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## modular-arithmetic

Thomas Chust

### Description

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.

``` Copyright (c) 2010, Thomas Chust

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following
conditions are met:

* Redistributions of source code must retain the above copyright notice, this list of conditions and the following
disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following
disclaimer in the documentation and/or other materials provided with the distribution.
* 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.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS
OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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### Version history

1.0.1
Fixed borked setup script
1.0.0
Initial release