< , > , <= , >= , != , = , Not , And , Or , IsFreeOf , IsZeroVector , IsNonObject , IsEven , IsOdd , IsFunction , IsAtom , IsString , IsNumber , IsInteger , IsList , IsBound , IsBoolean , IsNegativeNumber , IsNegativeInteger , IsPositiveNumber , IsPositiveInteger , IsNotZero , IsNonZeroInteger , IsInfinity , IsConstant , Predicates

Predicates


x < y (prec. 9)

x < y : Return True if "x" is smaller than "y", False otherwise.


x > y (prec. 9)

x > y : Return True if "x" is larger than "y", False otherwise.


x <= y (prec. 9)

x <= y : Return True if "x" is smaller than or equals "y", False otherwise.


x >= y (prec. 9)

x >= y : Return True if "x" is larger than or equals "y", False otherwise.


x!=y (prec. 9)

x!=y : Return True if "x" is not equal to "y", False otherwise.


x=y (prec. 9)

x=y : This operator performs the same action as Equals(x,y). It returns True if x and y would be displayed on screen the same, False otherwise.


Not

Internal function
Calling Sequence:
Not bool
Parameters:
bool - a boolean expression
Description:
Not returns the logical negation of the argument bool. If bool is False it returns True, and if the argument is True Not returns False. If the argument is neither True nor False it returns the entire expression with evaluated arguments.
Examples:
In> Not True
Out> False;
In> Not False
Out> True;
In> Not(a)
Out> Not a;
See Also:
And , Or ,


And

Internal function
Calling Sequence:
a1 And a2
And(a1,a2,a3,...,an)
Parameters:
a1 .. an - boolean values (True or False)
Description:
This function returns True if all arguments are true. The And operation is lazy, it returns False as soon as a False argument is found (from left to right). If an argument other than True or False is encountered a new And expression is returned with all arguments that didn't evaluate to True or False yet.
Examples:
In> True And False
Out> False;
In> And(True,True)
Out> True;
In> False And a
Out> False;
In> True And a
Out> And(a);
In> And(True,a,True,b)
Out> b And a;
See Also:
Or , Not ,


Or

Internal function
Calling Sequence:
a1 Or a2
Or(a1,a2,a3,...,an)
Parameters:
a1 .. an - boolean values (True or False)
Description:
This function returns True if an argument is encountered that is true (scanning from left to right). The Or operation is lazy, it returns True as soon as a True argument is found (from left to right). If an argument other than True or False is encountered a new Or expression is returned with all arguments that didn't evaluate to True or False yet.
Examples:
In> True Or False
Out> True;
In> False Or a
Out> Or(a);
In> Or(False,a,b,True)
Out> True;
See Also:
And , Not ,


IsFreeOf(expression,variable) or IsFreeOf(expression,{varlist})

Returns wether "expression" depends on "variable". "expression" is evaluated beforehand. Example: "IsFreeOf(x+y,x);" evaluates to "False".

When a list of variables is passed, IsFreeOf returns True iff the expression is independent of all the variables listed. "IsFreeOf(x+y,{a,b});" would return True, and "IsFreeOf(x+y,{a,x});" would return False.


IsZeroVector(vector)

Returns wether "vector" only contains zeroes. "vector" should be a list.


IsNonObject(x)

IsNonObject(x) : returns true if x is not of the form Object(...).


IsEven(n) and IsOdd(n)

Returns whether the integer n is even or odd (an integer n is even if n divided by 2 is also an integer).


IsFunction(expr)

IsFunction(expr) : Predicate that checks the type of a object. cos(a) is a function.


IsAtom(expr)

IsAtom(expr) : Predicate that checks the type of a object. Atoms are any object that can be represented with a text string (that is, excluding lists).


IsString(expr)

IsString(expr) : Predicate that checks the type of a object. Strings have the form "string", that is, with quotes.


IsNumber(expr)

IsNumber(expr) : Predicate that checks the type of a object. 1.2 or 1 are numbers.


IsInteger(expr)

IsInteger(expr) : Predicate that checks the type of a object. 1 is a integer.


IsList(expr)

IsList(expr) : Predicate that checks the type of a object. {cos,a} is a list.


IsBound(var)

IsBound(var) :Predicate that checks the type of a object. IsBound checks to see if variable var is bound.


IsBoolean

Standard math library
Calling Sequence:
IsBoolean(expression)
Parameters:
expression - an expression
Description:
IsBoolean returns True if the argument is of a boolean type. This means it has to be either True, False, or an expression involving functions that return a boolean result, like =, >, <, >=, <=, !=, And, Not, Or.
Examples:
In> IsBoolean(a)
Out> False;
In> IsBoolean(True)
Out> True;
In> IsBoolean(a And b)
Out> True;

See Also:
True , False ,


Predicates on numbers

These predicates return whether the argument is a number, and of a specific type.


IsNegativeNumber(n)


IsNegativeInteger(n)


IsPositiveNumber(n)


IsPositiveInteger(n)


IsNotZero(n)


IsNonZeroInteger(n)


IsInfinity(n)

Returns True if the argument is either Infinity or -Infinity


IsConstant

Standard math library
Calling Sequence:
IsConstant(expression)
Parameters:
expression - some expression
Description:
IsConstant returns True if the expression is some constant or a function with constant arguments. It does this by checking that no variables are referenced in the expression.
Examples:
In> IsConstant(Cos(x))
Out> False;
In> IsConstant(Cos(2))
Out> True;
In> IsConstant(Cos(2+x))
Out> False;
See Also:
IsNumber , IsInteger ,