
intmodp Specification SheetComputer Algebra Kit (c) 1993,00 by Comp.Alg.Objects. All Rights Reserved.
IntegerModpInherits from: CAObjectMaturity Index: Relatively immature
Class DescriptionInstances 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 typesCreationIdentityAdditionMultiplicationCharacteristicPrintingMethodsmodulus:+modulus:(unsigned short)aPrimeCreates 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)aPrimeCreates 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)modulusReturns the modulus, a prime number equal to or less than USHRT_MAX_PRIME.
intValue (int)intValueReturns a representant of the modular number in the range [0,modulus[.
intValue:intValue:(int)aValueReturns a new object for aValue, modulo the modulus of the receiving object.
zerozero oneone minusOneminusOne divide:divide:bMultiplies the object by the inverse of b. Returns nil if b is zero (has no inverse).
characteristic (int)characteristicReturns the modulus of the object.
frobeniusfrobeniusSimply returns a new reference to the object itself, since the pth power of an integer modulo p is equal to that integer.
frobeniusInversefrobeniusInverseSimply returns a new reference to the object itself, since the pth power of an integer modulo p is equal to that integer. This method also returns zero for the zero object.
printsLeadingSign (BOOL)printsLeadingSignReturns NO, because representants are taken positive for printing.
printOn:printOn:(IOD)aFilePrints a (nonnegative) representant of the integer modulo p.
