---
name: "IntegerModp"
section: "3poc"
platform: "linux"
package: "objc-poc"
version: "3.1.26-2"
release: "Debian 3.0 (Woody)"
platforms: ["linux"]
url: "https://new.carta.tech/IntegerModp/3poc"
---

# IntegerModp(3poc)

Portable Object Compiler IntegerModp class

## NAME

IntegerModp - Portable Object Compiler IntegerModp class

## 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**

\* modulus:\
 \* int:modulus:

**Identity**

\* hash\
 \* isEqual:\
 \* modulus\
 \* intValue\
 \* intValue:

**Addition**

\* zero\
 \* isZero\
 \* isOpposite:\
 \* negate\
 \* double\
 \* add:\
 \* subtract:

**Multiplication**

\* one\
 \* minusOne\
 \* isOne\
 \* isMinusOne\
 \* square\
 \* multiply:\
 \* inverse\
 \* divide:

**Characteristic**

\* characteristic\
 \* frobenius\
 \* frobeniusInverse

**Printing**

\* printsLeadingSign\
 \* printOn:

## 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 greater than 2 and less than or equal to USHRT\_MAX\_PRIME.

int:modulus:

\+ **int** :(int) *intValue* **modulus** :(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 greater than 2 and less than or equal to USHRT\_MAX\_PRIME.

modulus

\- ( unsigned short ) **modulus**

Returns the modulus, a prime number greater than 2 and 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.