# Input/output¶

This chapter contains commands to use for input and output. All output commands write to the same destination stream, called the “current output”. This is initially the screen, but may be redirected by some commands. Similarly, most input commands read from the “current input” stream, which can also be redirected. The exception to this rule are the commands for reading script files, which simply read a specified file.

FullForm(expr)

print an expression in LISP-format

Param expr

expression to be printed in LISP-format

Evaluates “expr”, and prints it in LISP-format on the current output. It is followed by a newline. The evaluated expression is also returned. This can be useful if you want to study the internal representation of a certain expression.

Example

In> FullForm(a+b+c);
(+ (+ a b )c )
Out> a+b+c;
In> FullForm(2*I*b^2);
(* (Complex 0 2 )(^ b 2 ))
Out> Complex(0,2)*b^2;


The first example shows how the expression $$a+b+c$$ is internally represented. In the second example, $$2i$$ is first evaluated to Complex(0,2) before the expression is printed.

LispRead(), Listify(), Unlist()

Echo(item)
Echo(items)

high-level printing routine

Param item

the item to be printed

Param items

a list of items to be printed

If passed a single item, {Echo} will evaluate it and print it to the current output, followed by a newline. If {item} is a string, it is printed without quotation marks. If there is one argument, and it is a list, {Echo} will print all the entries in the list subsequently to the current output, followed by a newline. Any strings in the list are printed without quotation marks. All other entries are followed by a space. {Echo} can be called with a variable number of arguments, they will all be printed, followed by a newline. {Echo} always returns True.

Example

In> Echo(5+3);
8
Out> True;
In> Echo({"The square of two is ", 2*2});
The square of two is 4
Out> True;
In> Echo("The square of two is ", 2*2);
The square of two is 4
Out> True;
Note that one must use the second calling format if one wishes to
print a list:
In> Echo({a,b,c});
a b c
Out> True;
In> Echo({{a,b,c}});
{a,b,c}
Out> True;

PrettyForm(expr)

print an expression nicely with ASCII art

Param expr

an expression

PrettyForm() renders an expression in a nicer way, using ascii art. This is generally useful when the result of a calculation is more complex than a simple number.

Example

In> Taylor(x,0,9)Sin(x)
Out> x-x^3/6+x^5/120-x^7/5040+x^9/362880;
In> PrettyForm(%)
3    5      7       9
x    x      x       x
x - -- + --- - ---- + ------
6    120   5040   362880
Out> True;


EvalFormula(), PrettyPrinter'Set()

EvalFormula(expr)

print an evaluation nicely with ASCII art

Param expr

an expression

Show an evaluation in a nice way, using PrettyPrinter'Set() to show ‘input = output’.

Example

In> EvalFormula(Taylor(x,0,7)Sin(x))
3    5
x    x
Taylor( x , 0 , 5 , Sin( x ) ) = x - -- + ---
6    120

TeXForm(expr)

export expressions to LaTeX

Param expr

an expression to be exported

TeXForm() returns a string containing LaTeX representation of the yacas expression expr. Currently the exporter handles most expression types but not all.

CForm(expr)

export expression to C code

Param expr

expression to be exported

CForm() returns a string containing C code that attempts to implement the yacas expression expr. Currently the exporter handles most expression types but not all.

IsCFormable(expr)
IsCFormable(expr, funclist)

check possibility to export expression to C code

Param expr

expression to be exported (this argument is not evaluated)

Param funclist

list of “allowed” function atoms

IsCFormable() returns True if the yacas expression expr can be exported into C code. This is a check whether the C exporter CForm() can be safely used on the expression. A yacas expression is considered exportable if it contains only functions that can be translated into C (e.g. UnList() cannot be exported). All variables and constants are considered exportable. The verbose option prints names of functions that are not exportable. The second calling format of IsCFormable() can be used to allow certain function names that will be available in the C code.

Example

In> IsCFormable(Sin(a1)+2*Cos(b1))
Out> True;
In> V(IsCFormable(1+func123(b1)))
IsCFormable: Info: unexportable function(s):
func123
Out> False;


This returned False because the function func123() is not available in C. We can explicitly allow this function and then the expression will be considered exportable:

In> IsCFormable(1+func123(b1), {func123})
Out> True;


Write(expr, ...)

low-level printing routine

Param expr

expression to be printed

The expression expr is evaluated and written to the current output. Note that Write() accepts an arbitrary number of arguments, all of which are written to the current output (see second example). Write() always returns True.

