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Public Member Functions | Static Public Member Functions | Private Member Functions | Static Private Member Functions | Private Attributes | List of all members
Term Class Reference

Term represents a product of variables which does not include a coefficient. More...

#include <Term.h>

Public Member Functions

 Term ()
 
 Term (const Term &term)
 
 Term (const Exponent *exponents, size_t varCount)
 
 Term (size_t varCount)
 This object is initialized to the identity, i.e. the exponent vector is the zero vector. More...
 
 Term (const string &str)
 Accepts a whitespace-separated list of integers as exponent vector. More...
 
 ~Term ()
 
 operator Exponent * ()
 
 operator const Exponent * () const
 
Exponent * begin ()
 
const Exponent * begin () const
 
Exponent * end ()
 
const Exponent * end () const
 
size_t getVarCount () const
 
Exponent operator[] (int offset) const
 
Exponent operator[] (unsigned int offset) const
 
Exponent operator[] (unsigned long offset) const
 
Exponent operator[] (unsigned long long offset) const
 
Exponent & operator[] (int offset)
 
Exponent & operator[] (unsigned int offset)
 
Exponent & operator[] (unsigned long offset)
 
Exponent & operator[] (unsigned long long offset)
 
bool operator== (const Term &term) const
 
bool operator== (const Exponent *term) const
 
bool operator!= (const Term &term) const
 
bool operator!= (const Exponent *term) const
 
Term & operator= (const Term &term)
 
Term & operator= (const Exponent *exponents)
 
bool divides (const Term &term) const
 
bool divides (const Exponent *term) const
 
bool dominates (const Term &term) const
 
bool dominates (const Exponent *term) const
 
bool strictlyDivides (const Term &term) const
 
bool strictlyDivides (const Exponent *term) const
 
void lcm (const Term &a, const Term &b, int position)
 
void lcm (const Term &a, const Term &b)
 
void lcm (const Exponent *a, const Exponent *b)
 
void gcd (const Term &a, const Term &b)
 
void gcd (const Exponent *a, const Exponent *b)
 
void product (const Term &a, const Term &b)
 Set this object equal to the product of a and b. More...
 
void product (const Exponent *a, const Exponent *b)
 
void setToIdentity ()
 
bool isIdentity () const
 
bool isSquareFree () const
 
size_t getFirstNonZeroExponent () const
 
size_t getMiddleNonZeroExponent () const
 
size_t getFirstMaxExponent () const
 
size_t getMaxExponent () const
 
size_t getSizeOfSupport () const
 
size_t getHashCode () const
 
bool sharesNonZeroExponent (const Exponent *a) const
 
bool sharesNonZeroExponent (const Term &a) const
 
bool hasSameSupport (const Term &a) const
 
bool hasSameSupport (const Exponent *a) const
 
void colon (const Term &a, const Term &b)
 
void colon (const Exponent *a, const Exponent *b)
 
void encodedDual (const Term &dualOf, const Term &point)
 
void encodedDual (const Exponent *dualOf, const Exponent *point)
 
void decrement ()
 
void swap (Term &term)
 
void reset (size_t newVarCount)
 
void clear ()
 
void print (FILE *file) const
 
void print (ostream &out) const
 

Static Public Member Functions

static bool divides (const Exponent *a, const Exponent *b, size_t varCount)
 Returns whether a divides b. More...
 
static bool dominates (const Exponent *a, const Exponent *b, size_t varCount)
 Returns whether a dominates b, i.e. whether b divides a. More...
 
static bool strictlyDivides (const Exponent *a, const Exponent *b, size_t varCount)
 Returns whether a strictly divides b. More...
 
static void lcm (Exponent *res, const Exponent *a, const Exponent *b, size_t varCount)
 Sets res equal to the least commom multiple of a and b. More...
 
static void gcd (Exponent *res, const Exponent *a, const Exponent *b, size_t varCount)
 Sets res equal to the greatest common divisor of a and b. More...
 
static void product (Exponent *res, const Exponent *a, const Exponent *b, size_t varCount)
 Sets res equal to the product of a and b. More...
 
static void setToIdentity (Exponent *res, size_t varCount)
 Set res equal to $1=x^{(0,\ldots,0)}$, i.e. set each entry of res equal to 0. More...
 
static bool isIdentity (const Exponent *a, size_t varCount)
 Returns whether a is 1, i.e. whether all entries of a are 0. More...
 
