name{ezgcd} and \nameref{gcd} are on, greatest common divisors are
-computed using the EZ GCD algorithm that uses modular arithmetic (and is
-usually faster).  Default is \name{off}.
-
-\begin{Comments}
-As a side effect of the gcd calculation, the expressions involved are
-factored, though not the heavy-duty factoring of \nameref{factorize}. The
-EZ GCD algorithm was introduced in a paper by J. Moses and D.Y.Y. Yun in
-\meta{Proceedings of the ACM}, 1973, pp. 159-166.
-
-Note that the \nameref{gcd} switch must also be on for \name{ezgcd} to have
-effect.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{FACTOR}
-\index{output}
-When the \name{factor} switch is on, input expressions and results are
-automatically factored.
-
-\begin{Examples}
-
-on factor; \\
-
-aa := 3*x**3*a + 6*x**2*y*a + 3*x**3*b + 6*x**2*y*b\\
-+ x*y*a + 2*y**2*a + x*y*b + 2*y**2*b;
-			     &     AA := (A + B)*(3*X^{2} + Y)*(X + 2*Y) \\
-off factor; \\
-aa;                          &
-     3*A*X^{3} + 6*A*X^{2}*Y + A*X*Y + 2*A*Y^{2}  + 3*B*X^{3} + 6*B*X^{2}*Y\\
-+ B*X*Y + 2*B*Y^{2} \\
-on factor; \\
-ab := x**2 - 2;              &     AB := X^{2} - 2
-\end{Examples}
-
-\begin{Comments}
-REDUCE factors univariate and multivariate polynomials with 
-integer coefficients, finding any factors that also have integer coefficients.
-The factoring is done by reducing multivariate problems to univariate
-ones  with symbolic coefficients, and then solving the univariate ones modulo 
-small primes.  The results of these calculations are merged to
-determine the factors of the original polynomial.  The factorizer normally
-selects evaluation points and primes using a random number generator.  
-Thus, the detailed factoring behavior may be different each time any
-particular problem is tackled.
-
-When the \name{factor} switch is turned on, the \nameref{exp} switch is
-turned off, and when the \name{factor} switch is turned off, the
-\nameref{exp} switch is turned on, whether it was on previously or not.
-
-When the switch \nameref{trfac} is on, informative messages are generated at
-each call to the factorizer.  The \nameref{trallfac} switch causes the
-production of a more verbose trace message.  It takes precedence over
-\name{trfac} if they are both on.
-
-To factor a polynomial explicitly and store the results, use the operator 
-\nameref{factorize}.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{FAILHARD}
-\index{integration}
-When the \name{failhard} switch is on, the integration operator \nameref{int} 
-terminates with an error message if the integral cannot be done in closed 
-terms.
-Default is off.
-
-\begin{Comments}
-Use the \name{failhard} switch when you are dealing with complicated integrals
-and want to know immediately if REDUCE was unable to handle them.  The
-integration operator sometimes returns a formal integration form that is
-more complicated than the original expression, when it is unable to
-complete the integration.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{FORT}
-\index{FORTRAN}
-When \name{fort} is on, output is given Fortran-compatible syntax.  Default
-is \name{off}.
-
-\begin{Examples}
-on fort; \\
-df(sin(7*x + y),x);          &     ANS=7.*COS(7*X+Y) \\
-on rounded; \\
-b := log(sin(pi/5 + n*pi));  &
-	       B=LOG(SIN(3.14159265359*N+0.628318530718))
-\end{Examples}
-
-\begin{Comments}
-REDUCE results can be written to a file (using \nameref{out}) and used as data
-by Fortran programs when \name{fort} is in effect.  \name{fort} knows about
-correct statement length, continuation characters, defining a symbol when 
-it is first used, and other Fortran details.
-
-The \nameref{GENTRAN} package offers many more possibilities than the
-\name{fort} switch.  It produces Fortran (or C or Ratfor) code from REDUCE
-procedures or structured specifications, including facilities for producing
-double precision output.
-\end{Comments}
-\end{Switch}
-
-\begin{Switch}{FORTUPPER}
-\index{FORTRAN}
-When \name{fortupper} is on, any Fortran-style output appears in upper case.
-Default is \name{off}.
-
-\begin{Examples}
-on fort; \\
-df(sin(7*x + y),x);          &     ans=7.*cos(7*x+y) \\
-on fortupper; \\
-df(sin(7*x + y),x);          &     ANS=7.*COS(7*X+Y) \\
-\end{Examples}
-\end{Switch}
-
-
-\begin{Switch}{FULLPREC}
-\index{precision}\index{rounded}
-Trailing zeroes of rounded numbers to the full system precision are
-normally not printed.  If this information is needed, for example to get a
-more understandable indication of the accuracy of certain data, the switch
-\name{fullprec} can be turned on.
-
-\begin{Examples}
-on rounded; \\
-1/2;  & 0.5 \\
-on fullprec; \\
-ws; & 0.500000000000
-\end{Examples}
-
-\begin{Comments}
-This is just an output options which neither influences
-the accuracy of the computation nor does it give additional
-information about the precision of the results.
-See also \nameref{scientific_notation}.
-\end{Comments}
-\end{Switch}
-
-\begin{Switch}{FULLROOTS}
-\index{solve}\index{polynomial}
-Since roots of cubic and quartic polynomials can often be very
-messy, a switch \name{fullroots} controls the production
-of results in closed form. \nameref{solve} will apply the
-formulas for explicit forms for degrees 3 and 4 only if
-\name{fullroots} is \name{on}. Otherwise the result forms
-are built using \nameref{root\_of}. Default is \name{off}.
-\end{Switch}
-
-\begin{Switch}{GC}
-\index{memory}
-With the \name{gc} switch, you can turn the garbage collection messages on
-or off.  The form of the message depends on the particular Lisp used for
-the REDUCE implementation.
-
-\begin{Comments}
-See \nameref{reclaim} for an explanation of garbage collection.  REDUCE does
-garbage collection when needed even if you have turned the notices off.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{GCD}
-\index{greatest common divisor}\index{rational expression}
-When \name{gcd} is on, common factors in numerators and denominators of
-expressions are canceled.  Default is \name{off}.
-
-\begin{Examples}
-\begin{multilineinput}
-
-(2*(f*h)**2 - f**2*g*h - (f*g)**2 - f*h**3 + f*h*g**2
-   - h**4 + g*h**3)/(f**2*h - f**2*g - f*h**2 + 2*f*g*h
-   - f*g**2 - g*h**2 + g**2*h);
-\end{multilineinput}         &
-\rfrac{F^{2}*G^{2} + F^{2}*G*H - 2*F^{2}*H^{2} - F*G^{2}*H + F*H^{3} - G*H^{3} +
- H^{4}}
-       {F^{2}*G - F^{2}*H + F*G^{2} - 2*F*G*H + F*H^{2} - G^{2}*H + G*H^{2}} \\
-on gcd; \\
-ws;                          &       \rfrac{F*G + 2*F*H + H^{2}}{F + G} \\
-e2 := a*c + a*d + b*c + b*d; &      E2 := A*C + A*D + B*C + B*D \\
-off exp;  \\
-e2;                          &      (A + B)*(C + D)
-\end{Examples}
-
-\begin{Comments}
-Even with \name{gcd} off, a check is automatically made for common variable
-and numerical products in the numerators and denominators of expression,
-and the appropriate cancellations made.  Thus the example demonstrating the
-use of \name{gcd} is somewhat complicated.  Note when \nameref{exp} is off,
-\name{gcd} has the side effect of factoring the expression.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{HORNER}
-\index{output}\index{polynomial}
-When the \name{horner} switch is on, polynomial expressions are printed
-in Horner's form for faster and safer numerical evaluation. Default
-is \name{off}. The leading variable of the expression is selected as
-Horner variable. To select the Horner variable explicitly use the 
-\nameref{korder} declaration.
-
-\begin{Examples}
-on horner;\\
-(13p-4q)^3;&
-( - 64)*q^3  + p*(624*q^2  + p*(( - 2028)*q + p*2197))\\
-korder q;\\
-ws;&
-2197*p^3  + q*(( - 2028)*p^2  + q*(624*p + q*(-64)))
-\end{Examples}
-\end{Switch}
-
-
-\begin{Switch}{IFACTOR}
-\index{integer}\index{factorize}
-When the \name{ifactor} switch is on, any integer terms appearing as a result
-of the \nameref{factorize} command are factored themselves into primes.  Default
-is \name{off}.  If the argument of \name{factorize} is an integer,
-\name{ifactor} has no effect, since the integer is always factored.
-
-\begin{Examples}
-factorize(4*x**2 + 28*x + 48);      &    \{4,X + 3,X + 4\} \\
-factorize(22587);                   &    \{3,7529\} \\
-on ifactor; \\
-factorize(4*x**2 + 28*x + 48);      &    \{2,2,X + 4,X + 3\} \\
-factorize(22587);                   &    \{3,7529\}
-\end{Examples}
-
-\begin{Comments}
-Constant terms that appear within nonconstant
-polynomial factors are not factored.
-
-The \name{ifactor} switch affects only factoring done specifically
-with \nameref{factorize}, not on factoring done automatically when the
-\nameref{factor} switch is on.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{INT}
-\index{interactive}
-The \name{int} switch specifies an interactive mode of operation.  Default
-\name{on}.
-
-\begin{Comments}
-There is no reason to turn \name{int} off during interactive calculations,
-since there are no benefits to be gained.  If you do have \name{int} off
-while inputting a file, and REDUCE finds an error, it prints the message
-``Continuing with parsing only."  In this state, REDUCE accepts only
-\nameref{end}\name{;} or \nameref{bye}\name{;} from the keyboard;
-everything else is ignored, even the command \name{on int}.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{INTSTR}
-\index{output}
-If \name{intstr} (for ``internal structure'') is on, arguments of an
-operator are printed in a more structured form.
-
-\begin{Examples}
-operator f; \\
-f(2x+2y); & F(2*X + 2*Y) \\
-on intstr; \\
-ws; & F(2*(X + Y))
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{LCM}
-\index{rational expression}
-The \name{lcm} switch instructs REDUCE to compute the least common multiple
-of denominators whenever rational expressions occur.  Default is \name{on}.
-
-\begin{Examples}
-off lcm; \\
-z := 1/(x**2 - y**2) + 1/(x-y)**2;  
-			     &     Z := \rfrac{2*X*(X - Y)}{X^{4} - 2*X^{3}*Y + 
-2*X*Y^{3} - Y^{4}} \\
-on lcm; \\
-z;                           &     \rfrac{2*X*(X - Y)}{X^{4} - 2*X^{3}*Y + 2*X*Y
-^{3} - Y^{4}} \\
-zz := 1/(x**2 - y**2) + 1/(x-y)**2;
-			     &     ZZ := \rfrac{2*X}{X^{3} - X^{2}*Y - X*Y^{2} +
- Y^{3}} \\
-on gcd; \\
-z;                           &     \rfrac{2*X}{X^{3} - X^{2}*Y - X*Y^{2} + Y^{3}
-}
-\end{Examples}
-
-\begin{Comments}
-Note that \name{lcm} has effect only when rational expressions are first
-combined.  It does not examine existing structures for simplifications on
-display.  That is shown above when \IFTEX{$z$}{z} is entered with
-\name{lcm} off.  It remains unsimplified even after \name{lcm} is turned
-back on.  However, a new variable containing the same expression is
-simplified on entry.  The switch \nameref{gcd} does examine existing
-structures, as shown in the last example line above.
-
-Full greatest common divisor calculations become expensive if work with
-large rational expressions is required.  A considerable savings of time
-can be had if a full gcd check is made only when denominators are combined,
-and only a partial check for numerators.  This is the effect of the \name{lcm}
-switch.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{LESSSPACE}
-\index{output}
-You can turn on the switch \name{lessspace} if you want fewer
-blank lines in your output.
-\end{Switch}
-
-
-\begin{Switch}{LIMITEDFACTORS}
-\index{factorize}\index{polynomial}
-To get limited factorization in cases where it is too expensive to use
-full multivariate polynomial factorization, the switch
-\name{limitedfactors} can be turned on.  In that case, only ``inexpensive''
-factoring operations, such as square-free factorization, will be used
-when \nameref{factorize} is called.
-
-\begin{Examples}
-a := (y-x)^2*(y^3+2x*y+5)*(y^2-3x*y+7)$ \\
-factorize a; &
-\begin{multilineoutput}{7cm}
-\{ - X + Y,
- X - Y,
- 2*X*Y + Y^{3} + 5,
- 3*X*Y - Y^{2} - 7\}
-\end{multilineoutput} \\
-on limitedfactors; \\
-factorize a; &
-\begin{multilineoutput}{7cm}
-\{ - X + Y,
- X - Y,
- 6*X^{2}*Y^{2} + 3*X*Y^{4} - 2*X*Y^{3} + X*Y - Y^{5} - 7*Y^{3} - 5*Y^{2} - 35\}
-\end{multilineoutput}
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{LIST}
-The \name{list} switch causes REDUCE to print each term in any sum on
-separate lines.