Example

In> Write(1);
1Out> True;
In> Write(1,2);
1 2Out> True;


Write does not write a newline, so the Out> prompt immediately follows the output of Write().

WriteString(string)

low-level printing routine for strings

Param string

the string to be printed

The expression string is evaluated and written to the current output without quotation marks. The argument should be a string. WriteString() always returns True.

Example

In> Write("Hello, world!");
"Hello, world!"Out> True;
In> WriteString("Hello, world!");
Hello, world!Out> True;


This example clearly shows the difference between Write() and WriteString(). Note that Write() and WriteString() do not write a newline, so the Out> prompt immediately follows the output.

Space()
Space(n)

print one or more spaces

Param n

the number of spaces to print

Space() prints one space on the current output. The second form prints n spaces on the current output. The result is always True.

Example

In> Space(5);
Out> True;

NewLine()
NewLine(n)

print one or more newline characters

Param n

the number of newline characters to print

NewLine() prints a newline character on the current output. The second form prints n newlines on the current output. The result is always True.

Example

In> NewLine();

Out> True;

FromFile(name) body

connect current input to a file

Param name

name of the file to read

Param body

expression to be evaluated

The current input is connected to the file name. Then the expression body is evaluated. If some functions in body try to read from current input, they will read from the file name. Finally, the file is closed and the result of evaluating body is returned.

Example

Suppose that the file foo contains 2 + 5;:

In> FromFile("foo") res := Read();
Out> 2+5;
In> FromFile("foo") res := ReadToken();
Out> 2;

FromString(str) body

connect current input to a string

Param str

a string containing the text to parse

Param body

expression to be evaluated

The commands in body are executed, but every read is done from the string str. The result of evaluating body is returned.

Example

In> FromString("2+5; this is never read") res := Read();
Out> 2+5;
In> FromString("2+5; this is never read") res := Eval(Read());
Out> 7;

ToFile(name) body

connect current output to a file

Param name

name of the file to write the result to

Param body

expression to be evaluated

The current output is connected to the file name. Then the expression body is evaluated. Everything that the commands in body prints ends up in the file name. Finally, the file is closed and the result of evaluating body is returned. If the file is opened again, the old contents will be overwritten. This is a limitation of ToFile(): one cannot append to a file that has already been created.

Example

Here is how one can create a file with C code to evaluate an expression:

In> ToFile("expr1.c") WriteString(CForm(Sqrt(x-y)*Sin(x)));
Out> True;


The file expr1.c was created in the current working directory and it contains the line sqrt(x-y)*sin(x).

As another example, take a look at the following command:

In> [ Echo("Result:");  PrettyForm(Taylor(x,0,9) Sin(x)); ];
Result:
3    5      7       9
x    x      x       x
x - -- + --- - ---- + ------
6    120   5040   362880
Out> True;


Now suppose one wants to send the output of this command to a file. This can be achieved as follows:

In> ToFile("out") [ Echo("Result:"); PrettyForm(Taylor(x,0,9) Sin(x)); ];
Out> True;


After this command the file out contains:

Result:
3    5      7       9
x    x      x       x
x - -- + --- - ---- + ------
6    120   5040   362880


ToString() body

connect current output to a string

Param body

expression to be evaluated

The commands in body are executed. Everything that is printed, by Echo() for instance, is collected in a string and this string is returned.

Example

In> str := ToString() [ WriteString("The square of 8 is "); Write(8^2); ];
Out> "The square of 8 is  64";

Read()

read an expression from current input

Read an expression from the current input, and return it unevaluated. When the end of an input file is encountered, the token atom {EndOfFile} is returned.

Example

In> FromString("2+5;") Read();
Out> 2+5;
Out> EndOfFile;

ToStdout() body

select initial output stream for output

Param body

expression to be evaluated

When using ToString() or ToFile(), it might happen that something needs to be written to the (initial) standard output (typically the screen). ToStdout() can be used to select this stream.

ReadCmdLineString(prompt)

read an expression from command line and return in string

Param prompt

string representing the prompt shown on screen

This function allows for interactive input similar to the command line. When using this function, the history from the command line is also available. The result is returned in a string, so it still needs to be parsed. This function will typically be used in situations where one wants a custom read-eval-print loop.

