canonicalform.h File Reference

Header for factory's main class CanonicalForm. More...

#include <iostream>
#include <stdint.h>
#include "cf_defs.h"
#include "variable.h"
#include "factory/cf_gmp.h"
#include "factory/templates/ftmpl_list.h"
#include "factory/templates/ftmpl_array.h"
#include "factory/templates/ftmpl_afactor.h"
#include "factory/templates/ftmpl_factor.h"
#include "factory/templates/ftmpl_matrix.h"
#include "si_log2.h"
#include "omalloc/omallocClass.h"
#include "cf_inline.cc"

Go to the source code of this file.

Data Structures
class	CanonicalForm
	factory's main class More...

Macros
#define	OSTREAM   std::ostream
#define	ISTREAM   std::istream
#define	CF_INLINE
#define	CF_NO_INLINE
#define	CF_INLINE   inline

Typedefs
typedef AFactor< CanonicalForm >	CFAFactor
typedef List< CFAFactor >	CFAFList
typedef ListIterator< CFAFactor >	CFAFListIterator
typedef Factor< CanonicalForm >	CFFactor
typedef List< CFFactor >	CFFList
typedef ListIterator< CFFactor >	CFFListIterator
typedef List< CanonicalForm >	CFList
typedef ListIterator< CanonicalForm >	CFListIterator
typedef Array< CanonicalForm >	CFArray
typedef Matrix< CanonicalForm >	CFMatrix
typedef List< CFList >	ListCFList
typedef ListIterator< CFList >	ListCFListIterator
typedef List< int >	IntList
typedef ListIterator< int >	IntListIterator
typedef List< Variable >	Varlist
typedef ListIterator< Variable >	VarlistIterator
typedef Array< int >	Intarray

Functions
int	is_imm (const InternalCF *const ptr)
CF_INLINE CanonicalForm	operator+ (const CanonicalForm &, const CanonicalForm &)
	CF_INLINE CanonicalForm operator +, -, *, /, % ( const CanonicalForm & lhs, const CanonicalForm & rhs ) More...
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm	operator- (const CanonicalForm &, const CanonicalForm &)
CF_INLINE CanonicalForm	operator* (const CanonicalForm &, const CanonicalForm &)
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm	operator/ (const CanonicalForm &, const CanonicalForm &)
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm	operator% (const CanonicalForm &, const CanonicalForm &)
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm	div (const CanonicalForm &, const CanonicalForm &)
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm	mod (const CanonicalForm &, const CanonicalForm &)
CanonicalForm FACTORY_PUBLIC	blcm (const CanonicalForm &f, const CanonicalForm &g)
CanonicalForm FACTORY_PUBLIC	power (const CanonicalForm &f, int n)
	exponentiation More...
CanonicalForm FACTORY_PUBLIC	power (const Variable &v, int n)
	exponentiation More...
CanonicalForm FACTORY_PUBLIC	gcd (const CanonicalForm &, const CanonicalForm &)
CanonicalForm FACTORY_PUBLIC	gcd_poly (const CanonicalForm &f, const CanonicalForm &g)
	CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) More...
CanonicalForm FACTORY_PUBLIC	lcm (const CanonicalForm &, const CanonicalForm &)
	CanonicalForm lcm ( const CanonicalForm & f, const CanonicalForm & g ) More...
CanonicalForm FACTORY_PUBLIC	pp (const CanonicalForm &)
	CanonicalForm pp ( const CanonicalForm & f ) More...
CanonicalForm FACTORY_PUBLIC	content (const CanonicalForm &)
	CanonicalForm content ( const CanonicalForm & f ) More...
CanonicalForm FACTORY_PUBLIC	content (const CanonicalForm &, const Variable &)
	CanonicalForm content ( const CanonicalForm & f, const Variable & x ) More...
CanonicalForm FACTORY_PUBLIC	icontent (const CanonicalForm &f)
	CanonicalForm icontent ( const CanonicalForm & f ) More...
CanonicalForm FACTORY_PUBLIC	vcontent (const CanonicalForm &f, const Variable &x)
	CanonicalForm vcontent ( const CanonicalForm & f, const Variable & x ) More...
CanonicalForm FACTORY_PUBLIC	swapvar (const CanonicalForm &, const Variable &, const Variable &)
	swapvar() - swap variables x1 and x2 in f. More...
CanonicalForm FACTORY_PUBLIC	replacevar (const CanonicalForm &, const Variable &, const Variable &)
	CanonicalForm replacevar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 ) More...
int	getNumVars (const CanonicalForm &f)
	int getNumVars ( const CanonicalForm & f ) More...
CanonicalForm	getVars (const CanonicalForm &f)
	CanonicalForm getVars ( const CanonicalForm & f ) More...
CanonicalForm	apply (const CanonicalForm &f, void(*mf)(CanonicalForm &, int &))
	CanonicalForm apply ( const CanonicalForm & f, void (*mf)( CanonicalForm &, int & ) ) More...
CanonicalForm	mapdomain (const CanonicalForm &f, CanonicalForm(*mf)(const CanonicalForm &))
	CanonicalForm mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) ) More...
int *	degrees (const CanonicalForm &f, int *degs=0)
	int * degrees ( const CanonicalForm & f, int * degs ) More...
int	totaldegree (const CanonicalForm &f)
	int totaldegree ( const CanonicalForm & f ) More...
int	totaldegree (const CanonicalForm &f, const Variable &v1, const Variable &v2)
	int totaldegree ( const CanonicalForm & f, const Variable & v1, const Variable & v2 ) More...
int	size (const CanonicalForm &f, const Variable &v)
	int size ( const CanonicalForm & f, const Variable & v ) More...
int	size (const CanonicalForm &f)
	int size ( const CanonicalForm & f ) More...
int	size_maxexp (const CanonicalForm &f, int &maxexp)
CanonicalForm	reduce (const CanonicalForm &f, const CanonicalForm &M)
	polynomials in M.mvar() are considered coefficients M univariate monic polynomial the coefficients of f are reduced modulo M More...
bool	hasFirstAlgVar (const CanonicalForm &f, Variable &a)
	check if poly f contains an algebraic variable a More...
CanonicalForm	leftShift (const CanonicalForm &F, int n)
	left shift the main variable of F by n More...
CanonicalForm	lc (const CanonicalForm &f)
CanonicalForm	Lc (const CanonicalForm &f)
CanonicalForm	LC (const CanonicalForm &f)
CanonicalForm	LC (const CanonicalForm &f, const Variable &v)
int	degree (const CanonicalForm &f)
int	degree (const CanonicalForm &f, const Variable &v)
int	taildegree (const CanonicalForm &f)
CanonicalForm	tailcoeff (const CanonicalForm &f)
CanonicalForm	tailcoeff (const CanonicalForm &f, const Variable &v)
int	level (const CanonicalForm &f)
Variable	mvar (const CanonicalForm &f)
CanonicalForm	num (const CanonicalForm &f)
CanonicalForm	den (const CanonicalForm &f)
int	sign (const CanonicalForm &a)
CanonicalForm	deriv (const CanonicalForm &f, const Variable &x)
CanonicalForm	sqrt (const CanonicalForm &a)
int	ilog2 (const CanonicalForm &a)
CanonicalForm	mapinto (const CanonicalForm &f)
CanonicalForm	head (const CanonicalForm &f)
int	headdegree (const CanonicalForm &f)
void FACTORY_PUBLIC	setCharacteristic (int c)
void	setCharacteristic (int c, int n)
void	setCharacteristic (int c, int n, char name)
int FACTORY_PUBLIC	getCharacteristic ()
int	getGFDegree ()
CanonicalForm	getGFGenerator ()
void FACTORY_PUBLIC	On (int)
	switches More...
void FACTORY_PUBLIC	Off (int)
	switches More...
bool FACTORY_PUBLIC	isOn (int)
	switches More...