-
-\begin{Examples}
-x**2*(y**2 + 2*y) + x*(y**2 + z)/(2*a);
-			    &     \rfrac{X*(2*A*X*Y^{2} + 4*A*X*Y + Y^{2} +
-Z)}{2*A} \\
-on list; \\
-ws;                         &
-\begin{multilineoutput}{6cm}
-(X*(2*A*X*Y^{2}
-  + 4*A*X*Y
-  + Y^{2}
-  + Z))/(2*A)
-\end{multilineoutput}
-\end{Examples}
-\end{Switch}
-
-
-\begin{Switch}{LISTARGS}
-\index{list}\index{argument}\index{operator}
-If an operator other than those specifically defined for lists is given a
-single argument that is a list, then the result of this operation will be
-a list in which that operator is applied to each element of the list.
-This process can be inhibited globally by turning on the switch
-\name{listargs}.
-
-\begin{Examples}
-log {a,b,c}; & {LOG(A),LOG(B),LOG(C)} \\
-on listargs; \\
-log {a,b,c}; & LOG({A,B,C})
-\end{Examples}
-
-\begin{Comments}
-It is possible to inhibit such distribution for a specific operator by
-using the declaration \nameref{listargp}.  In addition, if an operator has
-more than one argument, no such distribution occurs, so \name{listargs}
-has no effect.
-\end{Comments}
-
-\end{Switch}
-
-
-\begin{Switch}{MCD}
-\index{rational expression}
-When \name{mcd} is on, sums and differences of rational expressions are put
-on a common denominator.  Default is \name{on}.
-
-\begin{Examples}
-a/(x+1) + b/5;               &         \rfrac{5*A + B*X + B}{5*(X + 1)} \\
-off mcd; \\
-a/(x+1) + b/5;               &        (X + 1)^{-1}*A + 1/5*B \\
-1/6 + 1/7;                   &        13/42
-\end{Examples}
-
-\begin{Comments}
-Even with \name{mcd} off, rational expressions involving only numbers are still
-put over a common denominator.  
-
-Turning \name{mcd} off is useful when explicit negative powers are needed,
-or if no greatest common divisor calculations are desired, or when
-differentiating complicated rational expressions.  Results when \name{mcd}
-is off are no longer in canonical form, and expressions equivalent to zero
-may not simplify to 0.  Some operations, such as factoring cannot be done
-while \name{mcd} is off.  This option should therefore be used with some
-caution.  Turning \name{mcd} off is most valuable in intermediate parts of
-a complicated calculation, and should be turned back on for the last stage.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{MODULAR}
-\index{modular}
-When \name{modular} is on, polynomial coefficients are reduced by the
-modulus set by \nameref{setmod}.  If no modulus has been set, \name{modular}
-has no effect.
-
-\begin{Examples}
-setmod 2;                    &          1 \\
-on modular;                             \\
-(x+y)**2;                    &          X^{2} + Y^{2} \\
-145*x**2 + 20*x**3 + 17 + 15*x*y;
-			     &          X^{2} + X*Y + 1
-\end{Examples}
-
-\begin{Comments}
-Modular operations are only conducted on the coefficients, not the
-exponents.  The modulus is not restricted to being prime.  When the modulus
-is prime, division by a number not relatively prime to the modulus results
-in a \meta{Zero divisor} error message.  When the modulus is a composite
-number, division by a power of the modulus results in an error message, but
-division by an integer which is a factor of the modulus does not.
-The representation of modular number can be influenced by 
-\nameref{balanced\_mod}.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{MSG}
-\index{output}
-When \name{msg} is off, the printing of warning messages is suppressed.  Error
-messages are still printed.
-
-\begin{Comments}
-Warning messages include those about redimensioning an \nameref{array} 
-or declaring an \nameref{operator} where one is expected.  
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{MULTIPLICITIES}
-\index{solve}
-When \nameref{solve} is applied to a set of equations with multiple roots,
-solution multiplicities are normally stored in the global variable
-\nameref{root\_multiplicities} rather than the solution list.  If you want
-the multiplicities explicitly displayed, the switch \name{multiplicities}
-should be turned on.  In this case, \name{root_multiplicities} has no value.
-
-\begin{Examples}
-solve(x^2=2x-1,x); & {X=1} \\
-root_multiplicities; & {2} \\
-on multiplicities; \\
-solve(x^2=2x-1,x); & {X=1,X=1} \\
-root_multiplicities; &
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{NAT}
-\index{output}
-When \name{nat} is on, output is printed to the screen in natural form, with
-raised exponents.  \name{nat} should be turned off when outputting expressions
-to a file for future input.  Default is \name{on}.
-
-\begin{Examples}
-(x + y)**3;                  &          X^{3} + 3*X^{2}*Y + 3*X*Y^{2} + Y^{3} \\
-off nat; \\
-(x + y)**3;                  &          X**3 + 3*X**2*Y + 3*X*Y**2 + Y**3\$ \\
-on fort; \\
-(x + y)**3;                  &          ANS=X**3+3.*X**2*Y+3.*X*Y**2+Y**3
-\end{Examples}
-\begin{Comments}
-With \name{nat} off, a dollar sign is printed at the end of each expression.
-An output file written with \name{nat} off is ready to be read into REDUCE
-using the command \nameref{in}.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{NERO}
-\index{output}
-When \name{nero} is on, zero assignments (such as matrix elements) are not
-printed.
-
-\begin{Examples}
-matrix a;
-a := mat((1,0),(0,1));       & \begin{multilineoutput}{6cm}
-A(1,1) := 1
-A(1,2) := 0
-A(2,1) := 0
-A(2,2) := 1
-\end{multilineoutput}\\
-on nero; \\
-a;                           &  \begin{multilineoutput}{6cm}
-MAT(1,1) := 1
-MAT(2,2) := 1
-\end{multilineoutput}\\
-a(1,2);                      & \explanationo{nothing is printed.} \\
-b := 0;                     &  \explanationo{nothing is printed.} \\
-off nero; \\
-b := 0;                     &          B := 0
-\end{Examples}
-\begin{Comments}
-\name{nero} is often used when dealing with large sparse matrices, to avoid
-being overloaded with zero assignments.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{NOARG}
-\index{output}\index{derivative}
-When \nameref{dfprint} is on, expressions in the differentiation operator
-\nameref{df} are printed in a more ``natural'' notation, with the
-differentiation variables appearing as subscripts.  When \name{noarg}
-is on (the default), the arguments of the differentiated operator are also
-suppressed.
-
-\begin{Examples}
-operator f; \\
-df(f x,x); & DF(F(X),X); \\
-on dfprint; \\
-ws;  & F_{X} \\
-off noarg; \\
-ws; & F(X)_{X}
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{NOLNR}
-\index{integration}
-When \name{nolnr} is on, the linear properties of the integration operator
-\nameref{int} are suppressed if the integral cannot be found in closed terms.
-
-\begin{Comments}
-REDUCE uses the linear properties of integration to attempt to break down
-an integral into manageable pieces.  If an integral cannot be found in
-closed terms, these pieces are returned.  When the \name{nolnr} switch is off,
-as many of the pieces as possible are integrated.  When it is on, if any piece
-fails, the rest of them remain unevaluated.
-\end{Comments}
-\end{Switch}
-
-
-%\begin{Switch}{NORNDBF}
-%
-%***** To be added *****
-%
-%\end{Switch}
-
-
-\begin{Switch}{NOSPLIT}
-\index{output}
-Under normal circumstances, the printing routines try to break an expression
-across lines at a natural point.  This is a fairly expensive process.  If
-you are not overly concerned about where the end-of-line breaks come, you
-can speed up the printing of expressions by turning off the switch
-\name{nosplit}.  This switch is normally on.
-
-\end{Switch}
-
-
-\begin{Switch}{NUMVAL}
-\index{rounded}
-With \nameref{rounded} on, elementary functions with numerical arguments
-will return a numerical answer where appropriate.  If you wish to inhibit
-this evaluation, \name{numval} should be turned off.  It is normally on.
-
-\begin{Examples}
-on rounded; \\
-cos 3.4; & - 0.966798192579 \\
-off numval; \\
-cos 3.4; & COS(3.4)
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{OUTPUT}
-\index{output}
-When \name{output} is off, no output is printed from any REDUCE calculation.
-The calculations have their usual effects other than printing.  Default is
-\name{on}.
-
-\begin{Comments}
-Turn output \name{off} if you do not wish to see output when executing
-large files, or to save the time REDUCE spends formatting large expressions
-for display.  Results are still available with \nameref{ws}, or in their
-assigned variables. 
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{OVERVIEW}
-\index{factorize}
-When \name{overview} is on, the amount of detail reported by the factorizer
-switches \nameref{trfac} and \nameref{trallfac} is reduced.
-
-\end{Switch}
-
-
-\begin{Switch}{PERIOD}
-\index{output}\index{integer}
-When \name{period} is on, periods are added after integers in
-Fortran-compatible output (when \nameref{fort} is on).  There is no effect
-when \name{fort} is off.  Default is \name{on}.
-\end{Switch}
-
-
-\begin{Switch}{PRECISE}
-\index{simplification}\index{square root}
-When the \name{precise} switch is on, simplification of roots of even
-powers returns absolute values, a more precise answer mathematically.
-Default is \name{on}.
-
-\begin{Examples}
-sqrt(x**2);                  &        X \\
-(x**2)**(1/4);               &        SQRT(X) \\
-on precise; \\
-sqrt(x**2);                  &        ABS(X) \\
-(x**2)**(1/4);               &        SQRT(ABS(X))
-\end{Examples}
-
-\begin{Comments}
-In many types of mathematical work, simplification of powers and surds can
-proceed by the fastest means of simplifying the exponents arithmetically.
-When it is important to you that the positive root be returned, turn
-\name{precise} on.  One situation where this is important is when graphing
-square-root expressions such as \IFTEX{$\sqrt{x^2+y^2}$}{sqrt(x^2+y^2)} to
-avoid a spike caused by REDUCE simplifying
-\IFTEX{$\sqrt{y^2}$}{sqrt(y^2)} to \IFTEX{$y$}{y} when \IFTEX{$x$}{x} is
-zero.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{PRET}
-\index{output}
-When \name{pret} is on, input is printed in standard REDUCE format and then
-evaluated.
-
-\begin{Examples}
-on pret; \\
- (x+1)^3;                     &
-\begin{multilineoutput}{6cm}
- (x + 1)**3;
-X^{3} + 3*X^{2} + 3*X + 1
-\end{multilineoutput} \\
-\begin{multilineinput}
-
-procedure fac(n);
-   if not (fixp(n) and n>=0)
-     then rederr "Choose nonneg. integer only"
-    else for i := 0:n-1 product i+1;
-\end{multilineinput}     &
-\begin{multilineoutput}{8cm}
-procedure fac n;
-   if not (fixp n and n>=0)
-     then rederr "Choose nonneg. integer only"
-    else for i := 0:n - 1 product i + 1;
-
-FAC
-\end{multilineoutput}\\
-
-fac 5;                    & \begin{multilineoutput}{6cm}
-fac 5;
-120
-\end{multilineoutput}
-
-\end{Examples}
-
-\begin{Comments}
-Note that all input is converted to lower case except strings (which keep
-the same case) all operators with a single argument have had the
-parentheses removed, and all infix operators have had a space added on each
-side.  In addition, syntactical constructs like
-\name{if}\ldots\name{then}\ldots\name{else} are printed in a standard format.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{PRI}
-\index{output}
-When \name{pri} is on, the declarations \nameref{order} and \nameref{factor} can
-be used, and the switches \nameref{allfac}, \nameref{div}, \nameref{rat}, 
-and \nameref{revpri} take effect when they are on.  Default is \name{on}.
-
-\begin{Comments}
-Printing of expressions is faster with \name{pri} off.  The expressions are
-then returned in one standard form, without any of the display options that
-can be used to feature or display various parts of the expression.  You can
-also gain insight into REDUCE's representation of expressions with
-\name{pri} off.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{RAISE}
-\index{input}\index{character}
-When \name{raise} is on, lower case letters are automatically converted to
-upper case on input.  \name{raise} is normally on.
-
-\begin{Comments}
-This conversion affects the internal representation of the letter, and is
-independent of the case with which a letter is printed, which is normally
-lower case.
-\end{Comments}
-
-\end{Switch}
-
-
-\begin{Switch}{RAT}
-\index{output}
-When the \name{rat} switch is on, and kernels have been selected to display
-with the \nameref{factor} declaration, the denominator is printed with each
-term rather than one common denominator at the end of an expression.
-
-\begin{Examples}
-(x+1)/x + x**2/sin y;        
-          &     \rfrac{SIN(Y)*X + SIN(Y) + X^{3}}{SIN(Y)*X} \
-\
-factor x; \\
-(x+1)/x + x**2/sin y;        
-          &     \rfrac{X^{3} + X*SIN(Y) + SIN(Y)}{X*SIN(Y)} \
-\
-on rat;  \\
-(x+1)/x + x**2/sin y;       
-          &     \rfrac{X^{2}}{SIN(Y)} + 1 + X^{-1}
-\end{Examples}
-
-\begin{Comments}
-The \name{rat} switch only has effect when the \nameref{pri} switch is on.
-When \name{pri} is off, regardless of the setting of \name{rat}, the
-printing behavior is as if \name{rat} were off.  \name{rat} only has
-effect upon the display of expressions, not their internal form.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{RATARG}
-\index{rational expression}\index{polynomial}
-When \name{ratarg} is on, rational expressions can be given to operators
-such as \nameref{coeff} and \nameref{lterm} that normally require
-polynomials in one of their arguments.  When \name{ratarg} is off, rational
-expressions cause an error message.
-
-\begin{Examples}
-aa := x/y**2 + 1/x + y/x**2; 
-    &    AA := \rfrac{X^{3} + X*Y^{2} + Y^{3}}{X^{2}*Y^{2}} \\
-coeff(aa,x);                 &
-   ***** \rfrac{X^{3} + X*Y^{2} + Y^{3}}{X^{2}*Y^{2}} invalid as POLYNOMIAL\\
-on ratarg; \\
-coeff(aa,x);                
-    & \{\rfrac{Y}{X^{2}},\rfrac{1}{X^{2}},0,\rfrac{1}{X^{2}*Y^{2}}\}
-\end{Examples}
-\end{Switch}
-
-
-\begin{Switch}{RATIONAL}
-\index{rational expression}\index{polynomial}
-When \name{rational} is on, polynomial expressions with rational coefficients
-are produced.
-
-\begin{Examples}
-x/2 + 3*y/4;                 &       \rfrac{2*X + 3*Y}{4} \\
-(x**2 + 5*x + 17)/2;         &       \rfrac{X^{2} + 5*X + 17}{2} \\
-on rational; \\
-x/2 + 3y/4;                  &       \rfrac{1}{2}*(X + \rfrac{3}{2}*Y) \\
-(x**2 + 5*x + 17)/2;         &       \rfrac{1}{2}*(X^{2} + 5*X + 17)
-\end{Examples}
-
-\begin{Comments}
-By using \name{rational}, polynomial expressions with rational
-coefficients can be used in some commands that expect polynomials.  With
-\name{rational} off, such a polynomial becomes a rational expression, with
-denominator the least common multiple of the denominators of the rational
-number coefficients.  % The \nameref{factorize} command does not accept
-% polynomials with rational coefficients.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{RATIONALIZE}
-\index{rational expression}\index{simplification}\index{complex}
-When the \name{rationalize} switch is on, denominators of rational expressions
-that contain complex numbers or root expressions are simplified by 
-multiplication by their conjugates.
-
-\begin{Examples}
-qq := (1+sqrt(3))/(sqrt(3)-7);  &   QQ := \rfrac{SQRT(3) + 1}{SQRT(3) - 7} \\
-on rationalize; \\
-qq;                             &   \rfrac{- 4*SQRT(3) - 5}{23} \\
-2/(4 + 6**(1/3));               &     \rfrac{6^{2/3} - 4*6^{1/3} + 16}{35} \\
-(i-1)/(i+3);                    &   \rfrac{2*I - 1}{5} \\
-off rationalize; \\
-(i-1)/(i+3);                    &   \rfrac{I - 1}{I + 3}
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{RATPRI}
-\index{output}\index{rational expression}
-When the \name{ratpri} switch is on, rational expressions and fractions are
-printed as two lines separated by a fraction bar, rather than in a linear
-style.  Default is \name{on}.
-
-\begin{Examples}
-3/17;                        &            \rfrac{3}{17} \\
-2/b + 3/y;                   &            \rfrac{3*B + 2*Y}{B*Y} \\
-off ratpri; \\
-3/17;                        &            3/17 \\
-2/b + 3/y;                   &            (3*B + 2*Y)/(B*Y)
-\end{Examples}
-\end{Switch}
-
-
-\begin{Switch}{REVPRI}
-\index{output}
-When the \name{revpri} switch is on, terms are printed in reverse order from
-the normal printing order.
-
-\begin{Examples}
-x**5 + x**2 + 18 + sqrt(y);  &    SQRT(Y) + X^{5} + X^{2} + 18 \\
-a + b + c + w;               &    A + B + C + W \\
-on revpri; \\
-x**5 + x**2 + 18 + sqrt(y);  &    17 + X^{2} + X^{5} + SQRT(Y) \\
-a + b + c + w;               &    W + C + B + A
-\end{Examples}
-
-\begin{Comments}
-Turn \name{revpri} on when you want to display a polynomial in ascending
-rather than descending order.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{RLISP88}
-\index{lisp}
-Rlisp '88 is a superset of the Rlisp that has been traditionally used for
-the support of REDUCE.  It is fully documented in the book Marti, J.B.,
-``{RLISP} '88:  An Evolutionary Approach to Program Design and Reuse'',
-World Scientific, Singapore (1993).  It supports different looping
-constructs from the traditional Rlisp, and treats ``-'' as a letter unless
-separated by spaces.  Turning on the switch \name{rlisp88} converts to
-Rlisp '88 parsing conventions in symbolic mode, and enables the use of
-Rlisp '88 extensions.  Turning off the switch reverts to the traditional
-Rlisp and the previous mode ( (\nameref{symbolic} or \nameref{algebraic})
-in force before \name{rlisp88} was turned on.
-
-\end{Switch}
-
-
-\begin{Switch}{ROUNDALL}
-\index{rounded}\index{rational expression}\index{floating point}
-In \nameref{rounded} mode, rational numbers are normally converted to a
-floating point representation.  If \name{roundall} is off, this conversion
-does not occur.  \name{roundall} is normally \name{on}.
-
-\begin{Examples}
-on rounded; \\
-1/2; & 0.5 \\
-off roundall; \\
-1/2; \rfrac{1}{2}
-\end{Examples}
-
-\end{Switch}
-
-
-\begin{Switch}{ROUNDBF}
-When \nameref{rounded} is on, the normal defaults cause underflows to be
-converted to zero.  If you really want the small number that results in
-such cases, \name{roundbf} can be turned on.
-
-\begin{Examples}
-on rounded; \\
-exp(-100000.1^2); & 0 \\
-on roundbf; \\
-exp(-100000.1^2); & 1.18441281937E-4342953505
-\end{Examples}
-
-\begin{Comments}
-If a polynomial is input in \nameref{rounded} mode at the default
-precision into any \nameref{roots} function, and it is not possible to
-represent any of the coefficients of the polynomial precisely in the
-system floating point representation, the switch \name{roundbf} will be
-automatically turned on.  All rounded computation will use the internal
-bigfloat representation until the user subsequently turns \name{roundbf}
-off. (A message is output to indicate that this condition is in effect.)
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{ROUNDED}
-\index{floating point}
-When \name{rounded} is on, floating-point arithmetic is enabled, with
-precision initially at a system default value, which is usually 12 digits.
-The precise number can be found by the command \nameref{precision}(0).
-\begin{Examples}
-pi;                          &            PI \\
-35/217;                      &            \rfrac{5}{31} \\
-on rounded; \\
-pi;                          &            3.14159265359 \\
-35/217;                      &            0.161 \\
-sqrt(3);                     &            1.73205080756
-\end{Examples}
-\begin{Comments}
-If more than the default number of decimal places are required, use the
-\nameref{precision} command to set the required number.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{SAVESTRUCTR}
-\index{STRUCTR OPERATOR}
-When \name{savestructr} is on, results of the \nameref{structr} command are
-returned as a list whose first element is the representation for the
-expression and the remaining elements are equations showing the
-relationships of the generated variables.
-
-\begin{Examples}
-off exp; \\
-structr((x+y)^3 + sin(x)^2);                          &
-\begin{multilineoutput}{6cm}
-ANS3
-   where
-      ANS3 := ANS1^{3} + ANS2^{2}
-      ANS2 := SIN(X)
-      ANS1 := X + Y
-\end{multilineoutput}\\
-ans3;                        &     ANS3 \\
-on savestructr; \\
-structr((x+y)^{3} + sin(x)^{2});                         &
-{ANS3,ANS3=ANS1^{3} + ANS2^{2},ANS2=SIN(X),ANS1=X + Y} \\
-ans3 where rest ws; &
-(X + Y)^{3} + SIN(X)^{2}
-\end{Examples}
-\begin{Comments}
-In normal operation, \nameref{structr} is only a display command.  With
-\name{savestructr} on, you can access the various parts of the expression
-produced by \name{structr}.
-
-The generic system names use the stem \name{ANS}.  You can change this to your
-own stem by the command \nameref{varname}.  REDUCE adds integers to this stem
-to make unique identifiers.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{SOLVESINGULAR}
-\index{solve}
-When \name{solvesingular} is on, singular or underdetermined systems of
-linear equations are solved, using arbitrary real, complex or integer
-variables in the answer.  Default is \name{on}.
-
-\begin{Examples}
-solve({2x + y,4x + 2y},{x,y});                          &
-                   \{\{X= - \rfrac{ARBCOMPLEX(1)}{2},Y=ARBCOMPLEX(1)\}\} \\
-solve({7x + 15y - z,x - y - z},{x,y,z});                &
-\begin{multilineoutput}{6cm}
-\{\{X=\rfrac{8*ARBCOMPLEX(3)}{11}
-  Y= - \rfrac{3*ARBCOMPLEX(3)}{11}
-  Z=ARBCOMPLEX(3)\}\}
-\end{multilineoutput}\\
-off solvesingular; \\
-solve({2x + y,4x + 2y},{x,y});                          &
-                   ***** SOLVE given singular equations \\
-solve({7x + 15y - z,x - y - z},{x,y,z});                &
-                   ***** SOLVE given singular equations
-\end{Examples}
-\begin{Comments}
-
-The integer following the identifier \nameref{arbcomplex} above is assigned by
-the system, and serves to identify the variable uniquely.  It has no other
-significance.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{TIME}
-\index{time}
-When \name{time} is on, the system time used in executing each REDUCE
-statement is printed after the answer is printed.
-
-\begin{Examples}
-on time;                     &       Time: 4940 ms \\
-df(sin(x**2 + y),y);         &
-\begin{multilineoutput}{6cm}
-COS(X  + Y^{2})
-Time: 180 ms
-\end{multilineoutput}\\
-solve(x**2 - 6*y,x);         &
-\begin{multilineoutput}{6cm}
-\{X= - SQRT(Y)*SQRT(6),
- X=SQRT(Y)*SQRT(6)\}
-Time: 320 ms
-\end{multilineoutput}
-\end{Examples}
-\begin{Comments}
-When \name{time} is first turned on, the time since the beginning of the
-REDUCE session is printed.  After that, the time used in computation,
-(usually in milliseconds, though this is system dependent) is printed after
-the results of each command.  Idle time or time spent typing in commands is
-not counted.  If \name{time} is turned off, the first reading after it is
-turned on again gives the time elapsed since it was turned off.  The time
-printed is CPU or wall clock time, depending on the system.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{TRALLFAC}
-\index{factorize}
-When \name{trallfac} is on, a more detailed trace of factorizer calls is
-generated.
-
-\begin{Comments}
-The \name{trallfac} switch takes precedence over \nameref{trfac} if they are
-both on. \name{trfac} gives a factorization trace with less detail in it.
-When the \nameref{factor} switch is on also, all input polynomials are sent to
-the factorizer automatically and trace information is generated.  The
-\nameref{out} command saves the results of the factoring, but not the trace.
-% You need to use the \name{dribble} command to save the trace text to a file.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{TRFAC}
-\index{factorize}
-When \name{trfac} is on, a narrative trace of any calls to the factorizer is
-generated.  Default is \name{off}.
-
-\begin{Comments}
-When the switch \nameref{factor} is on, and \name{trfac} is on, every input
-polynomial is sent to the factorizer, and a trace generated.  With
-\name{factor} off, only polynomials that are explicitly factored with the
-command \nameref{factorize} generate trace information.
-
-% Use the \name{dribble} or \name{logfile} command to save the trace text to
-% a file.
-The \nameref{out} command saves the results of the factoring, but not
-the trace.  The \nameref{trallfac} switch gives trace information to a
-greater level of detail.