static bool isSquareFree (const Exponent *a, size_t varCount)
 Returns whether a is square free, i.e. $v_i\leq 1$ for each $i$ where $a=x^v$. More...
 
static size_t getFirstNonZeroExponent (const Exponent *a, size_t varCount)
 Returns least var such that a[var] is non-zero. More...
 
static size_t getMiddleNonZeroExponent (const Exponent *a, size_t varCount)
 Returns a median element of the set of var's such that a[var] is non-zero. More...
 
static size_t getFirstMaxExponent (const Exponent *a, size_t varCount)
 Returns a var such that a[var] >= a[i] for all i. More...
 
static size_t getSizeOfSupport (const Exponent *a, size_t varCount)
 Returns the number of variables $x_i$ such that $x_i$ divides $a$. More...
 
static bool sharesNonZeroExponent (const Exponent *a, const Exponent *b, size_t varCount)
 Returns whether there is some $i$ such that $a_i=b_i>0$. More...
 
static size_t getHashCode (const Exponent *a, size_t varCount)
 
static bool hasSameSupport (const Exponent *a, const Exponent *b, size_t varCount)
 Returns whether $x_i|a\Leftrightarrow x_i|b$ for every variable $x_i$. More...
 
static void colon (Exponent *res, const Exponent *a, const Exponent *b, size_t varCount)
 Sets res equal to $a : b$. More...
 
static void encodedDual (Exponent *res, const Exponent *dualOf, const Exponent *point, size_t varCount)
 The parameter dualOf is interpreted to encode an irreducible ideal, and the dual of that reflected in point is a principal ideal. More...
 
static void decrement (Exponent *a, size_t varCount)
 Decrements each positive entry of a by one. More...
 
static void print (FILE *file, const Exponent *e, size_t varCount)
 Writes e to file in a format suitable for debug output. More...
 
static void print (ostream &out, const Exponent *e, size_t varCount)
 Writes e to out in a format suitable for debug output. More...
 

Private Member Functions

void initialize (const Exponent *exponents, size_t varCount)
 

Static Private Member Functions

static Exponent * allocate (size_t size)
 
static void deallocate (Exponent *p, size_t size)
 

Private Attributes

Exponent * _exponents
 
size_t _varCount
 

Detailed Description

Term represents a product of variables which does not include a coefficient.

This concept is also sometimes called a monomial or power product.

A term is represented as an array of Exponent and an integer indicating the length of the array, i.e. the number of variables. It is sometimes desirable to separate the length from the array, e.g. when representing an array of terms all of the same length, such as in representing the generators of a monomial ideal, in which case representing the length once for each generator would be wasteful. Thus Term has static versions of most methods where the number of variables is a separate parameter. In these cases it is allowed for the exponent array pointer to be null (i.e. equal to 0) if the length is zero.

Most methods on Term are inline to avoid function call overhead. This is significant because these methods tend to be called in the innermost loops of monomial ideal algorithms.

Todo:
Move the inline code out of the class declaration and add them as inline below the class declaration.
Todo:
Duplicate the comments for overloads using the copydoc Doxygen command.
Todo:
Rename term.h to Term.h.

Definition at line 49 of file Term.h.

Constructor & Destructor Documentation

◆ Term() [1/5]

Term::Term ( )
inline

Definition at line 51 of file Term.h.

◆ Term() [2/5]

Term::Term ( const Term &  term)
inline

Definition at line 52 of file Term.h.

◆ Term() [3/5]

Term::Term ( const Exponent *  exponents,
size_t  varCount 
)
inline

Definition at line 53 of file Term.h.

◆ Term() [4/5]

Term::Term ( size_t  varCount)
inline

This object is initialized to the identity, i.e. the exponent vector is the zero vector.

Definition at line 60 of file Term.h.

◆ Term() [5/5]

Term::Term ( const string &  str)

Accepts a whitespace-separated list of integers as exponent vector.

Definition at line 27 of file Term.cpp.

◆ ~Term()

Term::~Term ( )
inline

Definition at line 74 of file Term.h.

Member Function Documentation

◆ allocate()

Exponent * Term::allocate ( size_t  size)
staticprivate

Definition at line 86 of file Term.cpp.

◆ begin() [1/2]

Exponent* Term::begin ( )
inline

Definition at line 79 of file Term.h.

