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# Mod

 Modgives the remainder on division of m by n. Moduses an offset d.
• 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.
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:
 Out[1]=

Remainders mod 3 offset to start with 1:
 Out[1]=

Plot the sequence with fixed modulus:
 Out[1]=

Plot the sequence, varying the modulus:
 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:
The results have the same sign as the second argument:
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:
Binomial coefficients mod 2:
Mod 4 additive cellular automaton:
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