-\end{Comments}
-\end{Switch}
-
-\begin{Switch}{TRIGFORM}
-\index{solve}\index{polynomial}
-When \nameref{fullroots} is on, \nameref{solve} will compute the
-roots of a cubic or quartic polynomial is closed form. When 
-\name{trigform} is on, the roots will be expressed by trigonometric
-forms. Otherwise nested surds are used. Default is \name{on}.
-\end{Switch}
-
-
-\begin{Switch}{TRINT}
-\index{integration}
-When \name{trint} is on, a narrative tracing various steps in the
-integration process is produced.
-
-\begin{Comments}
-%Use the \name{dribble} or \name{logfile} command to save this text to a file.
-The \nameref{out} command saves the results of the integration, but not the
-trace.
-\end{Comments}
-\end{Switch}
-
-\begin{Switch}{TRNONLNR}
-\index{solve}
-When \name{trnonlnr} is on, a narrative tracing various steps in
-the process for solving non-linear equations is produced.
-
-\begin{Comments}
-\name{trnonlnr} can only be used after the solve package has been loaded
-(e.g., by an explicit call of \nameref{load\_package}).  The \nameref{out}
-command saves the results of the equation solving, but not the trace.
-\end{Comments}
-\end{Switch}
-
-
-\begin{Switch}{VAROPT}
-\index{solve}
-When \name{varopt} is on, the sequence of variables is optimized by
-\nameref{solve} with respect to execution speed. Otherwise, the sequence
-given in the call to \nameref{solve} is preserved. Default is \name{on}.
-
-In combination with the switch \nameref{arbvars}, \name{varopt} can be used
-to control variable elimination.
-
-\begin{Examples}
-off arbvars; \\
-solve({x+2z,x-3y},{x,y,z});				&
-		   \{\{y=\rfrac{x}{3},z= - \rfrac{x}{2}\}\} \\
-solve({x*y=1,z=x},{x,y,z});				&
-		   \{\{z=x,y=\rfrac{1}{x}\}\} \\
-off varopt; \\
-solve({x+2z,x-3y},{x,y,z});				&
-		   \{\{x= - 2*z,y= - \rfrac{2*z}{3}\}\} \\
-solve({x*y=1,z=x},{x,y,z});				&
-		   \{\{y=\rfrac{1}{z},x=z\}\} \\
-\end{Examples}
-\end{Switch}
-
+\section{General Switches}
+
+\begin{Introduction}{SWITCHES}
+Switches are set on or off using the commands \nameref{on} or
+\nameref{off}, respectively.
+The default setting of the switches described in this section is
+\nameref{off} unless stated otherwise. 
+\end{Introduction}
+
+\begin{Switch}{ALGINT}
+\index{integration}
+When the \name{algint} switch is on, the algebraic integration module (which
+must be loaded from the REDUCE library) is used for integration.
+
+\begin{Comments}
+Loading \name{algint} from the library automatically turns on the
+\name{algint} switch.  An error message will be given if \name{algint} is
+turned on when the \name{algint} has not been loaded from the library.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{ALLBRANCH}
+When \name{allbranch} is on, the operator \nameref{solve} selects all 
+branches of solutions. 
+When \name{allbranch} is off, it selects only the principal
+branches.  Default is \name{on}.
+
+\begin{Examples}
+
+solve(log(sin(x+3)),x);    &
+\begin{multilineoutput}{6cm}
+\{X=2*ARBINT(1)*PI - ASIN(1) - 3,
+ X=2*ARBINT(1)*PI + ASIN(1) + PI - 3\}
+\end{multilineoutput}\\
+off allbranch; \\
+solve(log(sin(x+3)),x);    &
+                 {X=ASIN(1) - 3}
+\end{Examples}
+
+\begin{Comments}
+\nameref{arbint}(1) indicates an arbitrary integer, which is given a
+unique identifier by REDUCE, showing that there are infinitely many
+solutions of this type.  When \name{allbranch} is off, the single
+canonical solution is given.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{ALLFAC}
+\index{output}
+The \name{allfac} switch, when on, causes REDUCE to factor out automatically
+common products in the output of expressions.  Default is \name{on}.
+
+\begin{Examples}
+x + x*y**3 + x**2*cos(z);  &      X*(COS(Z)*X + Y^{3}  + 1) \\
+off allfac; \\
+x + x*y**3 + x**2*cos(z);  &      COS(Z)*X^{2} + X*Y^{3}  + X
+\end{Examples}
+
+\begin{Comments}
+The \name{allfac} switch has no effect when \name{pri} is off.  Although the
+switch setting stays as it was, printing behavior is as if it were off.
+\end{Comments}
+\end{Switch}
+
+
+% \begin{Switch}{ALLPREC}
+%
+% \end{Switch}
+%
+%
+\begin{Switch}{ARBVARS}
+\index{solve}
+When \name{arbvars} is on, the solutions of singular or underdetermined
+systems of equations are presented in terms of arbitrary complex variables
+(see \nameref{arbcomplex}). Otherwise, the solution is parametrized in
+terms of some of the input variables. Default is \name{on}.
+
+\begin{Examples}
+solve({2x + y,4x + 2y},{x,y});                          &
+                   \{\{x= - \rfrac{arbcomplex(1)}{2},y=arbcomplex(1)\}\} \\
+solve({sqrt(x)+ y**3-1},{x,y});				&
+		   \{\{y=arbcomplex(2),x=y^6  - 2*y^3  + 1\}\} \\
+off arbvars; \\
+solve({2x + y,4x + 2y},{x,y});                          &
+                   \{\{x= - \rfrac{y}{2}\}\} \\
+solve({sqrt(x)+ y**3-1},{x,y});				&
+		   \{\{x=y^6  - 2*y^3  + 1\}\} \\
+\end{Examples}
+\begin{Comments}
+
+With \name{arbvars} off, the return value \name{\{\{\}\}} means that the
+equations given to \nameref{solve} imply no relation among the input
+variables.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{BALANCED\_MOD}
+\index{modular}
+\nameref{modular} numbers are normally produced in the range [0,...\meta{n}), 
+where
+\meta{n} is the current modulus.  With \name{balanced\_mod} on, the range
+[-\meta{n}/2,\meta{n}/2] is used instead.
+
+\begin{Examples}
+setmod 7; & 1 \\
+on modular; \\
+4; & 4 \\
+on balanced_mod; \\
+4; & -3
+\end{Examples}
+\end{Switch}
+
+
+\begin{Switch}{BFSPACE}
+\index{output}\index{floating point}
+Floating point numbers are normally printed in a compact notation (either
+fixed point or in scientific notation if \nameref{SCIENTIFIC\_NOTATION}
+has been used).  In some (but not all) cases, it helps comprehensibility
+if spaces are inserted in the number at regular intervals.  The switch
+\name{bfspace}, if on, will cause a blank to be inserted in the number after
+every five characters.
+\begin{Examples}
+on rounded; \\
+1.2345678;  & 1.2345678 \\
+on bfspace; \\
+1.2345678;  & 1.234 5678
+\end{Examples}
+\begin{Comments}
+\name{bfspace} is normally off.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{COMBINEEXPT}
+\index{exponent simplification}
+REDUCE is in general poor at surd simplification.  However, when the
+switch \name{combineexpt} is on, the system attempts to combine
+exponentials whenever possible.
+\begin{TEX}
+\begin{Examples}
+3^(1/2)*3^(1/3)*3^(1/6); & SQRT(3)*3^{\rfrac{1}{3}}*3^{\rfrac{1}{6}} \\
+on combineexpt; \\
+ws; & 1
+\end{Examples}
+\end{TEX}
+\begin{INFO}
+{\begin{Examples}
+3^(1/2)*3^(1/3)*3^(1/6); & SQRT(3)*3^{1/3}*3^{1/6} \\
+on combineexpt; \\
+ws; & 1
+\end{Examples}}
+\end{INFO}
+
+\end{Switch}
+
+
+\begin{Switch}{COMBINELOGS}
+\index{logarithm}
+In many cases it is desirable to expand product arguments of logarithms,
+or collect a sum of logarithms into a single logarithm.  Since these are
+inverse operations, it is not possible to provide rules for doing both at
+the same time and preserve the REDUCE concept of idempotent evaluation.
+As an alternative, REDUCE provides two switches \nameref{expandlogs} and
+\name{combinelogs} to carry out these operations.
+\begin{Examples}
+on expandlogs; \\
+log(x*y); & LOG(X) + LOG(Y) \\
+on combinelogs; \\
+ws; & LOG(X*Y)
+\end{Examples}
+
+\begin{Comments}
+At the present time, it is possible to have both switches on at once,
+which could lead to infinite recursion.  However, an expression is
+switched from one form to the other in this case.  Users should not rely
+on this behavior, since it may change in the next release.
+\end{Comments}
+
+\end{Switch}
+
+
+\begin{Switch}{COMP}
+\index{compiler}
+When \name{comp} is on, any succeeding function definitions are compiled
+into a faster-running form.  Default is \name{off}.
+
+\begin{Examples}
+\explanation{The following procedure finds Fibonacci numbers recursively.
+Create a new file ``refib" in your current directory with the following
+lines in it:} \\[6mm]
+\begin{multilineinput}
+procedure refib(n);
+   if fixp n and n >= 0 then
+     if n <= 1 then 1
+       else refib(n-1) + refib(n-2)
+    else rederr "nonnegative integer only";
+
+end;
+\end{multilineinput}\\
+\explanation{Now load REDUCE and run the following:}\\
+on time;                     &             Time: 100 ms \\
+
+in "refib"$                  &             Time: 0 ms \\
+
+                             &              REFIB \\
+
+                             &              Time: 260 ms \\
+
+                             &              Time: 20 ms \\
+
+refib(80);                   &             37889062373143906 \\
+
+                             &              Time: 14840 ms \\
+
+on comp;                     &             Time: 80 ms \\
+
+in "refib"$                  &             Time: 20 ms \\
+
+                             &              REFIB \\
+
+                              &             Time: 640 ms \\
+
+refib(80);                   &             37889062373143906 \\
+
+                               &            Time: 10940 ms
+\end{Examples}
+\begin{Comments}
+Note that the compiled procedure runs faster.  Your time messages will
+differ depending upon which system you have.  Compiled functions remain so
+for the duration of the REDUCE session, and are then lost.  They must be
+recompiled if wanted in another session.  With the switch \nameref{time} on
+as shown above, the CPU time used in executing the command is returned in
+milliseconds.  Be careful not to leave \name{comp} on unless you want it,
+as it makes the processing of procedures much slower.
+
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{COMPLEX}
+\index{complex}
+When the \name{complex} switch is on, full complex arithmetic is used in
+simplification, function evaluation, and factorization.  Default is \name{off}.
+
+\begin{Examples}
+
+factorize(a**2 + b**2);      &    \{A^{2}  + B^{2} \} \\
+on complex; \\
+
+factorize(a**2 + b**2);      &    \{A - I*B,A + I*B\} \\
+
+(x**2 + y**2)/(x + i*y);     &    X - I*Y \\
+
+on rounded;             &
+
+    *** Domain mode COMPLEX changed to COMPLEX\_FLOAT \\
+
+sqrt(-17);                   &    4.12310562562*I \\
+
+log(7*i);                    &    1.94591014906 + 1.57079632679*I
+\end{Examples}
+
+\begin{Comments}
+Complex floating-point can be done by turning on \nameref{rounded} in
+addition to \name{complex}.  With \name{complex} off however, REDUCE knows
+that \IFTEX{$i$}{i} is the square root of \IFTEX{$-1$}{-1} but will not
+carry out more complicated complex operations.  If you want complex
+denominators cleared by multiplication by their conjugates, turn on the
+switch \nameref{rationalize}.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{CREF}
+\index{cross reference}
+The switch \name{cref} invokes the CREF cross-reference program that
+processes a set of procedure definitions to produce a summary of their
+entry points, undefined procedures, non-local variables and so on.  The
+program will also check that procedures are called with a consistent
+number of arguments, and print a diagnostic message otherwise.
+
+The output is alphabetized on the first seven characters of each function
+name.
+
+To invoke the cross-reference program, \name{cref} is first turned on.
+This causes the program to load and the cross-referencing process to
+begin.  After all the required definitions are loaded, turning \name{cref}
+off will cause a cross-reference listing to be produced.
+
+\begin{Comments}
+
+Algebraic procedures in REDUCE are treated as if they were symbolic, so
+that algebraic constructs will actually appear as calls to symbolic
+functions, such as \name{aeval}.
+\end{Comments}
+
+\end{Switch}
+
+
+\begin{Switch}{CRAMER}
+\index{matrix}\index{linear system}\index{solve}
+When the \name{cramer} switch is on, \nameref{matrix} inversion 
+and linear equation
+solving (operator \nameref{solve}) is done by Cramer's rule, through exterior
+multiplication. Default is \name{off}.
