Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Mathematical Functions > Integer Functions > Mod >
BUILT-IN MATHEMATICA SYMBOLTutorials »|See Also »|More About »

Mod

Mod
gives the remainder on division of m by n.
Mod
uses an offset d.
MORE INFORMATION
  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • For integers m and n, Mod lies between and n-1.
  • Mod gives a result in the range to n, suitable for use in functions such as Part. »
  • Mod gives a result such that and .
  • The sign of Mod is always the same as the sign of n, at least so long as m and n are both real.
  • The arguments of Mod can be any numeric quantities, not necessarily integers. »
  • For positive x, Mod gives the fractional part of x.
  • For exact numeric quantities, Mod internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
  • Mod works with complex numbers, using its definition in terms of Quotient.
  • Mod automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Remainders mod 3:
Remainders mod 3 offset to start with 1:
Plot the sequence with fixed modulus:
Plot the sequence, varying the modulus:
Remainders mod 3:
In[1]:=
Click for copyable input
Out[1]=
 
Remainders mod 3 offset to start with 1:
In[1]:=
Click for copyable input
Out[1]=
 
Plot the sequence with fixed modulus:
In[1]:=
Click for copyable input
Out[1]=
 
Plot the sequence, varying the modulus:
In[1]:=
Click for copyable input
Out[1]=
Scope   (8)
Reduce an approximate number:
Reduce an exact numeric quantity:
Reduce mod :
Complex number:
Wilson's theorem:
Solve a modular equation:
Evaluate an integral:
Applications   (4)
Extract parts cyclically:
Select primes below 100 having the form of :
Simulate a particle bouncing in a non-commensurate box:
Define a notation for addition mod 2:
Properties & Relations   (2)
The results have the same sign as the second argument:
Possible Issues   (2)
Expressions generated by Mod can be difficult to evaluate with machine precision:
Machine-precision numerical evaluation gives the wrong answer:
Arbitrary precision gives the correct answer:
Some computations may require higher internal precision than the default:
Neat Examples   (3)
Binomial coefficients mod 2:
Mod 4 additive cellular automaton:
New in 1 | Last modified in 4
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF