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intmodp Specification Sheet

Computer Algebra Kit (c) 1993,00 by Comp.Alg.Objects. All Rights Reserved.

IntegerModp

Inherits from: CAObject

Maturity Index: Relatively immature

Class Description

Instances are integers modulo a small, prime number, the modulus of the object. The modulus can currently not be equal to two; it must be equal to or less than USHRT_MAX_PRIME (the largest prime number that fits in an unsigned short word, as defined in the header file cakit/IntegerModp.h). Objects belong to the same class in the sense of sameClass: iff. the moduli are equal.

Every integer mod p keeps its own copy of the modulus; you don't need to set a global modulus. As a consequence, it is possible to do multiple calculations modulo a different prime, even concurrenlty.

IntegerModp is the prototype, in the Computer Algebra Kit, of a field i.e., a structure where each (nonzero) element has a multiplicative inverse (see inField and inverse). Matrix (in Gaussian elimination) and Polynomial (in polynomial division) take advantage of the field structure of scalars, such as integers mod p.

Method types

Creation

Identity

Addition

Multiplication

Characteristic

Printing

Methods

modulus:

+modulus:(unsigned short)aPrime
Creates a new object, equal to zero, with modulus equal to aPrime. The modulus must be a prime number less than or equal to USHRT_MAX_PRIME.

int:modulus:

+int:(int)intValuemodulus:(unsigned short)aPrime
Creates a new object with modulus equal to aPrime. The value of the object is equal to intValue mod aPrime. The modulus must be a prime number less than or equal to USHRT_MAX_PRIME.

modulus

- (unsigned short)modulus
Returns the modulus, a prime number equal to or less than USHRT_MAX_PRIME.

intValue

- (int)intValue
Returns a representant of the modular number in the range [0,modulus[.

intValue:

-intValue:(int)aValue
Returns a new object for aValue, modulo the modulus of the receiving object.

zero

-zero

one

-one

minusOne

-minusOne

divide:

-divide:b
Multiplies the object by the inverse of b. Returns nil if b is zero (has no inverse).

characteristic

- (int)characteristic
Returns the modulus of the object.

frobenius

-frobenius
Simply returns a new reference to the object itself, since the p-th power of an integer modulo p is equal to that integer.

frobeniusInverse

-frobeniusInverse
Simply returns a new reference to the object itself, since the p-th power of an integer modulo p is equal to that integer. This method also returns zero for the zero object.

printsLeadingSign

- (BOOL)printsLeadingSign
Returns NO, because representants are taken positive for printing.

printOn:

-printOn:(IOD)aFile
Prints a (nonnegative) representant of the integer modulo p.