+
+\begin{Examples}
+on time;                     &             Time: 80 ms \\
+off output;                  &             Time: 100 ms \\[4mm]
+\begin{multilineinput}
+mm := mat((a,b,c,d,f),(a,a,c,f,b),(b,c,a,c,d), (c,c,a,b,f),
+          (d,a,d,e,f));
+\end{multilineinput} &             Time: 300 ms \\
+inverse := 1/mm;             &             Time: 18460 ms \\
+on cramer;                   &             Time: 80 ms \\
+cramersinv := 1/mm;          &             Time: 9260 ms
+\end{Examples}
+
+\begin{Comments}
+Your time readings will vary depending on the REDUCE version you use.
+After you invert the matrix, turn on \nameref{output} and ask for one of
+the elements of the inverse matrix, such as \name{cramersinv(3,2)}, so that
+you can see the size of the expressions produced.
+
+Inversion of matrices and the solution of linear equations with dense
+symbolic entries in many variables is generally considerably faster with
+\name{cramer} on.  However, inversion of numeric-valued matrices is
+slower.  Consider the matrices you're inverting before deciding whether to
+turn \name{cramer} on or off.  A substantial portion of the time in matrix
+inversion is given to formatting the results for printing.  To save this
+time, turn \name{output} off, as shown in this example or terminate the
+expression with a dollar sign instead of a semicolon.  The results are
+still available to you in the workspace associated with your prompt
+number, or you can assign them to an identifier for further use.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{DEFN}
+\index{lisp}
+When the switch \name{defn} is on, the Standard Lisp equivalent of the
+input statement or procedure is printed, but not evaluated.  Default is
+\name{off}.
+
+\begin{Examples}
+
+on defn; \\
+
+17/3;                        &         (AEVAL (LIST 'QUOTIENT 17 3)) \\
+
+df(sin(x),x,2);          
+         &         (AEVAL (LIST 'DF (LIST 'SIN 'X) 'X 2)) \\
+\begin{multilineinput}
+procedure coshval(a);
+   begin scalar g;
+      g := (exp(a) + exp(-a))/2;
+      return g
+   end;
+\end{multilineinput} &
+\begin{multilineoutput}{7cm}
+(AEVAL 
+  (PROGN 
+    (FLAG '(COSHVAL) 'OPFN) 
+    (DE COSHVAL (A) 
+      (PROG (G) 
+        (SETQ G 
+          (AEVAL 
+             (LIST 
+                'QUOTIENT 
+                (LIST 
+                   'PLUS 
+                   (LIST 'EXP A) 
+                   (LIST 'EXP (LIST 'MINUS A))) 
+                2))) 
+       (RETURN G)))) ) 
+\end{multilineoutput} \\
+
+coshval(1);                 &       (AEVAL (LIST 'COSHVAL 1)) \\
+
+off defn; \\
+
+coshval(1);                 &   Declare COSHVAL operator? (Y or N) \\
+
+n \\
+\begin{multilineinput}
+procedure coshval(a);
+   begin scalar g;
+      g := (exp(a) + exp(-a))/2;
+      return g
+   end;
+\end{multilineinput} &       COSHVAL \\
+
+on rounded; \\
+
+coshval(1);                 &       1.54308063482
+\end{Examples}
+
+\begin{Comments}
+The above function \name{coshval} finds the hyperbolic cosine (cosh) of its
+argument.  When \name{defn} is on, you can see the Standard Lisp equivalent
+of the function, but it is not entered into the system as shown by the
+message \name{Declare COSHVAL operator?}.  It must be reentered with
+\name{defn} off to be recognized.  This procedure is used as an example; a
+more efficient procedure would eliminate the unnecessary local variable
+with
+\begin{verbatim}
+      procedure coshval(a);
+         (exp(a) + exp(-a))/2;
+\end{verbatim}
+
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{DEMO}
+\index{interactive}\index{output}
+The \name{demo} switch is used for interactive files, causing the system
+to pause after each command in the file until you type a \key{Return}.
+Default is \name{off}.
+
+\begin{Comments}
+The switch \name{demo} has no effect on top level interactive
+statements.  Use it when you want to slow down operations in a file so
+you can see what is happening.
+
+You can either include the \name{on demo} command in the file, or enter
+it from the top level before bringing in any file.  Unlike the
+\nameref{pause} command, \name{on demo} does not permit you to interrupt
+the file for questions of your own.
+
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{DFPRINT}
+\index{output}\index{derivative}
+When \name{dfprint} is on, expressions in the differentiation operator
+\nameref{df} are printed in a more ``natural'' notation, with the
+differentiation variables appearing as subscripts.  In addition, if the
+switch \nameref{noarg} is on (the default), the arguments of the
+differentiated operator are suppressed.
+
+\begin{Examples}
+operator f; \\
+df(f x,x); & DF(F(X),X); \\
+on dfprint; \\
+ws;  & F_{X} \\
+df(f(x,y),x,y); & F_{X}_{,}_{Y} \\
+off noarg; \\
+ws; & F(X,Y)_{X}
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{DIV}
+\index{output}
+When \name{div} is on, the system divides any simple factors found in
+the denominator of an expression into the numerator.  Default is \name{off}.
+
+\begin{Examples}
+
+on div; \\
+
+a := x**2/y**2;             &      A := X^{2} *Y^{-2} \\
+
+b := a/(3*z);               &      B := \rfrac{1}{3}*X^{2} *Y^{-2}  *Z^{-1} \\
+
+off div; \\
+
+a;                           &    \rfrac{X^{2}}{Y^{2}}\\
+
+b;                           &   \rfrac{X^{2}}{3*Y^{2} *Z}
+                                       
+\end{Examples}
+
+\begin{Comments}
+The \name{div} switch only has effect when the \nameref{pri} switch is on.
+When \name{pri} is off, regardless of the setting of \name{div}, the
+printing behavior is as if \name{div} were off.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{ECHO}
+\index{output}
+The \name{echo} switch is normally off for top-level entry, and on when files
+are brought in.  If \name{echo} is turned on at the top level, your input
+statements are echoed to the screen (thus appearing twice).  Default
+\name{off} (but note default \name{on} for files).
+
+\begin{Comments}
+If you want to display certain portions of a file and not others, use the
+commands \name{off echo} and \name{on echo} inside the file.  If you want
+no display of the file, use the input command
+
+	\name{in} {\em filename}\name{\$}
+
+rather than using the semicolon delimiter.
+
+Be careful when you use commands within a file to generate another file.
+Since \name{echo} is on for files, the output file echoes input statements
+(unlike its behavior from the top level).  You should explicitly turn off
+\name{echo} when writing output, and turn it back on when you're done.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{ERRCONT}
+\index{error handling}
+When the \name{errcont} switch is on, error conditions do not stop file
+execution.  Error messages will be printed whether \name{errcont} is on or
+off.
+
+Default is \name{off}.
+
+\begin{Comments}
+\begin{TEX}
+The table below shows REDUCE behavior under the settings of \name{errcont} and
+\name{int} :
+
+  \begin{center}
+  \begin{tabular}{|l|l|p{9.5cm}|}
+\hline
+\multicolumn{3}{|c|}{Behavior in Case of Error in Files}\\
+\hline
+\multicolumn{1}{|c|}{errcont} &
+  \multicolumn{1}{c|}{int} &
+    \multicolumn{1}{c|}{Behavior when errors in files are encountered}\\
+\hline
+off & off &
+Message is printed and parsing continues, but no further statements are 
+executed; no commands from keyboard accepted except \verb|bye| or
+\verb|end| \\
+off & on &
+Message is printed, and you are asked if you wish to continue.  (This is the
+default behavior) \\
+on & off &
+Message is printed, and file continues to execute without pause \\
+on & on &
+Message is printed, and file continues to execute without pause\\
+\hline
+  \end{tabular}
+  \end{center}
+\end{TEX}
+\begin{INFO}
+The following describes what happens when an error occurs in a file under
+each setting of \name{errcont} and \name{int}:
+
+Both off:  Message is printed and parsing continues, but no further
+statements are executed; no commands from keyboard accepted except bye or
+end;
+
+\name{errcont} off, \name{int} on:  Message is printed, and you are asked
+if you wish to continue. (This is the default behavior);
+
+\name{errcont} on, \name{int} off:  Message is printed, and file continues
+to execute without pause;
+
+Both on: Message is printed, and file continues to execute without pause.
+\end{INFO}
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{EVALLHSEQP}
+\index{equation}
+Under normal circumstances, the right-hand-side of an \nameref{equation}
+is evaluated but not the left-hand-side.  This also applies to any
+substitutions made by the \nameref{sub} operator.  If both sides are to be
+evaluated, the switch \name{evallhseqp} should be turned on.
+
+\end{Switch}
+
+
+\begin{Switch}{EXP}
+\index{simplification}
+When the \name{exp} switch is on, powers and products of expressions are
+expanded.  Default is \name{on}.
+
+\begin{Examples}
+(x+1)**3;                    &     X^{3} + 3*X^{2} + 3*X + 1 \\
+(a + b*i)*(c + d*i);         &     A*C + A*D*I + B*C*I - B*D \\
+off exp; \\
+(x+1)**3;                    &     (X + 1)^{3} \\
+(a + b*i)*(c + d*i);         &       (A + B*I)*(C + D*I) \\
+length((x+1)**2/(y+1));      &     2
+\end{Examples}
+
+\begin{Comments}
+Note that REDUCE knows that \IFTEX{$i^2 = -1$}{i^2 = -1}.
+When \name{exp} is off, equivalent expressions may not simplify to the same
+form, although zero expressions still simplify to zero.  Several operators
+that expect a polynomial argument behave differently when \name{exp} is
+off, such as \nameref{length}.  Be cautious about leaving \name{exp} off.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{EXPANDLOGS}
+\index{logarithm}
+In many cases it is desirable to expand product arguments of logarithms,
+or collect a sum of logarithms into a single logarithm.  Since these are
+inverse operations, it is not possible to provide rules for doing both at
+the same time and preserve the REDUCE concept of idempotent evaluation.
+As an alternative, REDUCE provides two switches \name{expandlogs} and
+\nameref{combinelogs} to carry out these operations.  Both are off by default.
+\begin{Examples}
+on expandlogs; \\
+log(x*y); & LOG(X) + LOG(Y) \\
+on combinelogs; \\
+ws; & LOG(X*Y)
+\end{Examples}
+
+\begin{Comments}
+At the present time, it is possible to have both switches on at once,
+which could lead to infinite recursion.  However, an expression is
+switched from one form to the other in this case.  Users should not rely
+on this behavior, since it may change in the next release.
+\end{Comments}
+
+\end{Switch}
+
+
+\begin{Switch}{EZGCD}
+\index{greatest common divisor}\index{polynomial}
+When \name{ezgcd} and \nameref{gcd} are on, greatest common divisors are
+computed using the EZ GCD algorithm that uses modular arithmetic (and is
+usually faster).  Default is \name{off}.
+
+\begin{Comments}
+As a side effect of the gcd calculation, the expressions involved are
+factored, though not the heavy-duty factoring of \nameref{factorize}. The
+EZ GCD algorithm was introduced in a paper by J. Moses and D.Y.Y. Yun in
+\meta{Proceedings of the ACM}, 1973, pp. 159-166.
+
+Note that the \nameref{gcd} switch must also be on for \name{ezgcd} to have
+effect.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{FACTOR}
+\index{output}
+When the \name{factor} switch is on, input expressions and results are
+automatically factored.
+
+\begin{Examples}
+
+on factor; \\
+
+aa := 3*x**3*a + 6*x**2*y*a + 3*x**3*b + 6*x**2*y*b\\
++ x*y*a + 2*y**2*a + x*y*b + 2*y**2*b;
+			     &     AA := (A + B)*(3*X^{2} + Y)*(X + 2*Y) \\
+off factor; \\
+aa;                          &
+     3*A*X^{3} + 6*A*X^{2}*Y + A*X*Y + 2*A*Y^{2}  + 3*B*X^{3} + 6*B*X^{2}*Y\\
++ B*X*Y + 2*B*Y^{2} \\
+on factor; \\
+ab := x**2 - 2;              &     AB := X^{2} - 2
+\end{Examples}
+
+\begin{Comments}
+REDUCE factors univariate and multivariate polynomials with 
+integer coefficients, finding any factors that also have integer coefficients.
+The factoring is done by reducing multivariate problems to univariate
+ones  with symbolic coefficients, and then solving the univariate ones modulo 
+small primes.  The results of these calculations are merged to
+determine the factors of the original polynomial.  The factorizer normally
+selects evaluation points and primes using a random number generator.  
+Thus, the detailed factoring behavior may be different each time any
+particular problem is tackled.
+
+When the \name{factor} switch is turned on, the \nameref{exp} switch is
+turned off, and when the \name{factor} switch is turned off, the
+\nameref{exp} switch is turned on, whether it was on previously or not.
