# 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.

## 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

-one

-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.