Detailed Description

Header for factory's main class CanonicalForm.

Definition in file canonicalform.h.

Macro Definition Documentation

CF_INLINE [1/2]

#define CF_INLINE

Definition at line 54 of file canonicalform.h.

CF_INLINE [2/2]

#define CF_INLINE   inline

Definition at line 54 of file canonicalform.h.

CF_NO_INLINE

#define CF_NO_INLINE

Definition at line 47 of file canonicalform.h.

ISTREAM

#define ISTREAM   std::istream

Definition at line 17 of file canonicalform.h.

OSTREAM

#define OSTREAM   std::ostream

Definition at line 16 of file canonicalform.h.

Typedef Documentation

CFAFactor

typedef AFactor<CanonicalForm> CFAFactor

Definition at line 389 of file canonicalform.h.

CFAFList

typedef List<CFAFactor> CFAFList

Definition at line 390 of file canonicalform.h.

CFAFListIterator

typedef ListIterator<CFAFactor> CFAFListIterator

Definition at line 391 of file canonicalform.h.

CFArray

typedef Array<CanonicalForm> CFArray

Definition at line 397 of file canonicalform.h.

CFFactor

typedef Factor<CanonicalForm> CFFactor

Definition at line 392 of file canonicalform.h.

CFFList

typedef List<CFFactor> CFFList

Definition at line 393 of file canonicalform.h.

CFFListIterator

typedef ListIterator<CFFactor> CFFListIterator

Definition at line 394 of file canonicalform.h.

CFList

typedef List<CanonicalForm> CFList

Definition at line 395 of file canonicalform.h.

CFListIterator

typedef ListIterator<CanonicalForm> CFListIterator

Definition at line 396 of file canonicalform.h.

CFMatrix

typedef Matrix<CanonicalForm> CFMatrix

Definition at line 398 of file canonicalform.h.

Intarray

typedef Array<int> Intarray

Definition at line 405 of file canonicalform.h.

IntList

typedef List<int> IntList

Definition at line 401 of file canonicalform.h.

IntListIterator

typedef ListIterator<int> IntListIterator

Definition at line 402 of file canonicalform.h.

ListCFList

typedef List<CFList> ListCFList

Definition at line 399 of file canonicalform.h.

ListCFListIterator

typedef ListIterator<CFList> ListCFListIterator

Definition at line 400 of file canonicalform.h.

Varlist

typedef List<Variable> Varlist

Definition at line 403 of file canonicalform.h.

VarlistIterator

typedef ListIterator<Variable> VarlistIterator

Definition at line 404 of file canonicalform.h.

Function Documentation

apply()

CanonicalForm apply	(	const CanonicalForm &	f,
		void(*)(CanonicalForm &, int &)	mf
	)

CanonicalForm apply ( const CanonicalForm & f, void (*mf)( CanonicalForm &, int & ) )

apply() - apply mf to terms of f.