+
+When the switch \nameref{trfac} is on, informative messages are generated at
+each call to the factorizer.  The \nameref{trallfac} switch causes the
+production of a more verbose trace message.  It takes precedence over
+\name{trfac} if they are both on.
+
+To factor a polynomial explicitly and store the results, use the operator 
+\nameref{factorize}.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{FAILHARD}
+\index{integration}
+When the \name{failhard} switch is on, the integration operator \nameref{int} 
+terminates with an error message if the integral cannot be done in closed 
+terms.
+Default is off.
+
+\begin{Comments}
+Use the \name{failhard} switch when you are dealing with complicated integrals
+and want to know immediately if REDUCE was unable to handle them.  The
+integration operator sometimes returns a formal integration form that is
+more complicated than the original expression, when it is unable to
+complete the integration.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{FORT}
+\index{FORTRAN}
+When \name{fort} is on, output is given Fortran-compatible syntax.  Default
+is \name{off}.
+
+\begin{Examples}
+on fort; \\
+df(sin(7*x + y),x);          &     ANS=7.*COS(7*X+Y) \\
+on rounded; \\
+b := log(sin(pi/5 + n*pi));  &
+	       B=LOG(SIN(3.14159265359*N+0.628318530718))
+\end{Examples}
+
+\begin{Comments}
+REDUCE results can be written to a file (using \nameref{out}) and used as data
+by Fortran programs when \name{fort} is in effect.  \name{fort} knows about
+correct statement length, continuation characters, defining a symbol when 
+it is first used, and other Fortran details.
+
+The \nameref{GENTRAN} package offers many more possibilities than the
+\name{fort} switch.  It produces Fortran (or C or Ratfor) code from REDUCE
+procedures or structured specifications, including facilities for producing
+double precision output.
+\end{Comments}
+\end{Switch}
+
+\begin{Switch}{FORTUPPER}
+\index{FORTRAN}
+When \name{fortupper} is on, any Fortran-style output appears in upper case.
+Default is \name{off}.
+
+\begin{Examples}
+on fort; \\
+df(sin(7*x + y),x);          &     ans=7.*cos(7*x+y) \\
+on fortupper; \\
+df(sin(7*x + y),x);          &     ANS=7.*COS(7*X+Y) \\
+\end{Examples}
+\end{Switch}
+
+
+\begin{Switch}{FULLPREC}
+\index{precision}\index{rounded}
+Trailing zeroes of rounded numbers to the full system precision are
+normally not printed.  If this information is needed, for example to get a
+more understandable indication of the accuracy of certain data, the switch
+\name{fullprec} can be turned on.
+
+\begin{Examples}
+on rounded; \\
+1/2;  & 0.5 \\
+on fullprec; \\
+ws; & 0.500000000000
+\end{Examples}
+
+\begin{Comments}
+This is just an output options which neither influences
+the accuracy of the computation nor does it give additional
+information about the precision of the results.
+See also \nameref{scientific_notation}.
+\end{Comments}
+\end{Switch}
+
+\begin{Switch}{FULLROOTS}
+\index{solve}\index{polynomial}
+Since roots of cubic and quartic polynomials can often be very
+messy, a switch \name{fullroots} controls the production
+of results in closed form. \nameref{solve} will apply the
+formulas for explicit forms for degrees 3 and 4 only if
+\name{fullroots} is \name{on}. Otherwise the result forms
+are built using \nameref{root\_of}. Default is \name{off}.
+\end{Switch}
+
+\begin{Switch}{GC}
+\index{memory}
+With the \name{gc} switch, you can turn the garbage collection messages on
+or off.  The form of the message depends on the particular Lisp used for
+the REDUCE implementation.
+
+\begin{Comments}
+See \nameref{reclaim} for an explanation of garbage collection.  REDUCE does
+garbage collection when needed even if you have turned the notices off.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{GCD}
+\index{greatest common divisor}\index{rational expression}
+When \name{gcd} is on, common factors in numerators and denominators of
+expressions are canceled.  Default is \name{off}.
+
+\begin{Examples}
+\begin{multilineinput}
+
+(2*(f*h)**2 - f**2*g*h - (f*g)**2 - f*h**3 + f*h*g**2
+   - h**4 + g*h**3)/(f**2*h - f**2*g - f*h**2 + 2*f*g*h
+   - f*g**2 - g*h**2 + g**2*h);
+\end{multilineinput}         &
+\rfrac{F^{2}*G^{2} + F^{2}*G*H - 2*F^{2}*H^{2} - F*G^{2}*H + F*H^{3} - G*H^{3} +
+ H^{4}}
+       {F^{2}*G - F^{2}*H + F*G^{2} - 2*F*G*H + F*H^{2} - G^{2}*H + G*H^{2}} \\
+on gcd; \\
+ws;                          &       \rfrac{F*G + 2*F*H + H^{2}}{F + G} \\
+e2 := a*c + a*d + b*c + b*d; &      E2 := A*C + A*D + B*C + B*D \\
+off exp;  \\
+e2;                          &      (A + B)*(C + D)
+\end{Examples}
+
+\begin{Comments}
+Even with \name{gcd} off, a check is automatically made for common variable
+and numerical products in the numerators and denominators of expression,
+and the appropriate cancellations made.  Thus the example demonstrating the
+use of \name{gcd} is somewhat complicated.  Note when \nameref{exp} is off,
+\name{gcd} has the side effect of factoring the expression.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{HORNER}
+\index{output}\index{polynomial}
+When the \name{horner} switch is on, polynomial expressions are printed
+in Horner's form for faster and safer numerical evaluation. Default
+is \name{off}. The leading variable of the expression is selected as
+Horner variable. To select the Horner variable explicitly use the 
+\nameref{korder} declaration.
+
+\begin{Examples}
+on horner;\\
+(13p-4q)^3;&
+( - 64)*q^3  + p*(624*q^2  + p*(( - 2028)*q + p*2197))\\
+korder q;\\
+ws;&
+2197*p^3  + q*(( - 2028)*p^2  + q*(624*p + q*(-64)))
+\end{Examples}
+\end{Switch}
+
+
+\begin{Switch}{IFACTOR}
+\index{integer}\index{factorize}
+When the \name{ifactor} switch is on, any integer terms appearing as a result
+of the \nameref{factorize} command are factored themselves into primes.  Default
+is \name{off}.  If the argument of \name{factorize} is an integer,
+\name{ifactor} has no effect, since the integer is always factored.
+
+\begin{Examples}
+factorize(4*x**2 + 28*x + 48);      &    \{4,X + 3,X + 4\} \\
+factorize(22587);                   &    \{3,7529\} \\
+on ifactor; \\
+factorize(4*x**2 + 28*x + 48);      &    \{2,2,X + 4,X + 3\} \\
+factorize(22587);                   &    \{3,7529\}
+\end{Examples}
+
+\begin{Comments}
+Constant terms that appear within nonconstant
+polynomial factors are not factored.
+
+The \name{ifactor} switch affects only factoring done specifically
+with \nameref{factorize}, not on factoring done automatically when the
+\nameref{factor} switch is on.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{INT}
+\index{interactive}
+The \name{int} switch specifies an interactive mode of operation.  Default
+\name{on}.
+
+\begin{Comments}
+There is no reason to turn \name{int} off during interactive calculations,
+since there are no benefits to be gained.  If you do have \name{int} off
+while inputting a file, and REDUCE finds an error, it prints the message
+``Continuing with parsing only."  In this state, REDUCE accepts only
+\nameref{end}\name{;} or \nameref{bye}\name{;} from the keyboard;
+everything else is ignored, even the command \name{on int}.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{INTSTR}
+\index{output}
+If \name{intstr} (for ``internal structure'') is on, arguments of an
+operator are printed in a more structured form.
+
+\begin{Examples}
+operator f; \\
+f(2x+2y); & F(2*X + 2*Y) \\
+on intstr; \\
+ws; & F(2*(X + Y))
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{LCM}
+\index{rational expression}
+The \name{lcm} switch instructs REDUCE to compute the least common multiple
+of denominators whenever rational expressions occur.  Default is \name{on}.
+
+\begin{Examples}
+off lcm; \\
+z := 1/(x**2 - y**2) + 1/(x-y)**2;  
+			     &     Z := \rfrac{2*X*(X - Y)}{X^{4} - 2*X^{3}*Y + 
+2*X*Y^{3} - Y^{4}} \\
+on lcm; \\
+z;                           &     \rfrac{2*X*(X - Y)}{X^{4} - 2*X^{3}*Y + 2*X*Y
+^{3} - Y^{4}} \\
+zz := 1/(x**2 - y**2) + 1/(x-y)**2;
+			     &     ZZ := \rfrac{2*X}{X^{3} - X^{2}*Y - X*Y^{2} +
+ Y^{3}} \\
+on gcd; \\
+z;                           &     \rfrac{2*X}{X^{3} - X^{2}*Y - X*Y^{2} + Y^{3}
+}
+\end{Examples}
+
+\begin{Comments}
+Note that \name{lcm} has effect only when rational expressions are first
+combined.  It does not examine existing structures for simplifications on
+display.  That is shown above when \IFTEX{$z$}{z} is entered with
+\name{lcm} off.  It remains unsimplified even after \name{lcm} is turned
+back on.  However, a new variable containing the same expression is
+simplified on entry.  The switch \nameref{gcd} does examine existing
+structures, as shown in the last example line above.
+
+Full greatest common divisor calculations become expensive if work with
+large rational expressions is required.  A considerable savings of time
+can be had if a full gcd check is made only when denominators are combined,
+and only a partial check for numerators.  This is the effect of the \name{lcm}
+switch.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{LESSSPACE}
+\index{output}
+You can turn on the switch \name{lessspace} if you want fewer
+blank lines in your output.
+\end{Switch}
+
+
+\begin{Switch}{LIMITEDFACTORS}
+\index{factorize}\index{polynomial}
+To get limited factorization in cases where it is too expensive to use
+full multivariate polynomial factorization, the switch
+\name{limitedfactors} can be turned on.  In that case, only ``inexpensive''
+factoring operations, such as square-free factorization, will be used
+when \nameref{factorize} is called.
+
+\begin{Examples}
+a := (y-x)^2*(y^3+2x*y+5)*(y^2-3x*y+7)$ \\
+factorize a; &
+\begin{multilineoutput}{7cm}
+\{ - X + Y,
+ X - Y,
+ 2*X*Y + Y^{3} + 5,
+ 3*X*Y - Y^{2} - 7\}
+\end{multilineoutput} \\
+on limitedfactors; \\
+factorize a; &
+\begin{multilineoutput}{7cm}
+\{ - X + Y,
+ X - Y,
+ 6*X^{2}*Y^{2} + 3*X*Y^{4} - 2*X*Y^{3} + X*Y - Y^{5} - 7*Y^{3} - 5*Y^{2} - 35\}
+\end{multilineoutput}
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{LIST}
+The \name{list} switch causes REDUCE to print each term in any sum on
+separate lines.
+
+\begin{Examples}
+x**2*(y**2 + 2*y) + x*(y**2 + z)/(2*a);
+			    &     \rfrac{X*(2*A*X*Y^{2} + 4*A*X*Y + Y^{2} +
+Z)}{2*A} \\
+on list; \\
+ws;                         &
+\begin{multilineoutput}{6cm}
+(X*(2*A*X*Y^{2}
+  + 4*A*X*Y
+  + Y^{2}
+  + Z))/(2*A)
+\end{multilineoutput}
+\end{Examples}
+\end{Switch}
+
+
+\begin{Switch}{LISTARGS}
+\index{list}\index{argument}\index{operator}
+If an operator other than those specifically defined for lists is given a
+single argument that is a list, then the result of this operation will be
+a list in which that operator is applied to each element of the list.
+This process can be inhibited globally by turning on the switch
+\name{listargs}.
+
+\begin{Examples}
+log {a,b,c}; & {LOG(A),LOG(B),LOG(C)} \\
+on listargs; \\
+log {a,b,c}; & LOG({A,B,C})
+\end{Examples}
+
+\begin{Comments}
+It is possible to inhibit such distribution for a specific operator by
+using the declaration \nameref{listargp}.  In addition, if an operator has
+more than one argument, no such distribution occurs, so \name{listargs}
+has no effect.
+\end{Comments}
+
+\end{Switch}
+
+
+\begin{Switch}{MCD}
+\index{rational expression}
+When \name{mcd} is on, sums and differences of rational expressions are put
+on a common denominator.  Default is \name{on}.
+
+\begin{Examples}
+a/(x+1) + b/5;               &         \rfrac{5*A + B*X + B}{5*(X + 1)} \\
+off mcd; \\
+a/(x+1) + b/5;               &        (X + 1)^{-1}*A + 1/5*B \\
+1/6 + 1/7;                   &        13/42
+\end{Examples}
+
+\begin{Comments}
+Even with \name{mcd} off, rational expressions involving only numbers are still
+put over a common denominator.  