◆ begin() [2/2]

const Exponent* Term::begin ( ) const
inline

Definition at line 80 of file Term.h.

◆ clear()

void Term::clear ( )
inline

Definition at line 562 of file Term.h.

◆ colon() [1/3]

void Term::colon ( const Exponent *  a,
const Exponent *  b 
)
inline

Definition at line 496 of file Term.h.

◆ colon() [2/3]

void Term::colon ( const Term &  a,
const Term &  b 
)
inline

Definition at line 490 of file Term.h.

◆ colon() [3/3]

static void Term::colon ( Exponent *  res,
const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Sets res equal to $a : b$.

$a : b$ is read as "a colon b", and it is defined as $lcm(a, b) / b$.

Definition at line 476 of file Term.h.

◆ deallocate()

void Term::deallocate ( Exponent *  p,
size_t  size 
)
staticprivate

Definition at line 98 of file Term.cpp.

◆ decrement() [1/2]

void Term::decrement ( )
inline

Definition at line 539 of file Term.h.

◆ decrement() [2/2]

static void Term::decrement ( Exponent *  a,
size_t  varCount 
)
inlinestatic

Decrements each positive entry of a by one.

Definition at line 532 of file Term.h.

◆ divides() [1/3]

static bool Term::divides ( const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Returns whether a divides b.

Definition at line 152 of file Term.h.

◆ divides() [2/3]

bool Term::divides ( const Exponent *  term) const
inline

Definition at line 166 of file Term.h.

◆ divides() [3/3]

bool Term::divides ( const Term &  term) const
inline

Definition at line 161 of file Term.h.

◆ dominates() [1/3]

static bool Term::dominates ( const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Returns whether a dominates b, i.e. whether b divides a.

Definition at line 172 of file Term.h.

◆ dominates() [2/3]

bool Term::dominates ( const Exponent *  term) const
inline

Definition at line 187 of file Term.h.

◆ dominates() [3/3]

bool Term::dominates ( const Term &  term) const
inline

Definition at line 182 of file Term.h.

◆ encodedDual() [1/3]

void Term::encodedDual ( const Exponent *  dualOf,
const Exponent *  point 
)
inline

Definition at line 527 of file Term.h.

◆ encodedDual() [2/3]

void Term::encodedDual ( const Term &  dualOf,
const Term &  point 
)
inline

Definition at line 521 of file Term.h.

◆ encodedDual() [3/3]

static void Term::encodedDual ( Exponent *  res,
const Exponent *  dualOf,
const Exponent *  point,
size_t  varCount 
)
inlinestatic

The parameter dualOf is interpreted to encode an irreducible ideal, and the dual of that reflected in point is a principal ideal.

The generated of this ideal is written to res. This requires that dualOf divides point, as otherwise that dual is not defined.

Definition at line 505 of file Term.h.

◆ end() [1/2]

Exponent* Term::end ( )
inline

Definition at line 82 of file Term.h.

◆ end() [2/2]

const Exponent* Term::end ( ) const
inline

Definition at line 83 of file Term.h.

◆ gcd() [1/3]

void Term::gcd ( const Exponent *  a,
const Exponent *  b 
)
inline

Definition at line 275 of file Term.h.

◆ gcd() [2/3]

void Term::gcd ( const Term &  a,
const Term &  b 
)
inline

Definition at line 269 of file Term.h.

◆ gcd() [3/3]

static void Term::gcd ( Exponent *  res,
const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Sets res equal to the greatest common divisor of a and b.

Definition at line 255 of file Term.h.

◆ getFirstMaxExponent() [1/2]

size_t Term::getFirstMaxExponent ( ) const
inline

Definition at line 390 of file Term.h.

◆ getFirstMaxExponent() [2/2]

static size_t Term::getFirstMaxExponent ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Returns a var such that a[var] >= a[i] for all i.

Definition at line 381 of file Term.h.

◆ getFirstNonZeroExponent() [1/2]

size_t Term::getFirstNonZeroExponent ( ) const
inline

Definition at line 354 of file Term.h.

◆ getFirstNonZeroExponent() [2/2]

static size_t Term::getFirstNonZeroExponent ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Returns least var such that a[var] is non-zero.

Returns varCount if the entries of a are all zero.

Definition at line 346 of file Term.h.

◆ getHashCode() [1/2]

size_t Term::getHashCode ( ) const
inline

Definition at line 431 of file Term.h.