Calls mf( f[i], i ) for each term f[i]*x^i of f and builds a new term from the result. If f is in a coefficient domain, mf( f, i ) should result in an i == 0, since otherwise it is not clear which variable to use for the resulting term.

An example:

void
diff( CanonicalForm & f, int & i )
{
   f = f * i;
   if ( i > 0 ) i--;
}

Then apply( f, diff ) is differentiation of f with respect to the main variable of f.

Definition at line 402 of file cf_ops.cc.

{
    if ( f.inCoeffDomain() )
    {
        int exp = 0;
        CanonicalForm result = f;
        mf( result, exp );
        ASSERT( exp == 0, "illegal result, do not know what variable to use" );
        return result;
    }
    else
    {
        CanonicalForm result, coeff;
        CFIterator i;
        int exp;
        Variable x = f.mvar();
        for ( i = f; i.hasTerms(); i++ )
        {
            coeff = i.coeff();
            exp = i.exp();
            mf( coeff, exp );
            if ( ! coeff.isZero() )
                result += power( x, exp ) * coeff;
        }
        return result;
    }
}

blcm()

CanonicalForm FACTORY_PUBLIC blcm	(	const CanonicalForm &	f,
		const CanonicalForm &	g
	)

Definition at line 1816 of file canonicalform.cc.

{
    if ( f.isZero() || g.isZero() )
        return CanonicalForm( 0L );
/*
    else if (f.isOne())
        return g;
    else if (g.isOne())
        return f;
*/
    else
        return (f / bgcd( f, g )) * g;
}

content() [1/2]

CanonicalForm FACTORY_PUBLIC content

(

const CanonicalForm &

f

)

CanonicalForm content ( const CanonicalForm & f )

content() - return content(f) with respect to main variable.

Normalizes result.

Definition at line 603 of file cf_gcd.cc.

{
    if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) )
    {
        CFIterator i = f;
        CanonicalForm result = abs( i.coeff() );
        i++;
        while ( i.hasTerms() && ! result.isOne() )
        {
            result = gcd( i.coeff(), result );
            i++;
        }
        return result;
    }
    else
        return abs( f );
}

content() [2/2]

CanonicalForm FACTORY_PUBLIC content	(	const CanonicalForm &	f,
		const Variable &	x
	)

CanonicalForm content ( const CanonicalForm & f, const Variable & x )

content() - return content(f) with respect to x.

x should be a polynomial variable.

Definition at line 629 of file cf_gcd.cc.

{
    if (f.inBaseDomain()) return f;
    ASSERT( x.level() > 0, "cannot calculate content with respect to algebraic variable" );
    Variable y = f.mvar();
 
    if ( y == x )
        return cf_content( f, 0 );
    else  if ( y < x )
        return f;
    else
        return swapvar( content( swapvar( f, y, x ), y ), y, x );
}

degree() [1/2]

int degree ( const CanonicalForm &  f )

inline

Definition at line 316 of file canonicalform.h.

{ return f.degree(); }

degree() [2/2]

int degree ( const CanonicalForm &  f, const Variable &  v  )

inline

Definition at line 319 of file canonicalform.h.

{ return f.degree( v ); }

degrees()

int * degrees	(	const CanonicalForm &	f,
		int *	degs
	)

int * degrees ( const CanonicalForm & f, int * degs )

degress() - return the degrees of all polynomial variables in f.

Returns 0 if f is in a coefficient domain, the degrees of f in all its polynomial variables in an array of int otherwise:

degrees( f, 0 )[i] = degree( f, Variable(i) )

If degs is not the zero pointer the degrees are stored in this array. In this case degs should be larger than the level of f. If degs is the zero pointer, an array of sufficient size is allocated automatically.

Definition at line 493 of file cf_ops.cc.

{
    if ( f.inCoeffDomain() )
    {
        if (degs != 0)
          return degs;
        else
          return 0;
    }
    else
    {
        int level = f.level();
        if ( degs == NULL )
            degs = NEW_ARRAY(int,level+1);
        for ( int i = level; i >= 0; i-- )
            degs[i] = 0;
        degreesRec( f, degs );
        return degs;
    }
}

den()

CanonicalForm den ( const CanonicalForm &  f )

inline

Definition at line 340 of file canonicalform.h.

{ return f.den(); }

deriv()

CanonicalForm deriv ( const CanonicalForm &  f, const Variable &  x  )

inline

Definition at line 346 of file canonicalform.h.

{ return f.deriv( x ); }

div()

CF_NO_INLINE FACTORY_PUBLIC CanonicalForm div	(	const CanonicalForm &	,
		const CanonicalForm &
	)

gcd()

CanonicalForm FACTORY_PUBLIC gcd	(	const CanonicalForm &	f,
		const CanonicalForm &	g
	)

Definition at line 685 of file cf_gcd.cc.

