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.See also
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;
See also
-
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;
See also
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
See also
-
TeXForm
(expr)¶ export expressions to LaTeX
- Param expr
an expression to be exported
TeXForm()
returns a string containing LaTeX representation of the yacas expressionexpr
. 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 expressionexpr
. 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()
returnsTrue
if the yacas expressionexpr
can be exported into C code. This is a check whether the C exporterCForm()
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 ofIsCFormable()
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 functionfunc123()
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 thatWrite()
accepts an arbitrary number of arguments, all of which are written to the current output (see second example).Write()
always returnsTrue
.- 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 ofWrite()
.See also
-
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 returnsTrue
.- 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()
andWriteString()
. Note thatWrite()
andWriteString()
do not write a newline, so theOut>
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 printsn
spaces on the current output. The result is alwaysTrue
.- 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 printsn
newlines on the current output. The result is alwaysTrue
.- 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 expressionbody
is evaluated. If some functions inbody
try to read from current input, they will read from the filename
. Finally, the file is closed and the result of evaluatingbody
is returned.- Example
Suppose that the file
foo
contains2 + 5;
:In> FromFile("foo") res := Read(); Out> 2+5; In> FromFile("foo") res := ReadToken(); Out> 2;
See also
-
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 stringstr
. The result of evaluatingbody
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;
See also
-
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 expressionbody
is evaluated. Everything that the commands inbody
prints ends up in the filename
. Finally, the file is closed and the result of evaluatingbody
is returned. If the file is opened again, the old contents will be overwritten. This is a limitation ofToFile()
: 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 linesqrt(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
See also
FromFile()
,ToString()
,Echo()
,Write()
,WriteString()
,PrettyForm()
,Taylor()
-
ToString
() body¶ connect current output to a string
- Param body
expression to be evaluated
The commands in
body
are executed. Everything that is printed, byEcho()
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";
See also
-
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; In> FromString("") Read(); Out> EndOfFile;
See also
-
ToStdout
() body¶ select initial output stream for output
- Param body
expression to be evaluated
When using
ToString()
orToFile()
, 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> FromString(ReadCmdLineString("Deriv> "):";")Read()); \ 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>
See also
-
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 atomEndOfFile
is returned. The yacas expressiona+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)))") \ LispRead(); Out> {Sin(x),-Cos(x)}; In> FromString("(+ a b)")LispRead() Out> a+b;
See also
FromFile()
,FromString()
,Read()
,ReadToken()
,FullForm()
,LispReadListed()
-
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 applyingListify()
toLispRead()
. The functionLispReadListed()
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};
See also
FromFile()
,FromString()
,Read()
,ReadToken()
,FullForm()
,LispRead()
-
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. The3
will be in the next token. (The results will be different if a non-default tokenizer is selected.)See also
FromFile()
,FromString()
,Read()
,LispRead()
,DefaultTokenizer()
-
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 returnsTrue
.See also
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 toUse()
or via theDefLoad()
mechanism, nothing happens. Otherwise all expressions in the file are read and evaluated.Use()
always returnsTrue
. The purpose of this function is to make sure that the file will at least have been loaded, but is not loaded twice.
-
DefLoad
(name)¶ load a
.def
file- Param name
name of the file (without the
.def
suffix)
The suffix
.def
is appended toname
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 filename
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.
-
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).
See also
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.See also
-
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;
See also
-
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 usingV()
. In verbose mode,InVerboseMode()
will returnTrue
, otherwise it will returnFalse
.- 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
See also
-
InVerboseMode
()¶ check for verbose output mode
In verbose mode,
InVerboseMode()
will returnTrue
, otherwise it will returnFalse
.- Example
In> InVerboseMode() Out> False In> V(InVerboseMode()) Out> True
See also
Echo()
,N()
,OldSolve()
,V()
-
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");
See also
-
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.
See also
OMRead()
, TrapError()
, XmlExplodeTag()
,
ReadToken()
, FromFile()
, FromString()
-
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.
See also
OMRead()
, TrapError()
, XmlExplodeTag()
,
ReadToken()
, FromFile()
, FromString()
-
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> "; In> FromString(str)OMRead() 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
See also
-
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> "; In> FromString(str)OMRead() Out> 2+Sin(a*3);
See also
-
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 In> FromString(ToString()OMForm(Limit(x,0,Right) 1/x))OMRead() Out> Limit(x,0,Right)1/x In> % Out> Infinity