Example

The following defines a function that when invoked keeps asking for an expression (the read step), and then takes the derivative of it (the eval step) and then uses PrettyForm() to display the result (the print step):

In> ReEvPr() := \
In>   While(True) [ \
In>     PrettyForm(Deriv(x) \
In> ];
Out> True;


Then one can invoke the command, from which the following interaction might follow:

In> ReEvPr()
Deriv> Sin(a^2*x/b)
/  2     \
| a  * x |    2
Cos| ------ | * a  * b
\   b    /
----------------------
2
b
Deriv> Sin(x)
Cos( x )
Deriv>

LispRead()

read expressions in LISP syntax

LispRead() reads an expression in the LISP syntax from the current input, and returns it unevaluated. When the end of an input file is encountered, the special token atom EndOfFile is returned. The yacas expression a+b is written in the LISP syntax as (+ a b). The advantage of this syntax is that it is less ambiguous than the infix operator grammar that yacas uses by default.

Example

In> FromString("(+ a b)") LispRead();
Out> a+b;
In> FromString("(List (Sin x) (- (Cos x)))") \
Out> {Sin(x),-Cos(x)};
In> FromString("(+ a b)")LispRead()
Out> a+b;

LispReadListed()

read expressions in LISP syntax

LispReadListed() reads a LISP expression and returns it in a list, instead of the form usual to yacas (expressions). The result can be thought of as applying Listify() to LispRead(). The function LispReadListed() is more useful for reading arbitrary LISP expressions, because the first object in a list can be itself a list (this is never the case for yacas expressions where the first object in a list is always a function atom).

Example

In> FromString("(+ a b)")LispReadListed()
Out> {+,a,b};

ReadToken()

read a token from current input

Read a token from the current input, and return it unevaluated. The returned object is a Yacas atom (not a string). When the end of an input file is encountered, the token atom {EndOfFile} is returned. A token is for computer languages what a word is for human languages: it is the smallest unit in which a command can be divided, so that the semantics (that is the meaning) of the command is in some sense a combination of the semantics of the tokens. Hence {a := foo} consists of three tokens, namely {a}, {:=}, and {foo}. The parsing of the string depends on the syntax of the language. The part of the kernel that does the parsing is the “tokenizer”. Yacas can parse its own syntax (the default tokenizer) or it can be instructed to parse XML or C++ syntax using the directives {DefaultTokenizer} or {XmlTokenizer}. Setting a tokenizer is a global action that affects all {ReadToken} calls.

Example

In> FromString("a := Sin(x)") While((tok := ReadToken()) != EndOfFile) Echo(tok);
a
:=
Sin
(
x
)
Out> True;


We can read some junk too:

In> FromString("-$3")ReadToken(); Out> -$;


The result is an atom with the string representation -$. Yacas assumes that -$ is an operator symbol yet to be defined. The 3 will be in the next token. (The results will be different if a non-default tokenizer is selected.)

Load(name)

evaluate all expressions in a file

Param name

name of the file to load

The file name is opened. All expressions in the file are read and evaluated. Load() always returns True.

Use(), DefLoad(), DefaultDirectory(), FindFile()

Use(name)

load a file, but not twice

Param name

name of the file to load

If the file name has been loaded before, either by an earlier call to Use() or via the DefLoad() mechanism, nothing happens. Otherwise all expressions in the file are read and evaluated. Use() always returns True. The purpose of this function is to make sure that the file will at least have been loaded, but is not loaded twice.

Load(), DefLoad(), DefaultDirectory()

DefLoad(name)

load a .def file

Param name

name of the file (without the .def suffix)

The suffix .def is appended to name and the file with this name is loaded. It should contain a list of functions, terminated by a closing brace \} (the end-of-list delimiter). This tells the system to load the file name as soon as the user calls one of the functions named in the file (if not done so already). This allows for faster startup times, since not all of the rules databases need to be loaded, just the descriptions on which files to load for which functions.

Load(), Use(), DefaultDirectory()

FindFile(name)

find a file in the current path

Param name

string, name of the file or directory to find

The result of this command is the full path to the file that would be opened when the command {Load(name)} would be invoked. This means that the input directories are subsequently searched for a file called “name”. If such a file is not found, {FindFile} returns an empty string. {FindFile(“”)} returns the name of the default directory (the first one on the search path).

Load(), DefaultDirectory()

PatchLoad(name)

execute commands between <? and ?> in file

Param name

string, name of the file to “patch”

PatchLoad() loads in a file and outputs the contents to the current output. The file can contain blocks delimited by <? and ?>. The piece of text between such delimiters is treated as a separate file with yacas instructions, which is then loaded and executed. All output of write statements in that block will be written to the same current output. This is similar to the way PHP works. You can have a static text file with dynamic content generated by yacas.

