MathNot , MathAnd , MathOr , BitAnd, BitOr, BitXor , Equals , GreaterThan, LessThan , Math... , Fast... , ShiftLeft, ShiftRight , IsPromptShown , MathLibrary .

Built-in (core) functions

Yacas comes with a small core of built-in functions and a large library of user-defined functions. Some of these core functions are documented in this chapter.

MathNot	built-in logical "not"
MathAnd	built-in logical "and"
MathOr	built-in logical "or"
BitAnd, BitOr, BitXor	bitwise arithmetic
Equals	check equality
GreaterThan, LessThan	comparison predicates
Math...	arbitrary-precision math functions
Fast...	double-precision math functions
ShiftLeft, ShiftRight	built-in bit shifts
IsPromptShown	test for the Yacas prompt option
MathLibrary	obtain current math library name

It is important for a developer to know which functions are built-in and cannot be redefined or Retract-ed. Also, core functions may be somewhat faster to execute than functions defined in the script library. All core functions are listed in the file yacasapi.cpp in the src/ subdirectory of the Yacas source tree. The declarations typically look like this:

SetCommand(LispSubtract, "MathSubtract");

Here LispSubtract is the Yacas internal name for the function and MathSubtract is the name visible to the Yacas language. Built-in bodied functions and infix operators are declared in the same file.

MathNot -- built-in logical "not"

Internal function

Calling format:

MathNot(expression)

Description:

Returns "False" if "expression" evaluates to "True", and vice versa.

MathAnd -- built-in logical "and"

Calling format:

MathAnd(...)

Description:

Lazy logical And: returns True if all args evaluate to True, and does this by looking at first, and then at the second argument, until one is False. If one of the arguments is False, And immediately returns False without evaluating the rest. This is faster, but also means that none of the arguments should cause side effects when they are evaluated.

MathOr -- built-in logical "or"

Internal function

Calling format:

MathOr(...)

MathOr is the basic logical "or" function. Similarly to And, it is lazy-evaluated. And(...) and Or(...) do also exist, defined in the script library. You can redefine them as infix operators yourself, so you have the choice of precedence. In the standard scripts they are in fact declared as infix operators, so you can write expr1 And expr.

BitAnd, BitOr, BitXor -- bitwise arithmetic

Internal function

Calling format:

BitAnd(n,m)
BitOr(n,m)
BitXor(n,m)

Description:

These functions return bitwise "and", "or" and "xor" of two numbers.

Equals -- check equality

Internal function

Calling format:

Equals(a,b)

Description:

Compares evaluated a and b recursively (stepping into expressions). So "Equals(a,b)" returns "True" if the expressions would be printed exactly the same, and "False" otherwise.

GreaterThan, LessThan -- comparison predicates

Internal function

Calling format:

LessThan(a,b), GreaterThan(a,b)

Parameters:

a, b -- numbers or strings

Description:

Comparing numbers or strings (lexicographically).

Example:

In> LessThan(1,1)
Out> False;
In> LessThan("a","b")
Out> True;

Possible names are "Internal" and "Gmp", indicating the internal math library libyacasnumbers and the GNU Multiple Precision library libgmp.

Example:

In>  MathLibrary()
Out> "Internal";

Full listing of core functions

The following Yacas functions are currently declared in yacasapi.cpp as core functions:

= And ApplyPure ArrayCreate ArrayGet ArraySet ArraySize Atom Berlekamp BitAnd BitOr BitXor Bodied CTokenizer Check Clear CommonLispTokenizer Concat ConcatStrings CurrentFile CurrentLine DefLoad DefLoadFunction DefaultDirectory DefaultTokenizer Delete DestructiveDelete DestructiveInsert DestructiveReplace DestructiveReverse DllEnumerate DllLoad DllUnload Equals Eval FastArcCos FastArcSin FastArcTan FastAssoc FastCos FastExp FastLog FastPower FastSin FastTan FindFile FindFunction FlatCopy FromBase FromFile FromString FullForm GarbageCollect GenericTypeName GetExtraInfo GetPrecision GreaterThan Head Hold HoldArg If Infix Insert IsAtom IsBodied IsBound IsFunction IsGeneric IsInfix IsInteger IsList IsNumber IsPostfix IsPrefix IsString LazyGlobal LeftPrecedence Length LessThan LispRead LispReadListed List Listify Load Local LocalSymbols MacroClear MacroLocal MacroRule MacroRuleBase MacroRuleBaseListed MacroRulePattern MacroSet MathAbs MathAdd MathAnd MathArcCos MathArcSin MathArcTan MathCeil MathCos MathDiv MathDivide MathExp MathFac MathFloor MathGcd MathLibrary MathLog MathMod MathMultiply MathNot MathNth MathOr MathPi MathPower MathSin MathSqrt MathSubtract MathTan MaxEvalDepth Not OpLeftPrecedence OpPrecedence OpRightPrecedence Or PatchLoad PatchString PatternCreate PatternMatches Postfix Precision Prefix PrettyPrinter Prog Read ReadToken Replace Retract RightAssociative RightPrecedence Rule RuleBase RuleBaseArgList RuleBaseDefined RuleBaseListed RulePattern Secure Set SetExtraInfo SetStringMid ShiftLeft ShiftRight String StringMid Subst SystemCall Tail ToBase ToFile ToString TraceExp TraceRule TraceStack Type UnFence UnList Use Version While Write WriteString XmlExplodeTag XmlTokenizer `

In addition, the following functions are declared with special syntax and precedence:

@ --- prefix (prec. 0).

BackQuote --- bodied (prec. KMaxPrecedence).

FromFile --- bodied (prec. KMaxPrecedence).

FromString --- bodied (prec. KMaxPrecedence).

LocalSymbols --- bodied (prec. KMaxPrecedence).

MacroRule --- bodied (prec. KMaxPrecedence).

MacroRulePattern --- bodied (prec. KMaxPrecedence).

Rule --- bodied (prec. KMaxPrecedence).

RulePattern --- bodied (prec. KMaxPrecedence).

Subst --- bodied (prec. KMaxPrecedence).

ToFile --- bodied (prec. KMaxPrecedence).

ToString --- bodied (prec. KMaxPrecedence).

TraceRule --- bodied (prec. KMaxPrecedence).

While --- bodied (prec. KMaxPrecedence).

_ --- prefix (prec. 0).

_ --- infix (prec. 0).

` --- prefix (prec. 0).