{
    bool b = f.isZero();
    if ( b || g.isZero() )
    {
        if ( b )
            return abs( g );
        else
            return abs( f );
    }
    if ( f.inPolyDomain() || g.inPolyDomain() )
    {
        if ( f.mvar() != g.mvar() )
        {
            if ( f.mvar() > g.mvar() )
                return cf_content( f, g );
            else
                return cf_content( g, f );
        }
        if (isOn(SW_USE_QGCD))
        {
          Variable m;
          if (
          (getCharacteristic() == 0) &&
          (hasFirstAlgVar(f,m) || hasFirstAlgVar(g,m))
          )
          {
            bool on_rational = isOn(SW_RATIONAL);
            CanonicalForm r=QGCD(f,g);
            On(SW_RATIONAL);
            CanonicalForm cdF = bCommonDen( r );
            if (!on_rational) Off(SW_RATIONAL);
            return cdF*r;
          }
        }
 
        if ( f.inExtension() && getReduce( f.mvar() ) )
            return CanonicalForm(1);
        else
        {
            if ( fdivides( f, g ) )
                return abs( f );
            else  if ( fdivides( g, f ) )
                return abs( g );
            if ( !( getCharacteristic() == 0 && isOn( SW_RATIONAL ) ) )
            {
                CanonicalForm d;
                d = gcd_poly( f, g );
                return abs( d );
            }
            else
            {
                CanonicalForm cdF = bCommonDen( f );
                CanonicalForm cdG = bCommonDen( g );
                CanonicalForm F = f * cdF, G = g * cdG;
                Off( SW_RATIONAL );
                CanonicalForm l = gcd_poly( F, G );
                On( SW_RATIONAL );
                return abs( l );
            }
        }
    }
    if ( f.inBaseDomain() && g.inBaseDomain() )
        return bgcd( f, g );
    else
        return 1;
}

gcd_poly()

CanonicalForm FACTORY_PUBLIC gcd_poly	(	const CanonicalForm &	f,
		const CanonicalForm &	g
	)

CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g )

gcd_poly() - calculate polynomial gcd.

This is the dispatcher for polynomial gcd calculation. Different gcd variants get called depending the input, characteristic, and on switches (cf_defs.h)

With the current settings from Singular (i.e. SW_USE_EZGCD= on, SW_USE_EZGCD_P= on, SW_USE_CHINREM_GCD= on, the EZ GCD variants are the default algorithms for multivariate polynomial GCD computations)

See also

gcd(), cf_defs.h

Definition at line 492 of file cf_gcd.cc.

{
  CanonicalForm fc, gc;
  bool fc_isUnivariate=f.isUnivariate();
  bool gc_isUnivariate=g.isUnivariate();
  bool fc_and_gc_Univariate=fc_isUnivariate && gc_isUnivariate;
  fc = f;
  gc = g;
  int ch=getCharacteristic();
  if ( ch != 0 )
  {
    if (0) {} // dummy, to be able to build without NTL and FLINT
    #if defined(HAVE_FLINT) && ( __FLINT_RELEASE >= 20503)
    if ( isOn( SW_USE_FL_GCD_P)
    && (CFFactory::gettype() != GaloisFieldDomain)
    #ifdef HAVE_NTL
    && (ch>10) // if we have NTL: it is better for char <11
    #endif
    &&(!hasAlgVar(fc)) && (!hasAlgVar(gc)))
    {
      return gcdFlintMP_Zp(fc,gc);
    }
    #endif
    #ifdef HAVE_NTL
    if ((!fc_and_gc_Univariate) && (isOn( SW_USE_EZGCD_P )))
    {
      fc= EZGCD_P (fc, gc);
    }
    #endif
    #if defined(HAVE_NTL) || defined(HAVE_FLINT)
    else if (isOn(SW_USE_FF_MOD_GCD) && !fc_and_gc_Univariate)
    {
      Variable a;
      if (hasFirstAlgVar (fc, a) || hasFirstAlgVar (gc, a))
        fc=modGCDFq (fc, gc, a);
      else if (CFFactory::gettype() == GaloisFieldDomain)
        fc=modGCDGF (fc, gc);
      else
        fc=modGCDFp (fc, gc);
    }
    #endif
    else
    fc = gcd_poly_p( fc, gc );
  }
  else if (!fc_and_gc_Univariate) /* && char==0*/
  {
    #if defined(HAVE_FLINT) && ( __FLINT_RELEASE >= 20503)
    if (( isOn( SW_USE_FL_GCD_0) )
    &&(!hasAlgVar(fc)) && (!hasAlgVar(gc)))
    {
      return gcdFlintMP_QQ(fc,gc);
    }
    else
    #endif
    #ifdef HAVE_NTL
    if ( isOn( SW_USE_EZGCD ) )
      fc= ezgcd (fc, gc);
    else
    #endif
    #if defined(HAVE_NTL) || defined(HAVE_FLINT)
    if (isOn(SW_USE_CHINREM_GCD))
      fc = modGCDZ( fc, gc);
    else
    #endif
    {
       fc = gcd_poly_0( fc, gc );
    }
  }
  else
  {
    fc = gcd_poly_0( fc, gc );
  }
  if ((ch>0)&&(!hasAlgVar(fc))) fc/=fc.lc();
  return fc;
}

getCharacteristic()

int FACTORY_PUBLIC getCharacteristic

(

)

Definition at line 70 of file cf_char.cc.

{
    return theCharacteristic;
}

getGFDegree()

int getGFDegree

(

)

Definition at line 75 of file cf_char.cc.

{
    //ASSERT( theDegree > 0, "not in GF(q)" );
    return theDegree;
}

getGFGenerator()

CanonicalForm getGFGenerator

(

)

Definition at line 81 of file cf_char.cc.

{
    ASSERT( theDegree > 1, "not in GF(q)" );
    return int2imm_gf( 1 );
}

getNumVars()

int getNumVars

(

const CanonicalForm &

f

)

int getNumVars ( const CanonicalForm & f )

getNumVars() - get number of polynomial variables in f.

Definition at line 314 of file cf_ops.cc.

{
    int n;
    if ( f.inCoeffDomain() )
        return 0;
    else  if ( (n = f.level()) == 1 )
        return 1;
    else
    {
        int * vars = NEW_ARRAY(int, n+1);
        int i;
        for ( i = n-1; i >=0; i-- ) vars[i] = 0;
 
        // look for variables
        for ( CFIterator I = f; I.hasTerms(); ++I )
            fillVarsRec( I.coeff(), vars );
 
        // count them
        int m = 0;
        for ( i = 1; i < n; i++ )
            if ( vars[i] != 0 ) m++;
 
        DELETE_ARRAY(vars);
        // do not forget to count our own variable
        return m+1;
    }
}

getVars()

CanonicalForm getVars

(

const CanonicalForm &

f

)

CanonicalForm getVars ( const CanonicalForm & f )

getVars() - get polynomial variables of f.

Return the product of all of them, 1 if there are not any.

Definition at line 350 of file cf_ops.cc.

{
    int n;
    if ( f.inCoeffDomain() )
        return 1;
    else  if ( (n = f.level()) == 1 )
        return Variable( 1 );
    else
    {
        int * vars = NEW_ARRAY(int, n+1);
        int i;
        for ( i = n; i >= 0; i-- ) vars[i] = 0;
 
        // look for variables
        for ( CFIterator I = f; I.hasTerms(); ++I )
            fillVarsRec( I.coeff(), vars );
 
        // multiply them all
        CanonicalForm result = 1;
        for ( i = n; i > 0; i-- )
            if ( vars[i] != 0 ) result *= Variable( i );
 
        DELETE_ARRAY(vars);
        // do not forget our own variable
        return f.mvar() * result;
    }
}

hasFirstAlgVar()

bool hasFirstAlgVar	(	const CanonicalForm &	f,
		Variable &	a
	)

check if poly f contains an algebraic variable a

Definition at line 679 of file cf_ops.cc.

{
  if( f.inBaseDomain() ) // f has NO alg. variable
    return false;
  if( f.level()<0 ) // f has only alg. vars, so take the first one
  {
    a = f.mvar();
    return true;
  }
  for(CFIterator i=f; i.hasTerms(); i++)
    if( hasFirstAlgVar( i.coeff(), a ))
      return true; // 'a' is already set
  return false;
}

head()

CanonicalForm head ( const CanonicalForm &  f )

inline

Definition at line 360 of file canonicalform.h.

{
    if ( f.level() > 0 )
        return power( f.mvar(), f.degree() ) * f.LC();
    else
        return f;
}

headdegree()

int headdegree ( const CanonicalForm &  f )

inline

Definition at line 369 of file canonicalform.h.

{ return totaldegree( head( f ) ); }

icontent()

CanonicalForm FACTORY_PUBLIC icontent

(

const CanonicalForm &

f

)

CanonicalForm icontent ( const CanonicalForm & f )

icontent() - return gcd over all coefficients of f which are in a coefficient domain.

Definition at line 74 of file cf_gcd.cc.

{
    return icontent( f, 0 );
}

ilog2()

int ilog2 ( const CanonicalForm &  a )

inline

Definition at line 352 of file canonicalform.h.

{ return a.ilog2(); }

is_imm()

int is_imm ( const InternalCF *const  ptr )

inline

Definition at line 65 of file canonicalform.h.

{
    // returns 0 if ptr is not immediate
    return ( ((int)((intptr_t)ptr)) & 3 );
}

isOn()

bool FACTORY_PUBLIC isOn

(

int

sw

)

switches

Definition at line 1971 of file canonicalform.cc.

{
    return cf_glob_switches.isOn( sw );
}

lc()

CanonicalForm lc ( const CanonicalForm &  f )

inline

Definition at line 304 of file canonicalform.h.

{ return f.lc(); }

Lc()

CanonicalForm Lc ( const CanonicalForm &  f )

inline

Definition at line 307 of file canonicalform.h.

{ return f.Lc(); }

LC() [1/2]

CanonicalForm LC ( const CanonicalForm &  f )

inline

Definition at line 310 of file canonicalform.h.

{ return f.LC(); }

LC() [2/2]

CanonicalForm LC ( const CanonicalForm &  f, const Variable &  v  )

inline

Definition at line 313 of file canonicalform.h.

{ return f.LC( v ); }

lcm()

CanonicalForm FACTORY_PUBLIC lcm	(	const CanonicalForm &	f,
		const CanonicalForm &	g
	)

CanonicalForm lcm ( const CanonicalForm & f, const CanonicalForm & g )

lcm() - return least common multiple of f and g.

The lcm is calculated using the formula lcm(f, g) = f * g / gcd(f, g).

Returns zero if one of f or g equals zero.

Definition at line 763 of file cf_gcd.cc.

{
    if ( f.isZero() || g.isZero() )
        return 0;
    else
        return ( f / gcd( f, g ) ) * g;
}

leftShift()

CanonicalForm leftShift	(	const CanonicalForm &	F,
		int	n
	)

left shift the main variable of F by n

Returns

if x is the main variable of F the result is F(x^n)

Definition at line 697 of file cf_ops.cc.

{
  ASSERT (n >= 0, "cannot left shift by negative number");
  if (F.inBaseDomain())
    return F;
  if (n == 0)
    return F;
  Variable x=F.mvar();
  CanonicalForm result= 0;
  for (CFIterator i= F; i.hasTerms(); i++)
    result += i.coeff()*power (x, i.exp()*n);
  return result;
}

level()

int level ( const CanonicalForm &  f )

inline

Definition at line 331 of file canonicalform.h.

{ return f.level(); }

mapdomain()

CanonicalForm mapdomain	(	const CanonicalForm &	f,
		CanonicalForm(*)(const CanonicalForm &)	mf
	)

CanonicalForm mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) )

mapdomain() - map all coefficients of f through mf.

Recursively descends down through f to the coefficients which are in a coefficient domain mapping each such coefficient through mf and returns the result.

Definition at line 440 of file cf_ops.cc.

{
    if ( f.inBaseDomain() )
        return mf( f );
    else
    {
        CanonicalForm result = 0;
        CFIterator i;
        Variable x = f.mvar();
        for ( i = f; i.hasTerms(); i++ )
            result += power( x, i.exp() ) * mapdomain( i.coeff(), mf );
        return result;
    }
}

mapinto()

CanonicalForm mapinto ( const CanonicalForm &  f )

inline

Definition at line 355 of file canonicalform.h.

{ return f.mapinto(); }

mod()

CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod	(	const CanonicalForm &	,
		const CanonicalForm &
	)

mvar()

Variable mvar ( const CanonicalForm &  f )

inline

Definition at line 334 of file canonicalform.h.

{ return f.mvar(); }

num()

CanonicalForm num ( const CanonicalForm &  f )

inline

Definition at line 337 of file canonicalform.h.

{ return f.num(); }

Off()

void FACTORY_PUBLIC Off

(

int

sw

)

switches

Definition at line 1964 of file canonicalform.cc.

{
    cf_glob_switches.Off( sw );
}

On()

void FACTORY_PUBLIC On

(

int

sw

)

switches

Definition at line 1957 of file canonicalform.cc.

{
    cf_glob_switches.On( sw );
}

operator%()

CF_NO_INLINE FACTORY_PUBLIC CanonicalForm operator%	(	const CanonicalForm &	,
		const CanonicalForm &
	)

operator*()

CF_INLINE CanonicalForm operator*	(	const CanonicalForm &	lhs,
		const CanonicalForm &	rhs
	)

See also

CanonicalForm::operator *=()

Definition at line 524 of file cf_inline.cc.

{
    CanonicalForm result( lhs );
    result *= rhs;
    return result;
}

operator+()

CF_INLINE CanonicalForm operator+	(	const CanonicalForm &	lhs,
		const CanonicalForm &	rhs
	)

CF_INLINE CanonicalForm operator +, -, *, /, % ( const CanonicalForm & lhs, const CanonicalForm & rhs )

operators +, -, *, /, %(), div(), mod() - binary arithmetic operators.

The binary operators have their standard (mathematical) semantics. As explained for the corresponding arithmetic assignment operators, the operators ‘/’ and ‘%’ return the quotient resp. remainder of (polynomial) division with remainder, whereas ‘div()’ and ‘mod()’ may be used for exact division and term-wise remaindering, resp.

It is faster to use the arithmetic assignment operators (e.g., ‘f += g;’) instead of the binary operators (‘f = f+g;’ ).

Type info:

lhs, rhs: CurrentPP

There are weaker preconditions for some cases (e.g., arithmetic operations with elements from Q or Z work in any domain), but type ‘CurrentPP’ is the only one guaranteed to work for all cases.

Developers note:

All binary operators have their corresponding ‘CanonicalForm’ assignment operators (e.g., ‘operator +()’ corresponds to ‘CanonicalForm::operator +=()’, ‘div()’ corresponds to `CanonicalFormdiv()).

And that is how they are implemented, too: Each of the binary operators first creates a copy of ‘lhs’, adds ‘rhs’ to this copy using the assignment operator, and returns the result.

See also

CanonicalForm::operator +=()

Definition at line 503 of file cf_inline.cc.

{
    CanonicalForm result( lhs );
    result += rhs;
    return result;
}

operator-()

CF_NO_INLINE FACTORY_PUBLIC CanonicalForm operator-	(	const CanonicalForm &	,
		const CanonicalForm &
	)

operator/()

CF_NO_INLINE FACTORY_PUBLIC CanonicalForm operator/	(	const CanonicalForm &	,
		const CanonicalForm &
	)

power() [1/2]

CanonicalForm FACTORY_PUBLIC power	(	const CanonicalForm &	f,
		int	n
	)

exponentiation

Definition at line 1896 of file canonicalform.cc.

{
  ASSERT( n >= 0, "illegal exponent" );
  if ( f.isZero() )
    return CanonicalForm(0L);
  else  if ( f.isOne() )
    return f;
  else  if ( f == -1 )
  {
    if ( n % 2 == 0 )
      return CanonicalForm(1L);
    else
      return CanonicalForm(-1L);
  }
  else  if ( n == 0 )
    return CanonicalForm(1L);
 
  //else if (f.inGF())
  //{
  //}
  else
  {
    CanonicalForm g,h;
    h=f;
    while(n%2==0)
    {
      h*=h;
      n/=2;
    }
    g=h;
    while(1)
    {
      n/=2;
      if(n==0)
        return g;
      h*=h;
      if(n%2!=0) g*=h;
    }
  }
}

power() [2/2]

CanonicalForm FACTORY_PUBLIC power	(	const Variable &	v,
		int	n
	)

exponentiation

Definition at line 1939 of file canonicalform.cc.

{
    //ASSERT( n >= 0, "illegal exponent" );
    if ( n == 0 )
        return 1;
    else  if ( n == 1 )
        return v;
    else  if (( v.level() < 0 ) && (hasMipo(v)))
    {
        CanonicalForm result( v, n-1 );
        return result * v;
    }
    else
        return CanonicalForm( v, n );
}

pp()

CanonicalForm FACTORY_PUBLIC pp

(

const CanonicalForm &

f

)

CanonicalForm pp ( const CanonicalForm & f )

pp() - return primitive part of f.

Returns zero if f equals zero, otherwise f / content(f).

Definition at line 676 of file cf_gcd.cc.

{
    if ( f.isZero() )
        return f;
    else
        return f / content( f );
}

reduce()

CanonicalForm reduce	(	const CanonicalForm &	f,
		const CanonicalForm &	M
	)

polynomials in M.mvar() are considered coefficients M univariate monic polynomial the coefficients of f are reduced modulo M

Definition at line 660 of file cf_ops.cc.

{
  if(f.inBaseDomain() || f.level() < M.level())
    return f;
  if(f.level() == M.level())
  {
    if(f.degree() < M.degree())
      return f;
    CanonicalForm tmp = mod (f, M);
    return tmp;
  }
  // here: f.level() > M.level()
  CanonicalForm result = 0;
  for(CFIterator i=f; i.hasTerms(); i++)
    result += reduce(i.coeff(),M) * power(f.mvar(),i.exp());
  return result;
}

replacevar()

CanonicalForm FACTORY_PUBLIC replacevar	(	const CanonicalForm &	f,
		const Variable &	x1,
		const Variable &	x2
	)

CanonicalForm replacevar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 )

replacevar() - replace all occurences of x1 in f by x2.

In contrast to swapvar(), x1 may be an algebraic variable, but x2 must be a polynomial variable.

Definition at line 271 of file cf_ops.cc.

{
    //ASSERT( x2.level() > 0, "cannot replace with algebraic variable" );
    if ( f.inBaseDomain() || x1 == x2 || ( x1 > f.mvar() ) )
        return f;
    else
    {
        sv_x1 = x1;
        sv_x2 = x2;
        return replacevar_between( f );
    }
}

setCharacteristic() [1/3]

void FACTORY_PUBLIC setCharacteristic

(

int

c

)

Definition at line 28 of file cf_char.cc.

{
    if ( c == 0 )
    {
        theDegree = 0;
        CFFactory::settype( IntegerDomain );
        theCharacteristic = 0;
    }
    else
    {
        theDegree = 1;
        CFFactory::settype( FiniteFieldDomain );
        ff_big = c > cf_getSmallPrime( cf_getNumSmallPrimes()-1 );
        if (c!=theCharacteristic)
        {
          if (c > 536870909) factoryError("characteristic is too large(max is 2^29)");
          ff_setprime( c );
        }
        theCharacteristic = c;
    }
}

setCharacteristic() [2/3]

void setCharacteristic	(	int	c,
		int	n
	)

setCharacteristic() [3/3]

void setCharacteristic	(	int	c,
		int	n,
		char	name
	)

Definition at line 61 of file cf_char.cc.

{
    ASSERT( c != 0 && n > 1, "illegal GF(q)" );
    setCharacteristic( c );
    gf_setcharacteristic( c, n, name );
    theDegree = n;
    CFFactory::settype( GaloisFieldDomain );
}

sign()

int sign ( const CanonicalForm &  a )

inline

Definition at line 343 of file canonicalform.h.

{ return a.sign(); }

size() [1/2]

int size

(

const CanonicalForm &

f

)

int size ( const CanonicalForm & f )

size() - return number of monomials in f which are in an coefficient domain.

Returns one if f is in an coefficient domain.

Definition at line 627 of file cf_ops.cc.

{
    if ( f.inCoeffDomain() )
        return 1;
    else
    {
        int result = 0;
        CFIterator i;
        for ( i = f; i.hasTerms(); i++ )
            result += size( i.coeff() );
        return result;
    }
}

size() [2/2]

int size	(	const CanonicalForm &	f,
		const Variable &	v
	)

int size ( const CanonicalForm & f, const Variable & v )

size() - count number of monomials of f with level higher or equal than level of v.

Returns one if f is in an base domain.

Definition at line 600 of file cf_ops.cc.

{
    if ( f.inBaseDomain() )
        return 1;
 
    if ( f.mvar() < v )
        // polynomials with level < v1 are counted as coefficients
        return 1;
    else
    {
        CFIterator i;
        int result = 0;
        // polynomials with level > v2 are not counted al all
        for ( i = f; i.hasTerms(); i++ )
            result += size( i.coeff(), v );
        return result;
    }
}

size_maxexp()

int size_maxexp	(	const CanonicalForm &	f,
		int &	maxexp
	)

Definition at line 641 of file cf_ops.cc.

{
    if ( f.inCoeffDomain() )
        return 1;
    else
    {
        if (f.degree()>maxexp) maxexp=f.degree();
        int result = 0;
        CFIterator i;
        for ( i = f; i.hasTerms(); i++ )
            result += size_maxexp( i.coeff(), maxexp );
        return result;
    }
}

sqrt()

CanonicalForm sqrt ( const CanonicalForm &  a )

inline

Definition at line 349 of file canonicalform.h.

{ return a.sqrt(); }

swapvar()

CanonicalForm FACTORY_PUBLIC swapvar	(	const CanonicalForm &	f,
		const Variable &	x1,
		const Variable &	x2
	)

swapvar() - swap variables x1 and x2 in f.

Returns the image of f under the map which maps x1 to x2 and x2 to x1. This is done quite efficiently because it is used really often. x1 and x2 should be polynomial variables.

Definition at line 168 of file cf_ops.cc.

{
    ASSERT( x1.level() > 0 && x2.level() > 0, "cannot swap algebraic Variables" );
    if ( f.inCoeffDomain() || x1 == x2 || ( x1 > f.mvar() && x2 > f.mvar() ) )
        return f;
    else
    {
        CanonicalForm result = 0;
        if ( x1 > x2 )
        {
            sv_x1 = x2; sv_x2 = x1;
        }
        else
        {
            sv_x1 = x1; sv_x2 = x2;
        }
        if ( f.mvar() < sv_x2 )
            // we only have to replace sv_x1 by sv_x2
            swapvar_between( f, result, 1, 0 );
        else
            // we really have to swap variables
            swapvar_rec( f, result, 1 );
        return result;
    }
}

tailcoeff() [1/2]

CanonicalForm tailcoeff ( const CanonicalForm &  f )

inline

Definition at line 325 of file canonicalform.h.

{ return f.tailcoeff(); }

tailcoeff() [2/2]

CanonicalForm tailcoeff ( const CanonicalForm &  f, const Variable &  v  )

inline

Definition at line 328 of file canonicalform.h.

{ return f.tailcoeff(v); }

taildegree()

int taildegree ( const CanonicalForm &  f )

inline

Definition at line 322 of file canonicalform.h.

{ return f.taildegree(); }

totaldegree() [1/2]

int totaldegree

(

const CanonicalForm &

f

)

int totaldegree ( const CanonicalForm & f )

totaldegree() - return the total degree of f.

If f is zero, return -1. If f is in a coefficient domain, return 0. Otherwise return the total degree of f in all polynomial variables.

Definition at line 523 of file cf_ops.cc.

{
    if ( f.isZero() )
        return -1;
    else if ( f.inCoeffDomain() )
        return 0;
    else
    {
        CFIterator i;
        int cdeg = 0, dummy;
        // calculate maximum over all coefficients of f, taking
        // in account our own exponent
        for ( i = f; i.hasTerms(); i++ )
            if ( (dummy = totaldegree( i.coeff() ) + i.exp()) > cdeg )
                cdeg = dummy;
        return cdeg;
    }
}

totaldegree() [2/2]

int totaldegree	(	const CanonicalForm &	f,
		const Variable &	v1,
		const Variable &	v2
	)

int totaldegree ( const CanonicalForm & f, const Variable & v1, const Variable & v2 )

totaldegree() - return the total degree of f as a polynomial in the polynomial variables between v1 and v2 (inclusively).

If f is zero, return -1. If f is in a coefficient domain, return 0. Also, return 0 if v1 > v2. Otherwise, take f to be a polynomial in the polynomial variables between v1 and v2 and return its total degree.

Definition at line 554 of file cf_ops.cc.

{
    if ( f.isZero() )
        return -1;
    else if ( v1 > v2 )
        return 0;
    else if ( f.inCoeffDomain() )
        return 0;
    else if ( f.mvar() < v1 )
        return 0;
    else if ( f.mvar() == v1 )
        return f.degree();
    else if ( f.mvar() > v2 )
    {
        // v2's level is larger than f's level, descend down
        CFIterator i;
        int cdeg = 0, dummy;
        // calculate maximum over all coefficients of f
        for ( i = f; i.hasTerms(); i++ )
            if ( (dummy = totaldegree( i.coeff(), v1, v2 )) > cdeg )
                cdeg = dummy;
        return cdeg;
    }
    else
    {
        // v1 < f.mvar() <= v2
        CFIterator i;
        int cdeg = 0, dummy;
        // calculate maximum over all coefficients of f, taking
        // in account our own exponent
        for ( i = f; i.hasTerms(); i++ )
            if ( (dummy = totaldegree( i.coeff(), v1, v2 ) + i.exp()) > cdeg )
                cdeg = dummy;
        return cdeg;
    }
}

vcontent()

CanonicalForm FACTORY_PUBLIC vcontent	(	const CanonicalForm &	f,
		const Variable &	x
	)

CanonicalForm vcontent ( const CanonicalForm & f, const Variable & x )

vcontent() - return content of f with repect to variables >= x.

The content is recursively calculated over all coefficients in f having level less than x. x should be a polynomial variable.

Definition at line 653 of file cf_gcd.cc.

{
    ASSERT( x.level() > 0, "cannot calculate vcontent with respect to algebraic variable" );
 
    if ( f.mvar() <= x )
        return content( f, x );
    else {
        CFIterator i;
        CanonicalForm d = 0;
        for ( i = f; i.hasTerms() && ! d.isOne(); i++ )
            d = gcd( d, vcontent( i.coeff(), x ) );
        return d;
    }
}