Nl()

the newline character

This function returns a string with one element in it, namely a newline character. This may be useful for building strings to send to some output in the end.

Example

In> WriteString("First line" : Nl() : "Second line" : Nl());
First line
Second line
Out> True;

V(expression)

set verbose output mode

Param expression

expression to be evaluated in verbose mode

V() will evaluate the expression in verbose mode. Various parts of yacas can show extra information about the work done while doing a calculation when using V(). In verbose mode, InVerboseMode() will return True, otherwise it will return False.

Example

In> OldSolve({x+2==0},{x})
Out> {{-2}};
In> V(OldSolve({x+2==0},{x}))
Entering OldSolve
From  x+2==0  it follows that  x  = -2
x+2==0  simplifies to  True
Leaving OldSolve
Out> {{-2}};
In> InVerboseMode()
Out> False
In> V(InVerboseMode())
Out> True

InVerboseMode()

check for verbose output mode

In verbose mode, InVerboseMode() will return True, otherwise it will return False.

Example

In> InVerboseMode()
Out> False
In> V(InVerboseMode())
Out> True

XmlExplodeTag(xmltext)

convert XML strings to tag objects

Param xmltext

string containing some XML tokens

{XmlExplodeTag} parses the first XML token in {xmltext} and returns a Yacas expression. The following subset of XML syntax is supported currently:

• {<TAG [options]>} – an opening tag

• {</TAG [options]>} – a closing tag

• {<TAG [options] />} – an open/close tag

• plain (non-tag) text

The tag options take the form {paramname=”value”}.

If given an XML tag, {XmlExplodeTag} returns a structure of the form {XmlTag(name,params,type)}. In the returned object, {name} is the (capitalized) tag name, {params} is an assoc list with the options (key fields capitalized), and type can be either “Open”, “Close” or “OpenClose”.

If given a plain text string, the same string is returned.

Example

In> XmlExplodeTag("some plain text")
Out> "some plain text";
In> XmlExplodeTag("<a name=\"blah blah\"
align=\"left\">")
Out> XmlTag("A",{{"ALIGN","left"},
{"NAME","blah blah"}},"Open");
In> XmlExplodeTag("</p>")
Out> XmlTag("P",{},"Close");
In> XmlExplodeTag("<br/>")
Out> XmlTag("BR",{},"OpenClose");

XmlTokenizer()

select the default syntax tokenizer for parsing the input

A “tokenizer” is an internal routine in the kernel that parses the input into Yacas expressions. This affects all input typed in by a user at the prompt and also the input redirected from files or strings using {FromFile} and {FromString} and read using {Read} or {ReadToken}. The Yacas environment currently supports some experimental tokenizers for various syntaxes. {DefaultTokenizer} switches to the tokenizer used for default Yacas syntax. {XmlTokenizer} switches to an XML syntax. Note that setting the tokenizer is a global side effect. One typically needs to switch back to the default tokenizer when finished reading the special syntax. Care needs to be taken when kernel errors are raised during a non-default tokenizer operation (as with any global change in the environment). Errors need to be caught with the {TrapError} function. The error handler code should re-instate the default tokenizer, or else the user will be unable to continue the session (everything a user types will be parsed using a non-default tokenizer). When reading XML syntax, the supported formats are the same as those of {XmlExplodeTag}. The parser does not validate anything in the XML input. After an XML token has been read in, it can be converted into an Yacas expression with {XmlExplodeTag}. Note that when reading XML, any plain text between tags is returned as one token. Any malformed XML will be treated as plain text.

Example

In> [XmlTokenizer(); q:=ReadToken(); \
DefaultTokenizer();q;]
<a>
Out> <a>;


Note that:

• after switching to {XmlTokenizer} the {In>} prompt disappeared; the user typed {<a>} and the {Out>} prompt with the resulting expression appeared.

• The resulting expression is an atom with the string representation {<a>}; it is not a string.