+
+Turning \name{mcd} off is useful when explicit negative powers are needed,
+or if no greatest common divisor calculations are desired, or when
+differentiating complicated rational expressions.  Results when \name{mcd}
+is off are no longer in canonical form, and expressions equivalent to zero
+may not simplify to 0.  Some operations, such as factoring cannot be done
+while \name{mcd} is off.  This option should therefore be used with some
+caution.  Turning \name{mcd} off is most valuable in intermediate parts of
+a complicated calculation, and should be turned back on for the last stage.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{MODULAR}
+\index{modular}
+When \name{modular} is on, polynomial coefficients are reduced by the
+modulus set by \nameref{setmod}.  If no modulus has been set, \name{modular}
+has no effect.
+
+\begin{Examples}
+setmod 2;                    &          1 \\
+on modular;                             \\
+(x+y)**2;                    &          X^{2} + Y^{2} \\
+145*x**2 + 20*x**3 + 17 + 15*x*y;
+			     &          X^{2} + X*Y + 1
+\end{Examples}
+
+\begin{Comments}
+Modular operations are only conducted on the coefficients, not the
+exponents.  The modulus is not restricted to being prime.  When the modulus
+is prime, division by a number not relatively prime to the modulus results
+in a \meta{Zero divisor} error message.  When the modulus is a composite
+number, division by a power of the modulus results in an error message, but
+division by an integer which is a factor of the modulus does not.
+The representation of modular number can be influenced by 
+\nameref{balanced\_mod}.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{MSG}
+\index{output}
+When \name{msg} is off, the printing of warning messages is suppressed.  Error
+messages are still printed.
+
+\begin{Comments}
+Warning messages include those about redimensioning an \nameref{array} 
+or declaring an \nameref{operator} where one is expected.  
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{MULTIPLICITIES}
+\index{solve}
+When \nameref{solve} is applied to a set of equations with multiple roots,
+solution multiplicities are normally stored in the global variable
+\nameref{root\_multiplicities} rather than the solution list.  If you want
+the multiplicities explicitly displayed, the switch \name{multiplicities}
+should be turned on.  In this case, \name{root_multiplicities} has no value.
+
+\begin{Examples}
+solve(x^2=2x-1,x); & {X=1} \\
+root_multiplicities; & {2} \\
+on multiplicities; \\
+solve(x^2=2x-1,x); & {X=1,X=1} \\
+root_multiplicities; &
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{NAT}
+\index{output}
+When \name{nat} is on, output is printed to the screen in natural form, with
+raised exponents.  \name{nat} should be turned off when outputting expressions
+to a file for future input.  Default is \name{on}.
+
+\begin{Examples}
+(x + y)**3;                  &          X^{3} + 3*X^{2}*Y + 3*X*Y^{2} + Y^{3} \\
+off nat; \\
+(x + y)**3;                  &          X**3 + 3*X**2*Y + 3*X*Y**2 + Y**3\$ \\
+on fort; \\
+(x + y)**3;                  &          ANS=X**3+3.*X**2*Y+3.*X*Y**2+Y**3
+\end{Examples}
+\begin{Comments}
+With \name{nat} off, a dollar sign is printed at the end of each expression.
+An output file written with \name{nat} off is ready to be read into REDUCE
+using the command \nameref{in}.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{NERO}
+\index{output}
+When \name{nero} is on, zero assignments (such as matrix elements) are not
+printed.
+
+\begin{Examples}
+matrix a;
+a := mat((1,0),(0,1));       & \begin{multilineoutput}{6cm}
+A(1,1) := 1
+A(1,2) := 0
+A(2,1) := 0
+A(2,2) := 1
+\end{multilineoutput}\\
+on nero; \\
+a;                           &  \begin{multilineoutput}{6cm}
+MAT(1,1) := 1
+MAT(2,2) := 1
+\end{multilineoutput}\\
+a(1,2);                      & \explanationo{nothing is printed.} \\
+b := 0;                     &  \explanationo{nothing is printed.} \\
+off nero; \\
+b := 0;                     &          B := 0
+\end{Examples}
+\begin{Comments}
+\name{nero} is often used when dealing with large sparse matrices, to avoid
+being overloaded with zero assignments.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{NOARG}
+\index{output}\index{derivative}
+When \nameref{dfprint} is on, expressions in the differentiation operator
+\nameref{df} are printed in a more ``natural'' notation, with the
+differentiation variables appearing as subscripts.  When \name{noarg}
+is on (the default), the arguments of the differentiated operator are also
+suppressed.
+
+\begin{Examples}
+operator f; \\
+df(f x,x); & DF(F(X),X); \\
+on dfprint; \\
+ws;  & F_{X} \\
+off noarg; \\
+ws; & F(X)_{X}
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{NOLNR}
+\index{integration}
+When \name{nolnr} is on, the linear properties of the integration operator
+\nameref{int} are suppressed if the integral cannot be found in closed terms.
+
+\begin{Comments}
+REDUCE uses the linear properties of integration to attempt to break down
+an integral into manageable pieces.  If an integral cannot be found in
+closed terms, these pieces are returned.  When the \name{nolnr} switch is off,
+as many of the pieces as possible are integrated.  When it is on, if any piece
+fails, the rest of them remain unevaluated.
+\end{Comments}
+\end{Switch}
+
+
+%\begin{Switch}{NORNDBF}
+%
+%***** To be added *****
+%
+%\end{Switch}
+
+
+\begin{Switch}{NOSPLIT}
+\index{output}
+Under normal circumstances, the printing routines try to break an expression
+across lines at a natural point.  This is a fairly expensive process.  If
+you are not overly concerned about where the end-of-line breaks come, you
+can speed up the printing of expressions by turning off the switch
+\name{nosplit}.  This switch is normally on.
+
+\end{Switch}
+
+
+\begin{Switch}{NUMVAL}
+\index{rounded}
+With \nameref{rounded} on, elementary functions with numerical arguments
+will return a numerical answer where appropriate.  If you wish to inhibit
+this evaluation, \name{numval} should be turned off.  It is normally on.
+
+\begin{Examples}
+on rounded; \\
+cos 3.4; & - 0.966798192579 \\
+off numval; \\
+cos 3.4; & COS(3.4)
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{OUTPUT}
+\index{output}
+When \name{output} is off, no output is printed from any REDUCE calculation.
+The calculations have their usual effects other than printing.  Default is
+\name{on}.
+
+\begin{Comments}
+Turn output \name{off} if you do not wish to see output when executing
+large files, or to save the time REDUCE spends formatting large expressions
+for display.  Results are still available with \nameref{ws}, or in their
+assigned variables. 
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{OVERVIEW}
+\index{factorize}
+When \name{overview} is on, the amount of detail reported by the factorizer
+switches \nameref{trfac} and \nameref{trallfac} is reduced.
+
+\end{Switch}
+
+
+\begin{Switch}{PERIOD}
+\index{output}\index{integer}
+When \name{period} is on, periods are added after integers in
+Fortran-compatible output (when \nameref{fort} is on).  There is no effect
+when \name{fort} is off.  Default is \name{on}.
+\end{Switch}
+
+
+\begin{Switch}{PRECISE}
+\index{simplification}\index{square root}
+When the \name{precise} switch is on, simplification of roots of even
+powers returns absolute values, a more precise answer mathematically.
+Default is \name{on}.
+
+\begin{Examples}
+sqrt(x**2);                  &        X \\
+(x**2)**(1/4);               &        SQRT(X) \\
+on precise; \\
+sqrt(x**2);                  &        ABS(X) \\
+(x**2)**(1/4);               &        SQRT(ABS(X))
+\end{Examples}
+
+\begin{Comments}
+In many types of mathematical work, simplification of powers and surds can
+proceed by the fastest means of simplifying the exponents arithmetically.
+When it is important to you that the positive root be returned, turn
+\name{precise} on.  One situation where this is important is when graphing
+square-root expressions such as \IFTEX{$\sqrt{x^2+y^2}$}{sqrt(x^2+y^2)} to
+avoid a spike caused by REDUCE simplifying
+\IFTEX{$\sqrt{y^2}$}{sqrt(y^2)} to \IFTEX{$y$}{y} when \IFTEX{$x$}{x} is
+zero.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{PRET}
+\index{output}
+When \name{pret} is on, input is printed in standard REDUCE format and then
+evaluated.
+
+\begin{Examples}
+on pret; \\
+ (x+1)^3;                     &
+\begin{multilineoutput}{6cm}
+ (x + 1)**3;
+X^{3} + 3*X^{2} + 3*X + 1
+\end{multilineoutput} \\
+\begin{multilineinput}
+
+procedure fac(n);
+   if not (fixp(n) and n>=0)
+     then rederr "Choose nonneg. integer only"
+    else for i := 0:n-1 product i+1;
+\end{multilineinput}     &
+\begin{multilineoutput}{8cm}
+procedure fac n;
+   if not (fixp n and n>=0)
+     then rederr "Choose nonneg. integer only"
+    else for i := 0:n - 1 product i + 1;
+
+FAC
+\end{multilineoutput}\\
+
+fac 5;                    & \begin{multilineoutput}{6cm}
+fac 5;
+120
+\end{multilineoutput}
+
+\end{Examples}
+
+\begin{Comments}
+Note that all input is converted to lower case except strings (which keep
+the same case) all operators with a single argument have had the
+parentheses removed, and all infix operators have had a space added on each
+side.  In addition, syntactical constructs like
+\name{if}\ldots\name{then}\ldots\name{else} are printed in a standard format.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{PRI}
+\index{output}
+When \name{pri} is on, the declarations \nameref{order} and \nameref{factor} can
+be used, and the switches \nameref{allfac}, \nameref{div}, \nameref{rat}, 
+and \nameref{revpri} take effect when they are on.  Default is \name{on}.
+
+\begin{Comments}
+Printing of expressions is faster with \name{pri} off.  The expressions are
+then returned in one standard form, without any of the display options that
+can be used to feature or display various parts of the expression.  You can
+also gain insight into REDUCE's representation of expressions with
+\name{pri} off.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{RAISE}
+\index{input}\index{character}
+When \name{raise} is on, lower case letters are automatically converted to
+upper case on input.  \name{raise} is normally on.
+
+\begin{Comments}
+This conversion affects the internal representation of the letter, and is
+independent of the case with which a letter is printed, which is normally
+lower case.
+\end{Comments}
+
+\end{Switch}
+
+
+\begin{Switch}{RAT}
+\index{output}
+When the \name{rat} switch is on, and kernels have been selected to display
+with the \nameref{factor} declaration, the denominator is printed with each
+term rather than one common denominator at the end of an expression.
+
+\begin{Examples}
+(x+1)/x + x**2/sin y;        
+          &     \rfrac{SIN(Y)*X + SIN(Y) + X^{3}}{SIN(Y)*X} \
+\
+factor x; \\
+(x+1)/x + x**2/sin y;        
+          &     \rfrac{X^{3} + X*SIN(Y) + SIN(Y)}{X*SIN(Y)} \
+\
+on rat;  \\
+(x+1)/x + x**2/sin y;       
+          &     \rfrac{X^{2}}{SIN(Y)} + 1 + X^{-1}
+\end{Examples}
+
+\begin{Comments}
+The \name{rat} switch only has effect when the \nameref{pri} switch is on.
+When \name{pri} is off, regardless of the setting of \name{rat}, the
+printing behavior is as if \name{rat} were off.  \name{rat} only has
+effect upon the display of expressions, not their internal form.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{RATARG}
+\index{rational expression}\index{polynomial}
+When \name{ratarg} is on, rational expressions can be given to operators
+such as \nameref{coeff} and \nameref{lterm} that normally require
+polynomials in one of their arguments.  When \name{ratarg} is off, rational
+expressions cause an error message.
+
+\begin{Examples}
+aa := x/y**2 + 1/x + y/x**2; 
+    &    AA := \rfrac{X^{3} + X*Y^{2} + Y^{3}}{X^{2}*Y^{2}} \\
+coeff(aa,x);                 &
+   ***** \rfrac{X^{3} + X*Y^{2} + Y^{3}}{X^{2}*Y^{2}} invalid as POLYNOMIAL\\
+on ratarg; \\
+coeff(aa,x);                
+    & \{\rfrac{Y}{X^{2}},\rfrac{1}{X^{2}},0,\rfrac{1}{X^{2}*Y^{2}}\}
+\end{Examples}
+\end{Switch}
+
+
+\begin{Switch}{RATIONAL}
+\index{rational expression}\index{polynomial}
+When \name{rational} is on, polynomial expressions with rational coefficients
+are produced.
