# Real Functions, Miscellaneous

Ceiling Function: Ceiling(x) = least integer >= x
See: Ceiling Function -- From MathWorld
and Wolfram Function Evaluation

Floor Function: Floor(x) = greatest integer <= x
See: Floor Function -- From MathWorld
and Wolfram Function Evaluation

Sign: Sign(x) = 0 if x = 0, Sign(x) = 1 if x > 0, else Sign(x) = −1.
It is 0 or the unit vector in the same direction as x.

Integer Part: Int(x) = Sign(x)*Floor(|x|)
See: Integer Part -- From MathWorld
and Wolfram Function Evaluation

Fractional Part: Frac(x) = Sign(x)*(|x| − Floor(|x|))
See: Fractional Part -- From MathWorld
and Wolfram Function Evaluation

Round: Round(x) = Integer nearest to x, (Round(6.5) = 7, Round(-6.5) = -7)
See: Nearest Integer Function -- From MathWorld
and Wolfram Function Evaluation

Equal: (x == y) = 1 (True) if x − y is 0, else (x == y) = 0 (False).
See: Equal -- From MathWorld
and Wolfram Mathematica Documentation

NotEqual: (x != y) = (x <> y) = 0 (False) if x − y is 0, else (x != y) = 1 (True).

Less: (x < y) = 1 (True) if x − y is negative, else (x < y) = 0 (False).
See: Less -- From MathWorld
and Wolfram Mathematica Documentation

Greater: (x > y) = 1 (True) if y − x is negative, else (x > y) = 0 (False).

LessEqual: (x <= y) = 1 (True) if (x < y) or (x == y), else (x <= y) = 0 (False).

GreaterEqual: (x >= y) = 1 (True) if (x > y) or (x == y), else (x >= y) = 0 (False).

Maximum: Max(x, y) = x or y,
If x == y, Max(x, y) = x,
Else if x > y, Max(x, y) = x,
Else Max(x, y) = y.
See: Maximum -- From MathWorld
and Wolfram Function Definition

Minimum: Min(x, y) = x or y,
If x == y, Min(x, y) = x,
Else if x > y, Min(x, y) = y,
Else Min(x, y) = x.
See: Minimum -- From MathWorld
and Wolfram Function Definition

Quotient Function: Quotient(x, y) = Floor(x/y),
but y != 0. Remainder Re = x − y * Floor(x/y).
The sign of Re is the same as y. y*Quotient(x, y) + Re = x.
See: Congruence -- From MathWorld
and Wolfram Function Definition

Remainder or Congruence Function: Mod(x, y) = x − y * Floor(x/y),
but y != 0. The sign of Mod(x, y) is the same as y.
This is the remainder of Quotient(x, y). y*Quotient(x, y) + Mod(x, y) = x.
See: Congruence -- From MathWorld
and Wolfram Function Definition

Magnitude Function: Mag(x, y) = SqRt(x^2 + y^2)
Mag(x, y) is Polar coordinates radius coordinate
of the Cartesian coordinates (x, y).
See: Polar Coordinates -- From MathWorld
and Wolfram Function Definition

Absolute value: Abs(x) = |x|, If x >= 0, |x| = x Else |x| = −x.

Negative: −x = 0 − x.

This page accessed times since Feb 14, 2006.
Page created by: hjsmithh@sbcglobal.net
Changes last made on Monday, 06-Aug-07 20:47:25 PDT