DefaultTokenizer()

select the default syntax tokenizer for parsing the input

A “tokenizer” is an internal routine in the kernel that parses the input into Yacas expressions. This affects all input typed in by a user at the prompt and also the input redirected from files or strings using {FromFile} and {FromString} and read using {Read} or {ReadToken}. The Yacas environment currently supports some experimental tokenizers for various syntaxes. {DefaultTokenizer} switches to the tokenizer used for default Yacas syntax. {XmlTokenizer} switches to an XML syntax. Note that setting the tokenizer is a global side effect. One typically needs to switch back to the default tokenizer when finished reading the special syntax. Care needs to be taken when kernel errors are raised during a non-default tokenizer operation (as with any global change in the environment). Errors need to be caught with the {TrapError} function. The error handler code should re-instate the default tokenizer, or else the user will be unable to continue the session (everything a user types will be parsed using a non-default tokenizer). When reading XML syntax, the supported formats are the same as those of {XmlExplodeTag}. The parser does not validate anything in the XML input. After an XML token has been read in, it can be converted into an Yacas expression with {XmlExplodeTag}. Note that when reading XML, any plain text between tags is returned as one token. Any malformed XML will be treated as plain text.

OMForm(expression)

convert Yacas expression to OpenMath

Param expression

expression to convert

{OMForm} prints an OpenMath representation of the input parameter {expression} to standard output. If a Yacas symbol does not have a mapping defined by {OMDef}, it is translated to and from OpenMath as the OpenMath symbol in the CD “yacas” with the same name as it has in Yacas.

Example

In> str:=ToString()OMForm(2+Sin(a*3))
Out> "<OMOBJ>
<OMA>
<OMS cd="arith1" name="plus"/>
<OMI>2</OMI>
<OMA>
<OMS cd="transc1" name="sin"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMV name="a"/>
<OMI>3</OMI>
</OMA>
</OMA>
</OMA>
</OMOBJ>
";
Out> 2+Sin(a*3);

In> OMForm(NotDefinedInOpenMath(2+3))
<OMOBJ>
<OMA>
<OMS cd="yacas" name="NotDefinedInOpenMath"/>
<OMA>
<OMS cd="arith1" name="plus"/>
<OMI>2</OMI>
<OMI>3</OMI>
</OMA>
</OMA>
</OMOBJ>
Out> True

OMRead()

read OpenMath expression and convert to Yacas

Param expression

expression to convert

{OMRead} reads an OpenMath expression from standard input and returns a normal Yacas expression that matches the input OpenMath expression. If a Yacas symbol does not have a mapping defined by {OMDef}, it is translated to and from OpenMath as the OpenMath symbol in the CD “yacas” with the same name as it has in Yacas.

Example

In> str:=ToString()OMForm(2+Sin(a*3))
Out> "<OMOBJ>
<OMA>
<OMS cd="arith1" name="plus"/>
<OMI>2</OMI>
<OMA>
<OMS cd="transc1" name="sin"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMV name="a"/>
<OMI>3</OMI>
</OMA>
</OMA>
</OMA>
</OMOBJ>
";
Out> 2+Sin(a*3);

OMDef(yacasForm, cd, name)

define translations from Yacas to OpenMath and vice-versa.

Param yacasForm

string with the name of a Yacas symbol, or a Yacas expression

Param cd

OpenMath Content Dictionary for the symbol

Param name

OpenMath name for the symbol

Param yacasToOM

rule for translating an application of that symbol in Yacas into an OpenMath expression

Param omToYacas

rule for translating an OpenMath expression into an application of this symbol in Yacas

{OMDef} defines the translation rules for symbols between the Yacas representation and {OpenMath}. The first parameter, {yacasForm}, can be a string or an expression. The difference is that when giving an expression only the {omToYacas} translation is defined, and it uses the exact expression given. This is used for {OpenMath} symbols that must be translated into a whole subexpression in Yacas, such as {set1:emptyset} which gets translated to an empty list as follows: In> OMDef( {}, “set1”,”emptyset” ) Out> True In> FromString(“<OMOBJ><OMS cd=”set1” name=”emptyset”/></OMOBJ> “)OMRead() Out> {} In> IsList(%) Out> True Otherwise, a symbol that is not inside an application (OMA) gets translated to the Yacas atom with the given name: In> OMDef( “EmptySet”, “set1”,”emptyset” ) Warning: the mapping for set1:emptyset was already defined as {} , but is redefined now as EmptySet Out> True In> FromString(“<OMOBJ><OMS cd=”set1” name=”emptyset”/></OMOBJ> “)OMRead() Out> EmptySet The definitions for the symbols in the Yacas library are in the *.rep script subdirectories. In those modules for which the mappings are defined, there is a file called {om.ys} that contains the {OMDef} calls. Those files are loaded in {openmath.rep/om.ys}, so any new file must be added to the list there, at the end of the file. A rule is represented as a list of expressions. Since both OM and Yacas expressions are actually lists, the syntax is the same in both directions. There are two template forms that are expanded before the translation:

• {$}: this symbol stands for the translation of the symbol applied in the original expression. • {_path}: a path into the original expression (list) to extract an element, written as an underscore applied to an integer or a list of integers. Those integers are indexes into expressions, and integers in a list are applied recursively starting at the original expression. For example, {_2} means the second parameter of the expression, while {_{3,2,1}} means the first parameter of the second parameter of the third parameter of the original expression. They can appear anywhere in the rule as expressions or subexpressions. Finally, several alternative rules can be specified by joining them with the {|} symbol, and each of them can be annotated with a post-predicate applied with the underscore {_} symbol, in the style of Yacas’ simplification rules. Only the first alternative rule that matches is applied, so the more specific rules must be written first. There are special symbols recognized by {OMForm} to output {OpenMath} constructs that have no specific parallel in Yacas, such as an OpenMath symbol having a {CD} and {name}: Yacas symbols have only a name. Those special symbols are: • {OMS(cd, name)}: {<OMS cd=”cd” name=”name”>} • {OMA(f x y …)}: {<OMA>f x y …</OMA>} • {OMBIND(binderSymbol, bvars, expression)}: {<OMBIND>binderSymbol bvars expression</OMBIND>}, where {bvars} must be produced by using {OMBVAR(…)}. • {OMBVAR(x y …)}: {<OMBVAR>x y …</OMBVAR>} • {OME(…)}: {<OME>…</OME>} When translating from OpenMath to Yacas, we just store unknown symbols as {OMS(“cd”, “name”)}. This way we don’t have to bother defining bogus symbols for concepts that Yacas does not handle, and we can evaluate expressions that contain them. Example In> OMDef( "Sqrt" , "arith1", "root", { :math:, _1, 2 }, :math:(_1)_(_2=2) | (_1^(1/_2)) ); Out> True In> OMForm(Sqrt(3)) <OMOBJ> <OMA> <OMS cd="arith1" name="root"/> <OMI>3</OMI> <OMI>2</OMI> </OMA> </OMOBJ> Out> True In> FromString("<OMOBJ><OMA><OMS cd=\"arith1\" name=\"root\"/><OMI>16</OMI><OMI>2</OMI></OMA></OMOBJ> ")OMRead() Out> Sqrt(16) In> FromString("<OMOBJ><OMA><OMS cd=\"arith1\" name=\"root\"/><OMI>16</OMI><OMI>3</OMI></OMA></OMOBJ> ")OMRead() Out> 16^(1/3) In> OMDef("Limit", "limit1", "limit", \ { :math:, _2, OMS("limit1", "under"), OMBIND(OMS("fns1", "lambda"), OMBVAR(_1), _4) }_(_3=Left) \ |{ :math:, _2, OMS("limit1", "above"), OMBIND(OMS("fns1", "lambda"), OMBVAR(_1), _4) }_(_3=Right) \ |{ :math:, _2, OMS("limit1", "both_sides"), OMBIND(OMS("fns1", "lambda"), OMBVAR(_1), _3) }, \ { :math:, _{3,2,1}, _1, Left, _{3,3}}_(_2=OMS("limit1", "below")) \ |{$, _{3,2,1}, _1, Right, _{3,3}}_(_2=OMS("limit1", "above")) \
|{\$, _{3,2,1}, _1, _{3,3}}                                    \
);
In> OMForm(Limit(x,0) Sin(x)/x)
<OMOBJ>
<OMA>
<OMS cd="limit1" name="limit"/>
<OMI>0</OMI>
<OMS cd="limit1" name="both_sides"/>
<OMBIND>
<OMS cd="fns1" name="lambda"/>
<OMBVAR>
<OMV name="x"/>
</OMBVAR>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMA>
<OMS cd="transc1" name="sin"/>
<OMV name="x"/>
</OMA>
<OMV name="x"/>
</OMA>
</OMBIND>
</OMA>
</OMOBJ>
Out> True
In> OMForm(Limit(x,0,Right) 1/x)
<OMOBJ>
<OMA>
<OMS cd="limit1" name="limit"/>
<OMI>0</OMI>
<OMS cd="limit1" name="above"/>
<OMBIND>
<OMS cd="fns1" name="lambda"/>
<OMBVAR>
<OMV name="x"/>
</OMBVAR>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMI>1</OMI>
<OMV name="x"/>
</OMA>
</OMBIND>
</OMA>
</OMOBJ>
Out> True