+
+\begin{Examples}
+x/2 + 3*y/4;                 &       \rfrac{2*X + 3*Y}{4} \\
+(x**2 + 5*x + 17)/2;         &       \rfrac{X^{2} + 5*X + 17}{2} \\
+on rational; \\
+x/2 + 3y/4;                  &       \rfrac{1}{2}*(X + \rfrac{3}{2}*Y) \\
+(x**2 + 5*x + 17)/2;         &       \rfrac{1}{2}*(X^{2} + 5*X + 17)
+\end{Examples}
+
+\begin{Comments}
+By using \name{rational}, polynomial expressions with rational
+coefficients can be used in some commands that expect polynomials.  With
+\name{rational} off, such a polynomial becomes a rational expression, with
+denominator the least common multiple of the denominators of the rational
+number coefficients.  % The \nameref{factorize} command does not accept
+% polynomials with rational coefficients.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{RATIONALIZE}
+\index{rational expression}\index{simplification}\index{complex}
+When the \name{rationalize} switch is on, denominators of rational expressions
+that contain complex numbers or root expressions are simplified by 
+multiplication by their conjugates.
+
+\begin{Examples}
+qq := (1+sqrt(3))/(sqrt(3)-7);  &   QQ := \rfrac{SQRT(3) + 1}{SQRT(3) - 7} \\
+on rationalize; \\
+qq;                             &   \rfrac{- 4*SQRT(3) - 5}{23} \\
+2/(4 + 6**(1/3));               &     \rfrac{6^{2/3} - 4*6^{1/3} + 16}{35} \\
+(i-1)/(i+3);                    &   \rfrac{2*I - 1}{5} \\
+off rationalize; \\
+(i-1)/(i+3);                    &   \rfrac{I - 1}{I + 3}
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{RATPRI}
+\index{output}\index{rational expression}
+When the \name{ratpri} switch is on, rational expressions and fractions are
+printed as two lines separated by a fraction bar, rather than in a linear
+style.  Default is \name{on}.
+
+\begin{Examples}
+3/17;                        &            \rfrac{3}{17} \\
+2/b + 3/y;                   &            \rfrac{3*B + 2*Y}{B*Y} \\
+off ratpri; \\
+3/17;                        &            3/17 \\
+2/b + 3/y;                   &            (3*B + 2*Y)/(B*Y)
+\end{Examples}
+\end{Switch}
+
+
+\begin{Switch}{REVPRI}
+\index{output}
+When the \name{revpri} switch is on, terms are printed in reverse order from
+the normal printing order.
+
+\begin{Examples}
+x**5 + x**2 + 18 + sqrt(y);  &    SQRT(Y) + X^{5} + X^{2} + 18 \\
+a + b + c + w;               &    A + B + C + W \\
+on revpri; \\
+x**5 + x**2 + 18 + sqrt(y);  &    17 + X^{2} + X^{5} + SQRT(Y) \\
+a + b + c + w;               &    W + C + B + A
+\end{Examples}
+
+\begin{Comments}
+Turn \name{revpri} on when you want to display a polynomial in ascending
+rather than descending order.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{RLISP88}
+\index{lisp}
+Rlisp '88 is a superset of the Rlisp that has been traditionally used for
+the support of REDUCE.  It is fully documented in the book Marti, J.B.,
+``{RLISP} '88:  An Evolutionary Approach to Program Design and Reuse'',
+World Scientific, Singapore (1993).  It supports different looping
+constructs from the traditional Rlisp, and treats ``-'' as a letter unless
+separated by spaces.  Turning on the switch \name{rlisp88} converts to
+Rlisp '88 parsing conventions in symbolic mode, and enables the use of
+Rlisp '88 extensions.  Turning off the switch reverts to the traditional
+Rlisp and the previous mode ( (\nameref{symbolic} or \nameref{algebraic})
+in force before \name{rlisp88} was turned on.
+
+\end{Switch}
+
+
+\begin{Switch}{ROUNDALL}
+\index{rounded}\index{rational expression}\index{floating point}
+In \nameref{rounded} mode, rational numbers are normally converted to a
+floating point representation.  If \name{roundall} is off, this conversion
+does not occur.  \name{roundall} is normally \name{on}.
+
+\begin{Examples}
+on rounded; \\
+1/2; & 0.5 \\
+off roundall; \\
+1/2; \rfrac{1}{2}
+\end{Examples}
+
+\end{Switch}
+
+
+\begin{Switch}{ROUNDBF}
+When \nameref{rounded} is on, the normal defaults cause underflows to be
+converted to zero.  If you really want the small number that results in
+such cases, \name{roundbf} can be turned on.
+
+\begin{Examples}
+on rounded; \\
+exp(-100000.1^2); & 0 \\
+on roundbf; \\
+exp(-100000.1^2); & 1.18441281937E-4342953505
+\end{Examples}
+
+\begin{Comments}
+If a polynomial is input in \nameref{rounded} mode at the default
+precision into any \nameref{roots} function, and it is not possible to
+represent any of the coefficients of the polynomial precisely in the
+system floating point representation, the switch \name{roundbf} will be
+automatically turned on.  All rounded computation will use the internal
+bigfloat representation until the user subsequently turns \name{roundbf}
+off. (A message is output to indicate that this condition is in effect.)
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{ROUNDED}
+\index{floating point}
+When \name{rounded} is on, floating-point arithmetic is enabled, with
+precision initially at a system default value, which is usually 12 digits.
+The precise number can be found by the command \nameref{precision}(0).
+\begin{Examples}
+pi;                          &            PI \\
+35/217;                      &            \rfrac{5}{31} \\
+on rounded; \\
+pi;                          &            3.14159265359 \\
+35/217;                      &            0.161 \\
+sqrt(3);                     &            1.73205080756
+\end{Examples}
+\begin{Comments}
+If more than the default number of decimal places are required, use the
+\nameref{precision} command to set the required number.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{SAVESTRUCTR}
+\index{STRUCTR OPERATOR}
+When \name{savestructr} is on, results of the \nameref{structr} command are
+returned as a list whose first element is the representation for the
+expression and the remaining elements are equations showing the
+relationships of the generated variables.
+
+\begin{Examples}
+off exp; \\
+structr((x+y)^3 + sin(x)^2);                          &
+\begin{multilineoutput}{6cm}
+ANS3
+   where
+      ANS3 := ANS1^{3} + ANS2^{2}
+      ANS2 := SIN(X)
+      ANS1 := X + Y
+\end{multilineoutput}\\
+ans3;                        &     ANS3 \\
+on savestructr; \\
+structr((x+y)^{3} + sin(x)^{2});                         &
+{ANS3,ANS3=ANS1^{3} + ANS2^{2},ANS2=SIN(X),ANS1=X + Y} \\
+ans3 where rest ws; &
+(X + Y)^{3} + SIN(X)^{2}
+\end{Examples}
+\begin{Comments}
+In normal operation, \nameref{structr} is only a display command.  With
+\name{savestructr} on, you can access the various parts of the expression
+produced by \name{structr}.
+
+The generic system names use the stem \name{ANS}.  You can change this to your
+own stem by the command \nameref{varname}.  REDUCE adds integers to this stem
+to make unique identifiers.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{SOLVESINGULAR}
+\index{solve}
+When \name{solvesingular} is on, singular or underdetermined systems of
+linear equations are solved, using arbitrary real, complex or integer
+variables in the answer.  Default is \name{on}.
+
+\begin{Examples}
+solve({2x + y,4x + 2y},{x,y});                          &
+                   \{\{X= - \rfrac{ARBCOMPLEX(1)}{2},Y=ARBCOMPLEX(1)\}\} \\
+solve({7x + 15y - z,x - y - z},{x,y,z});                &
+\begin{multilineoutput}{6cm}
+\{\{X=\rfrac{8*ARBCOMPLEX(3)}{11}
+  Y= - \rfrac{3*ARBCOMPLEX(3)}{11}
+  Z=ARBCOMPLEX(3)\}\}
+\end{multilineoutput}\\
+off solvesingular; \\
+solve({2x + y,4x + 2y},{x,y});                          &
+                   ***** SOLVE given singular equations \\
+solve({7x + 15y - z,x - y - z},{x,y,z});                &
+                   ***** SOLVE given singular equations
+\end{Examples}
+\begin{Comments}
+
+The integer following the identifier \nameref{arbcomplex} above is assigned by
+the system, and serves to identify the variable uniquely.  It has no other
+significance.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{TIME}
+\index{time}
+When \name{time} is on, the system time used in executing each REDUCE
+statement is printed after the answer is printed.
+
+\begin{Examples}
+on time;                     &       Time: 4940 ms \\
+df(sin(x**2 + y),y);         &
+\begin{multilineoutput}{6cm}
+COS(X  + Y^{2})
+Time: 180 ms
+\end{multilineoutput}\\
+solve(x**2 - 6*y,x);         &
+\begin{multilineoutput}{6cm}
+\{X= - SQRT(Y)*SQRT(6),
+ X=SQRT(Y)*SQRT(6)\}
+Time: 320 ms
+\end{multilineoutput}
+\end{Examples}
+\begin{Comments}
+When \name{time} is first turned on, the time since the beginning of the
+REDUCE session is printed.  After that, the time used in computation,
+(usually in milliseconds, though this is system dependent) is printed after
+the results of each command.  Idle time or time spent typing in commands is
+not counted.  If \name{time} is turned off, the first reading after it is
+turned on again gives the time elapsed since it was turned off.  The time
+printed is CPU or wall clock time, depending on the system.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{TRALLFAC}
+\index{factorize}
+When \name{trallfac} is on, a more detailed trace of factorizer calls is
+generated.
+
+\begin{Comments}
+The \name{trallfac} switch takes precedence over \nameref{trfac} if they are
+both on. \name{trfac} gives a factorization trace with less detail in it.
+When the \nameref{factor} switch is on also, all input polynomials are sent to
+the factorizer automatically and trace information is generated.  The
+\nameref{out} command saves the results of the factoring, but not the trace.
+% You need to use the \name{dribble} command to save the trace text to a file.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{TRFAC}
+\index{factorize}
+When \name{trfac} is on, a narrative trace of any calls to the factorizer is
+generated.  Default is \name{off}.
+
+\begin{Comments}
+When the switch \nameref{factor} is on, and \name{trfac} is on, every input
+polynomial is sent to the factorizer, and a trace generated.  With
+\name{factor} off, only polynomials that are explicitly factored with the
+command \nameref{factorize} generate trace information.
+
+% Use the \name{dribble} or \name{logfile} command to save the trace text to
+% a file.
+The \nameref{out} command saves the results of the factoring, but not
+the trace.  The \nameref{trallfac} switch gives trace information to a
+greater level of detail.
+\end{Comments}
+\end{Switch}
+
+\begin{Switch}{TRIGFORM}
+\index{solve}\index{polynomial}
+When \nameref{fullroots} is on, \nameref{solve} will compute the
+roots of a cubic or quartic polynomial is closed form. When 
+\name{trigform} is on, the roots will be expressed by trigonometric
+forms. Otherwise nested surds are used. Default is \name{on}.
+\end{Switch}
+
+
+\begin{Switch}{TRINT}
+\index{integration}
+When \name{trint} is on, a narrative tracing various steps in the
+integration process is produced.
+
+\begin{Comments}
+%Use the \name{dribble} or \name{logfile} command to save this text to a file.
+The \nameref{out} command saves the results of the integration, but not the
+trace.
+\end{Comments}
+\end{Switch}
+
+\begin{Switch}{TRNONLNR}
+\index{solve}
+When \name{trnonlnr} is on, a narrative tracing various steps in
+the process for solving non-linear equations is produced.
+
+\begin{Comments}
+\name{trnonlnr} can only be used after the solve package has been loaded
+(e.g., by an explicit call of \nameref{load\_package}).  The \nameref{out}
+command saves the results of the equation solving, but not the trace.
+\end{Comments}
+\end{Switch}
+
+
+\begin{Switch}{VAROPT}
+\index{solve}
+When \name{varopt} is on, the sequence of variables is optimized by
+\nameref{solve} with respect to execution speed. Otherwise, the sequence
+given in the call to \nameref{solve} is preserved. Default is \name{on}.
+
+In combination with the switch \nameref{arbvars}, \name{varopt} can be used
+to control variable elimination.
+
+\begin{Examples}
+off arbvars; \\
+solve({x+2z,x-3y},{x,y,z});				&
+		   \{\{y=\rfrac{x}{3},z= - \rfrac{x}{2}\}\} \\
+solve({x*y=1,z=x},{x,y,z});				&
+		   \{\{z=x,y=\rfrac{1}{x}\}\} \\
+off varopt; \\
+solve({x+2z,x-3y},{x,y,z});				&
+		   \{\{x= - 2*z,y= - \rfrac{2*z}{3}\}\} \\
+solve({x*y=1,z=x},{x,y,z});				&
+		   \{\{y=\rfrac{1}{z},x=z\}\} \\
+\end{Examples}
+\end{Switch}
+