◆ getHashCode() [2/2]

static size_t Term::getHashCode ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Definition at line 424 of file Term.h.

◆ getMaxExponent()

size_t Term::getMaxExponent ( ) const
inline

Definition at line 394 of file Term.h.

◆ getMiddleNonZeroExponent() [1/2]

size_t Term::getMiddleNonZeroExponent ( ) const
inline

Definition at line 376 of file Term.h.

◆ getMiddleNonZeroExponent() [2/2]

static size_t Term::getMiddleNonZeroExponent ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Returns a median element of the set of var's such that a[var] is non-zero.

Returns varCount is the entries of a are all zero.

Definition at line 361 of file Term.h.

◆ getSizeOfSupport() [1/2]

size_t Term::getSizeOfSupport ( ) const
inline

Definition at line 411 of file Term.h.

◆ getSizeOfSupport() [2/2]

static size_t Term::getSizeOfSupport ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Returns the number of variables $x_i$ such that $x_i$ divides $a$.

Definition at line 402 of file Term.h.

◆ getVarCount()

size_t Term::getVarCount ( ) const
inline

Definition at line 85 of file Term.h.

◆ hasSameSupport() [1/3]

bool Term::hasSameSupport ( const Exponent *  a) const
inline

Definition at line 468 of file Term.h.

◆ hasSameSupport() [2/3]

static bool Term::hasSameSupport ( const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Returns whether $x_i|a\Leftrightarrow x_i|b$ for every variable $x_i$.

Definition at line 446 of file Term.h.

◆ hasSameSupport() [3/3]

bool Term::hasSameSupport ( const Term &  a) const
inline

Definition at line 463 of file Term.h.

◆ initialize()

void Term::initialize ( const Exponent *  exponents,
size_t  varCount 
)
inlineprivate

Definition at line 587 of file Term.h.

◆ isIdentity() [1/2]

bool Term::isIdentity ( ) const
inline

Definition at line 324 of file Term.h.

◆ isIdentity() [2/2]

static bool Term::isIdentity ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Returns whether a is 1, i.e. whether all entries of a are 0.

Definition at line 316 of file Term.h.

◆ isSquareFree() [1/2]

bool Term::isSquareFree ( ) const
inline

Definition at line 339 of file Term.h.

◆ isSquareFree() [2/2]

static bool Term::isSquareFree ( const Exponent *  a,
size_t  varCount 
)
inlinestatic

Returns whether a is square free, i.e. $v_i\leq 1$ for each $i$ where $a=x^v$.

Definition at line 331 of file Term.h.

◆ lcm() [1/4]

void Term::lcm ( const Exponent *  a,
const Exponent *  b 
)
inline

Definition at line 250 of file Term.h.

◆ lcm() [2/4]

void Term::lcm ( const Term &  a,
const Term &  b 
)
inline

Definition at line 244 of file Term.h.

◆ lcm() [3/4]

void Term::lcm ( const Term &  a,
const Term &  b,
int  position 
)
inline

Definition at line 235 of file Term.h.

◆ lcm() [4/4]

static void Term::lcm ( Exponent *  res,
const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Sets res equal to the least commom multiple of a and b.

Definition at line 221 of file Term.h.

◆ operator const Exponent *()

Term::operator const Exponent * ( ) const
inline

Definition at line 77 of file Term.h.

◆ operator Exponent *()

Term::operator Exponent * ( )
inline

Definition at line 76 of file Term.h.

◆ operator!=() [1/2]

bool Term::operator!= ( const Exponent *  term) const
inline

Definition at line 131 of file Term.h.

◆ operator!=() [2/2]

bool Term::operator!= ( const Term &  term) const
inline

Definition at line 130 of file Term.h.

◆ operator=() [1/2]

Term& Term::operator= ( const Exponent *  exponents)
inline

Definition at line 145 of file Term.h.

◆ operator=() [2/2]

Term& Term::operator= ( const Term &  term)
inline

Definition at line 133 of file Term.h.

◆ operator==() [1/2]

bool Term::operator== ( const Exponent *  term) const

Definition at line 128 of file Term.cpp.

◆ operator==() [2/2]

bool Term::operator== ( const Term &  term) const
inline

Definition at line 125 of file Term.h.

◆ operator[]() [1/8]

Exponent& Term::operator[] ( int  offset)
inline

Definition at line 107 of file Term.h.

