Predicates relating to numbers

(directly go to documentation on : <, >, <=, >=, IsZero, IsRational. )

# 3. Predicates relating to numbers

< | test for "less than"
> | test for "greater than"
<= | test for "less or equal"
>= | test for "greater or equal"
IsZero | test whether argument is zero
IsRational | test whether argument is a rational

###

< -- test for "less than"

##### Standard library

##### Calling format:

    e1 < e2

Precedence: 90

##### Parameters:

`e1`, `e2` -- expressions to be compared

##### Description:

The two expression are evaluated. If both results are numeric, they are compared. If the first expression is smaller than the second one, the result is `True` and it is `False` otherwise. If either of the expression is not numeric, after evaluation, the expression is returned with evaluated arguments.

The word "numeric" in the previous paragraph has the following meaning. An expression is numeric if it is either a number (i.e. `IsNumber` returns `True`), or the quotient of two numbers, or an infinity (i.e. `IsInfinity` returns `True`). Yacas will try to coerce the arguments passed to this comparison operator to a real value before making the comparison.

##### Examples:

    In> 2 < 5;
    Out> True;
    In> Cos(1) < 5;
    Out> True;

##### See also:

IsNumber , IsInfinity , N .

###

> -- test for "greater than"

##### Standard library

##### Calling format:

    e1 > e2

Precedence: 90

##### Parameters:

`e1`, `e2` -- expressions to be compared

##### Description:

The two expression are evaluated. If both results are numeric, they are compared. If the first expression is larger than the second one, the result is `True` and it is `False` otherwise. If either of the expression is not numeric, after evaluation, the expression is returned with evaluated arguments.

The word "numeric" in the previous paragraph has the following meaning. An expression is numeric if it is either a number (i.e. `IsNumber` returns `True`), or the quotient of two numbers, or an infinity (i.e. `IsInfinity` returns `True`). Yacas will try to coerce the arguments passed to this comparison operator to a real value before making the comparison.

##### Examples:

    In> 2 > 5;
    Out> False;
    In> Cos(1) > 5;
    Out> False

##### See also:

IsNumber , IsInfinity , N .

###

<= -- test for "less or equal"

##### Standard library

##### Calling format:

    e1 <= e2

Precedence: 90

##### Parameters:

`e1`, `e2` -- expressions to be compared

##### Description:

The two expression are evaluated. If both results are numeric, they are compared. If the first expression is smaller than or equals the second one, the result is `True` and it is `False` otherwise. If either of the expression is not numeric, after evaluation, the expression is returned with evaluated arguments.

The word "numeric" in the previous paragraph has the following meaning. An expression is numeric if it is either a number (i.e. `IsNumber` returns `True`), or the quotient of two numbers, or an infinity (i.e. `IsInfinity` returns `True`). Yacas will try to coerce the arguments passed to this comparison operator to a real value before making the comparison.

##### Examples:

    In> 2 <= 5;
    Out> True;
    In> Cos(1) <= 5;
    Out> True

##### See also:

IsNumber , IsInfinity , N .

###

>= -- test for "greater or equal"

##### Standard library

##### Calling format:

    e1 >= e2

Precedence: 90

##### Parameters:

`e1`, `e2` -- expressions to be compared

##### Description:

The two expression are evaluated. If both results are numeric, they are compared. If the first expression is larger than or equals the second one, the result is `True` and it is `False` otherwise. If either of the expression is not numeric, after evaluation, the expression is returned with evaluated arguments.

The word "numeric" in the previous paragraph has the following meaning. An expression is numeric if it is either a number (i.e. `IsNumber` returns `True`), or the quotient of two numbers, or an infinity (i.e. `IsInfinity` returns `True`). Yacas will try to coerce the arguments passed to this comparison operator to a real value before making the comparison.

##### Examples:

    In> 2 >= 5;
    Out> False;
    In> Cos(1) >= 5;
    Out> False

##### See also:

IsNumber , IsInfinity , N .

###

IsZero -- test whether argument is zero

##### Standard library

##### Calling format:

    IsZero(n)

##### Parameters:

`n` -- number to test

##### Description:

`IsZero(n)` evaluates to `True` if "n" is zero. In case "n" is not a number, the function returns `False`.

##### Examples:

    In> IsZero(3.25)
    Out> False;
    In> IsZero(0)
    Out> True;
    In> IsZero(x)
    Out> False;

##### See also:

IsNumber , IsNotZero .

###

IsRational -- test whether argument is a rational

##### Standard library

##### Calling format:

    IsRational(expr)

##### Parameters:

`expr` -- expression to test

##### Description:

This commands tests whether the expression "expr" is a rational number, i.e. an integer or a fraction of integers.

##### Examples:

    In> IsRational(5)
    Out> False;
    In> IsRational(2/7)
    Out> True;
    In> IsRational(0.5)
    Out> False;
    In> IsRational(a/b)
    Out> False;
    In> IsRational(x + 1/x)
    Out> False;

##### See also:

Numer , Denom .