.TH "intmodp" 3 "Oct 12, 2003"
.SH IntegerModp
.PP
.B
Inherits from:

CAObject
.PP
.B
Maturity Index:

Relatively immature
.SH Class Description
.PP
Instances are integers modulo a small, prime number, the 
.I
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 
.B
unsigned short
word, as defined in the header file cakit/IntegerModp\&.h)\&.  Objects belong to the same class in the sense of 
.B
sameClass:
iff\&. the moduli are equal\&.
.PP
Every integer mod 
.I
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\&.
.PP
IntegerModp is the prototype, in the Computer Algebra Kit, of a 
.I
field
i\&.e\&., a structure where each (nonzero) element has a multiplicative inverse (see 
.B
inField
and 
.B
inverse
)\&.  Matrix (in Gaussian elimination) and Polynomial (in polynomial division) take advantage of the field structure of scalars, such as integers mod p\&.
.SH Method types
.PP 
.B
Creation
.RS 3
.br
* modulus:
.br
* int:modulus:
.RE
.PP 
.B
Identity
.RS 3
.br
* hash
.br
* isEqual:
.br
* modulus
.br
* intValue
.br
* intValue:
.RE
.PP 
.B
Addition
.RS 3
.br
* zero
.br
* isZero
.br
* isOpposite:
.br
* negate
.br
* double
.br
* add:
.br
* subtract:
.RE
.PP 
.B
Multiplication
.RS 3
.br
* one
.br
* minusOne
.br
* isOne
.br
* isMinusOne
.br
* square
.br
* multiply:
.br
* inverse
.br
* divide:
.RE
.PP 
.B
Characteristic
.RS 3
.br
* characteristic
.br
* frobenius
.br
* frobeniusInverse
.RE
.PP 
.B
Printing
.RS 3
.br
* printsLeadingSign
.br
* printOn:
.RE
.SH Methods
.PP 
modulus:
.RS 1
+
.B
modulus
:(unsigned short)
.I
aPrime
.RE
.PP
Creates a new object, equal to zero, with modulus equal to 
.I
aPrime
\&.  The modulus must be a prime number less than or equal to USHRT_MAX_PRIME\&.
.PP 
int:modulus:
.RS 1
+
.B
int
:(int)
.I
intValue
.B
modulus
:(unsigned short)
.I
aPrime
.RE
.PP
Creates a new object with modulus equal to 
.I
aPrime
\&.  The value of the object is equal to 
.I
intValue
mod 
.I
aPrime
\&.  The modulus must be a prime number less than or equal to USHRT_MAX_PRIME\&.
.PP 
hash
.RS 1
- (
unsigned
)
.B
hash
.RE
.PP
Returns a small integer that is the same for objects that are equal (in the sense of 
.B
isEqual:
)\&.
.PP 
isEqual:
.RS 1
- (
BOOL
)
.B
isEqual
:
.I
b
.RE
.PP 
modulus
.RS 1
- (
unsigned short
)
.B
modulus
.RE
.PP
Returns the modulus, a prime number equal to or less than USHRT_MAX_PRIME\&.
.PP 
intValue
.RS 1
- (
int
)
.B
intValue
.RE
.PP
Returns a representant of the modular number in the range [0,modulus[\&.
.PP 
intValue:
.RS 1
-
.B
intValue
:(int)
.I
aValue
.RE
.PP
Returns a new object for 
.I
aValue
, modulo the modulus of the receiving object\&.  
.PP 
zero
.RS 1
-
.B
zero
.RE
.PP 
isZero
.RS 1
- (
BOOL
)
.B
isZero
.RE
.PP
Whether the object is equal to zero\&.
.PP 
isOpposite:
.RS 1
- (
BOOL
)
.B
isOpposite
:
.I
b
.RE
.PP
Whether the object is the opposite of 
.I
b
\&.
.PP 
negate
.RS 1
-
.B
negate
.RE
.PP
Returns the opposite of the object\&.
.PP 
double
.RS 1
-
.B
double
.RE
.PP
Returns a new object, equal to the object multiplied by two i\&.e\&., added to itself\&.
.PP 
add:
.RS 1
-
.B
add
:
.I
b
.RE
.PP
Adds 
.I
b
to the object\&.  Returns a new object\&.
.PP 
subtract:
.RS 1
-
.B
subtract
:
.I
b
.RE
.PP
Subtracts 
.I
b
from the object\&.  Returns a new object\&.
.PP 
one
.RS 1
-
.B
one
.RE
.PP 
minusOne
.RS 1
-
.B
minusOne
.RE
.PP 
isOne
.RS 1
- (
BOOL
)
.B
isOne
.RE
.PP
Whether the object is equal to one\&.
.PP 
isMinusOne
.RS 1
- (
BOOL
)
.B
isMinusOne
.RE
.PP
Whether the object is equal to minus one\&.
.PP 
square
.RS 1
-
.B
square
.RE
.PP
Returns the square of the object i\&.e\&., a new object equal to the original object multiplied by itself\&.
.PP 
multiply:
.RS 1
-
.B
multiply
:
.I
b
.RE
.PP
Returns a new object, the product of the object multiplied (to the right) by 
.I
b
\&.  If the objects are pointer equal, this method is equivalent to 
.B
square
\&.
.PP 
inverse
.RS 1
-
.B
inverse
.RE
.PP
Returns the multiplicative inverse of the object (returns a new object)\&.  Returns 
.B
nil
if the object is equal to zero or cannot be inverted\&.
.PP 
divide:
.RS 1
-
.B
divide
:
.I
b
.RE
.PP
Multiplies the object by the inverse of 
.I
b
\&.  Returns 
.B
nil
if 
.I
b
is zero (has no inverse)\&.
.PP 
characteristic
.RS 1
- (
int
)
.B
characteristic
.RE
.PP
Returns the modulus of the object\&.
.PP 
frobenius
.RS 1
-
.B
frobenius
.RE
.PP
Simply returns a new reference to the object itself, since the 
.I
p
-th power of an integer modulo 
.I
p
is equal to that integer\&.
.PP 
frobeniusInverse
.RS 1
-
.B
frobeniusInverse
.RE
.PP
Simply returns a new reference to the object itself, since the 
.I
p
-th power of an integer modulo 
.I
p
is equal to that integer\&.  This method also returns zero for the zero object\&.
.PP 
printsLeadingSign
.RS 1
- (
BOOL
)
.B
printsLeadingSign
.RE
.PP
Returns NO, because representants are taken positive for printing\&.
.PP 
printOn:
.RS 1
-
.B
printOn
:(IOD)
.I
aFile
.RE
.PP
Prints a (nonnegative) representant of the integer modulo p\&.