Difference between revisions of "Mod"

Revision as of 00:20, 6 August 2016

Mod(x, y, pos)

The remainder (modulus) of «x» / «y».

The sign of the result of Mod(x,y) is the same as the sign of «x» -- i.e., if «x» is negative, then so is the result. The sign of «y» does not impact the sign of the result. This variation is the same convention used by the corresponding operator in C/C++ (ISO 1999), C#, Java, PHP, Visual Basic, AMPL and many other languages. Some languages, including MATLAB, Lisp, Fortran, and Ada, have two different modulo operators, with one corresponding to this convention. The modulo operator in a few other languages, including Mathematica, R and Excel, do not follow this convention (these use the sign of the denominator).

You can specify «pos» as true to force the result to be non-negative, in the range 0 ≤ Mod(x,y) < Abs(y). As «x» increases through all negative and positive numbers, the result cycles through this range.

Mod(x,1) extracts the fractional portion of a number.

Examples

Mod(20,7) → 6

Mod(-20,7) → -6

Mod(-20,-7) → -6

Mod(20,-7) → 6

Mod(-20,7,pos: true) → 1

Mod(Pi,1) → 0.141592653589793

Special uses

IsOdd and IsEven

To test whether an integer x is odd use Mod(x, 2) == 1, and similarly, to test whether an integer is even use Mod(x, 2) == 0.

IsInteger

To test whether a number x is an integer, use Mod(x,1) == 0

@@ Line 6: / Line 6: @@
 The remainder (modulus) of «x» / «y».
-The sign of the result of <code>Mod(x,y></code> is the same as the sign of «x» -- i.e., if «x» is negative, then so is the result. The sign of «y» does not impact the sign of the result. This variation is the same convention used by the corresponding operator in C/C++ (ISO 1999), C#, Java, PHP, Visual Basic, AMPL and many other languages. Some languages, including MATLAB, Lisp, Fortran, and Ada, have two different modulo operators, with one corresponding to this convention. The modulo operator in a few other languages, including Mathematica, R and Excel, do not follow this convention (these use the sign of the denominator).
+The sign of the result of <code>Mod(x,y)</code> is the same as the sign of «x» -- i.e., if «x» is negative, then so is the result. The sign of «y» does not impact the sign of the result. This variation is the same convention used by the corresponding operator in C/C++ (ISO 1999), C#, Java, PHP, Visual Basic, AMPL and many other languages. Some languages, including MATLAB, Lisp, Fortran, and Ada, have two different modulo operators, with one corresponding to this convention. The modulo operator in a few other languages, including Mathematica, R and Excel, do not follow this convention (these use the sign of the denominator).
-You can specify «pos» as true to force the result to be non-negative, in the range <code>0 &le; [[Mod]](x,y) < [[Abs]](y)</code>. As «x» increases through all negative and positive numbers, the result cycles through this range.
+You can specify «pos» as true to force the result to be non-negative, in the range <code>0 &le; Mod(x,y) < Abs(y)</code>. As «x» increases through all negative and positive numbers, the result cycles through this range.
 <code>Mod(x,1)</code> extracts the fractional portion of a number.
@@ Line 18: / Line 18: @@
 :<code>Mod(-20,-7) &rarr; -6</code>
 :<code>Mod(20,-7) &rarr; 6</code>
-:<code>Mod(-20,7,pos:true) &rarr; 1</code>
+:<code>Mod(-20,7,pos: true) &rarr; 1</code>
 :<code>Mod(Pi,1) &rarr; 0.141592653589793</code>
@@ Line 25: / Line 25: @@
 === IsOdd and IsEven ===
-To test whether an integer <code>x</code> is odd use <code>[[Mod]](x,2)=1</code>, and similarly, to test whether an integer is even use <code>[[Mod]](x,2)==0</code>.
+To test whether an integer <code>x</code> is odd use <code>Mod(x, 2) == 1</code>, and similarly, to test whether an integer is even use <code>Mod(x, 2) == 0</code>.
 === IsInteger ===
-To test whether a number <code>x</code> is an integer, use <code>[[Mod]](x,1)==0</code>
+To test whether a number <code>x</code> is an integer, use <code>Mod(x,1) == 0</code>
 ==See Also==
+* [[Abs]]
 * [[GCD]]
+* [[IsNumber]]
 * [[Array Abstraction]]
 * [[Math functions]]