◆ operator[]() [2/8]

Exponent Term::operator[] ( int  offset) const
inline

Definition at line 89 of file Term.h.

◆ operator[]() [3/8]

Exponent& Term::operator[] ( unsigned int  offset)
inline

Definition at line 112 of file Term.h.

◆ operator[]() [4/8]

Exponent Term::operator[] ( unsigned int  offset) const
inline

Definition at line 94 of file Term.h.

◆ operator[]() [5/8]

Exponent& Term::operator[] ( unsigned long long  offset)
inline

Definition at line 120 of file Term.h.

◆ operator[]() [6/8]

Exponent Term::operator[] ( unsigned long long  offset) const
inline

Definition at line 102 of file Term.h.

◆ operator[]() [7/8]

Exponent& Term::operator[] ( unsigned long  offset)
inline

Definition at line 116 of file Term.h.

◆ operator[]() [8/8]

Exponent Term::operator[] ( unsigned long  offset) const
inline

Definition at line 98 of file Term.h.

◆ print() [1/4]

void Term::print ( FILE *  file) const
inline

Definition at line 574 of file Term.h.

◆ print() [2/4]

void Term::print ( FILE *  file,
const Exponent *  e,
size_t  varCount 
)
static

Writes e to file in a format suitable for debug output.

Definition at line 110 of file Term.cpp.

◆ print() [3/4]

void Term::print ( ostream &  out) const
inline

Definition at line 578 of file Term.h.

◆ print() [4/4]

void Term::print ( ostream &  out,
const Exponent *  e,
size_t  varCount 
)
static

Writes e to out in a format suitable for debug output.

Definition at line 116 of file Term.cpp.

◆ product() [1/3]

void Term::product ( const Exponent *  a,
const Exponent *  b 
)
inline

Definition at line 297 of file Term.h.

◆ product() [2/3]

void Term::product ( const Term &  a,
const Term &  b 
)
inline

Set this object equal to the product of a and b.

Definition at line 291 of file Term.h.

◆ product() [3/3]

static void Term::product ( Exponent *  res,
const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Sets res equal to the product of a and b.

Definition at line 280 of file Term.h.

◆ reset()

void Term::reset ( size_t  newVarCount)
inline

Definition at line 551 of file Term.h.

◆ setToIdentity() [1/2]

void Term::setToIdentity ( )
inline

Definition at line 310 of file Term.h.

◆ setToIdentity() [2/2]

static void Term::setToIdentity ( Exponent *  res,
size_t  varCount 
)
inlinestatic

Set res equal to $1=x^{(0,\ldots,0)}$, i.e. set each entry of res equal to 0.

Definition at line 304 of file Term.h.

◆ sharesNonZeroExponent() [1/3]

bool Term::sharesNonZeroExponent ( const Exponent *  a) const
inline

Definition at line 435 of file Term.h.

◆ sharesNonZeroExponent() [2/3]

static bool Term::sharesNonZeroExponent ( const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Returns whether there is some $i$ such that $a_i=b_i>0$.

Definition at line 416 of file Term.h.

◆ sharesNonZeroExponent() [3/3]

bool Term::sharesNonZeroExponent ( const Term &  a) const
inline

Definition at line 439 of file Term.h.

◆ strictlyDivides() [1/3]

static bool Term::strictlyDivides ( const Exponent *  a,
const Exponent *  b,
size_t  varCount 
)
inlinestatic

Returns whether a strictly divides b.

$a$ strictly divides $b$ if $a * gcd(a, x_1...x_n)$ divides $b$ and $b\neq 1$, i.e. if, for each $i$, $u_i<b_i$ or $v_i=0$ where $a=x^u$, $b=x^v\neq x^0$.

Definition at line 196 of file Term.h.

◆ strictlyDivides() [2/3]

bool Term::strictlyDivides ( const Exponent *  term) const
inline

Definition at line 216 of file Term.h.

◆ strictlyDivides() [3/3]

bool Term::strictlyDivides ( const Term &  term) const
inline

Definition at line 211 of file Term.h.

◆ swap()

void Term::swap ( Term &  term)
inline

Definition at line 543 of file Term.h.

Member Data Documentation

◆ _exponents

Exponent* Term::_exponents
private

Definition at line 597 of file Term.h.

◆ _varCount

size_t Term::_varCount
private

Definition at line 598 of file Term.h.

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