modular-arithmetic

This library allows you to perform modular arithmetic on finite fields with arbitrarily large integer moduli.

API

[procedure] (xgcd a b)

Computes the "extended greatest common divisor" of a and b, ie. it returns the two values x and y that constitute the solution of the equation

 x*a + y*b = gcd(a, b)

[procedure] ((mod+ modulus) n ...)

Computes the sum of all n parameters just like the standard procedure + does, but operating on the finite field with the given modulus.

[procedure] ((mod- modulus) a n ...)

Computes the difference of a and all n parameters or the additive inverse of a just like the standard procedure - does, but operating on the finite field with the given modulus.

[procedure] ((mod* modulus) n ...)

Computes the product of all n parameters just like the standard procedure * does, but operating on the finite field with the given modulus.

[procedure] ((mod/ modulus) a n ...)

Computes the quotient of a and all n parameters or the multiplicative inverse of a just like the standard procedure / does, but operating on the finite field with the given modulus.

Note that a unique multiplicative inverse of an element in a finite field only exists if the element and the modulus are coprime. This procedure only works in that case.

[procedure] ((modexpt modulus) a b)

Computes a raised to the power of b modulo the given modulus, but does so far more efficiently than using

 (modulo (* a b) modulus).

If b is negative, the multiplicative inverse of a is raised to the power of (abs b).

[syntax] (with-modulus modulus body ...)

Overloads the symbols +, add1, -, sub1, *, / and expt inside body with the modular versions operating on the finite field with the given modulus instead of the standard arithmetic procedures.

License

 Copyright (c) 2010, Thomas Chust
 All rights reserved.
 
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 * Neither the name of the author nor the names of its contributors may be used to endorse or promote
     products derived from this software without specific prior written permission.
 
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Version history

1.0.1: Fixed borked setup script
1.0.0: Initial release

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