pnome-private.c File Reference

#include <stdio.h>
#include <string.h>
#include "boolean.h"
#include "arithmetique.h"
#include "vecteur.h"
#include "polynome.h"

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Functions
Pmonome	monome_del_var (Pmonome pm, Variable var)
	Pmonome monome_del_var(Pmonome pm, Variable var) PRIVATE returns a copy of monomial pm, where variable var is deleted. More...
bool	monome_colin (Pmonome pm1, Pmonome pm2)
	bool monome_colin(Pmonome pm1, Pmonome pm2) PRIVATE returns true if the two monomials are "colinear": same variables, same exponents. More...
bool	monome_equal (Pmonome pm1, Pmonome pm2)
	bool monome_equal(Pmonome pm1, Pmonome pm2) PRIVATE returns true if the two monomials are equal same coeff., same variables, same exponents. More...
float	Bernouilli (int i)
	float Bernouilli(int i) PRIVATE returns Bi = i-th Bernouilli number More...
int	factorielle (int n)
	int factorielle (int n) PRIVATE returns n! More...
double	intpower (double d, int n)
	double intpower(double d, int n) returns d^n for all integers n More...
bool	is_inferior_monome (Pmonome pm1, Pmonome pm2, int *is_inferior_var)
	bool is_inferior_monome(Pmonome pm1, pm2, int (*is_inferior_var)()) returns the qsort comparison (pm1<pm2) we follow the "lexicographic" order: decreasing powers of the main variable, (according to the variable order relation passed in is_inferior_var) the decreasing powers of the next main variable, ... More...

Function Documentation

Bernouilli()

float Bernouilli

(

int

i

)

float Bernouilli(int i) PRIVATE returns Bi = i-th Bernouilli number

later, we could compute bigger Bernouilli(i) with the recurrence

To please the gcc compiler

Definition at line 108 of file pnome-private.c.

{
    switch (i) {
    case  1: return((float) 1/6);
    case  2: return((float) 1/30);
    case  3: return((float) 1/42);
    case  4: return((float) 1/30);
    case  5: return((float) 5/66);
    case  6: return((float) 691/2730);
    case  7: return((float) 7/6); 
    case  8: return((float) 3617/510);
    case  9: return((float) 43867/798);
    case 10: return((float) 174611/330);
    case 11: return((float) 854513/138);
    case 12: return((float) 236364091/2730);
    default: polynome_error("Bernouilli(i)", "i=%d illegal\n", i);
        /* later, we could compute bigger Bernouilli(i) with the recurrence */
    }
    /* To please the gcc compiler */
    return 0.;
}

References polynome_error().

Referenced by polynome_sum_of_power().

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factorielle()

int factorielle

(

int

n

)

int factorielle (int n) PRIVATE returns n!

Definition at line 136 of file pnome-private.c.

{
    int fact = -1;
 
    if (n<0) 
        polynome_error("factorielle", "n=%d", n);
    else if (n<2) 
        fact = 1;
    else 
        fact = factorielle(n-1) * n;
 
    return fact;
}

References polynome_error().

Referenced by average_probability_matrix().

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intpower()

double intpower	(	double	d,
		int	n
	)

double intpower(double d, int n) returns d^n for all integers n

Definition at line 155 of file pnome-private.c.

{
    if (n>0) 
        return (intpower(d, n-1) * d);
    else if (n==0) 
        return((double) 1);
    else 
        return (intpower(d, n+1) / d);
}

Referenced by float_to_frac(), and polynome_sum_of_power().

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is_inferior_monome()

bool is_inferior_monome	(	Pmonome	pm1,
		Pmonome	pm2,
		int *	is_inferior_var
	)

bool is_inferior_monome(Pmonome pm1, pm2, int (*is_inferior_var)()) returns the qsort comparison (pm1<pm2) we follow the "lexicographic" order: decreasing powers of the main variable, (according to the variable order relation passed in is_inferior_var) the decreasing powers of the next main variable, ...

When pm1=pm2 we return false. When pm1 or pm2 is MONOME_NUL or MONOME_UNDEFINED we return false.

is_inferior_var is indeed to be understood as the qsort comparator method and so is ill-defined here. RK

Initial version: Pvecteur pv1 = vect_tri(monome_term(pm1), is_inferior_var); Pvecteur pv2 = vect_tri(monome_term(pm2), is_inferior_var);

Fabien's version: Pvecteur pv1 = vect_sort(monome_term(pm1), vect_compare); Pvecteur pv2 = vect_sort(monome_term(pm2), vect_compare);

Pbase pbsorted = (Pbase) vect_tri(pb, is_inferior_var);

Pbase pbsorted = (Pbase) vect_sort(pb, vect_compare);

The following test is added by L.Zhou .
We want the constant term at the end . Jul.15, 91

The following test is added by L.Zhou . Mar.26, 91

Definition at line 179 of file pnome-private.c.

{
    if (MONOME_UNDEFINED_P(pm1) || MONOME_UNDEFINED_P(pm2)
        ||    MONOME_NUL_P(pm1) || MONOME_NUL_P(pm2))
        return (false);
    else {
        /* Initial version:
           Pvecteur pv1 = vect_tri(monome_term(pm1), is_inferior_var);
           Pvecteur pv2 = vect_tri(monome_term(pm2), is_inferior_var);
           */
        /* Fabien's version:
        Pvecteur pv1 = vect_sort(monome_term(pm1), vect_compare);
        Pvecteur pv2 = vect_sort(monome_term(pm2), vect_compare);
        */
        Pvecteur pv1 = vect_sort(monome_term(pm1), is_inferior_var);
        Pvecteur pv2 = vect_sort(monome_term(pm2), is_inferior_var);
        Pbase pb = base_union((Pbase) pv1, (Pbase) pv2);
        /* Pbase pbsorted = (Pbase) vect_tri(pb, is_inferior_var); */
        /* Pbase pbsorted = (Pbase) vect_sort(pb, vect_compare); */
        Pbase pbsorted = (Pbase) vect_sort(pb, is_inferior_var);
        bool result = false;
 
        /* The following test is added by L.Zhou .    
           We want the constant term at the end . Jul.15, 91 */
        if ( term_cst(pv1) )
            return(true);
        else if ( term_cst(pv2) )
            return(false);
 
        /* The following test is added by L.Zhou .    Mar.26, 91 */
        if ( vect_coeff_sum(pv1) < vect_coeff_sum(pv2) )
            result = true;
        else if ( vect_coeff_sum(pv1) > vect_coeff_sum(pv2) )
            ;
        else {
            while (!BASE_NULLE_P(pbsorted)) {
                Variable var = vect_first_var((Pvecteur) pbsorted);
                Value power1 = vect_coeff(var, pv1);
                Value power2 = vect_coeff(var, pv2);
 
                if ( power1 < power2 ) {
                    result = true;
                    break;
                }
                else if ( power2 < power1 ) 
                    break;
                vect_erase_var((Pvecteur *) &pbsorted, var);
            }
        }
 
        vect_rm((Pvecteur) pbsorted);
        vect_rm((Pvecteur) pb);
        vect_rm(pv2);
        vect_rm(pv1);
 
        return (result);
    }
}

References BASE_NULLE_P, base_union(), is_inferior_var(), MONOME_NUL_P, monome_term, MONOME_UNDEFINED_P, term_cst, vect_coeff(), vect_coeff_sum(), vect_erase_var(), vect_first_var(), vect_rm(), and vect_sort().

Referenced by polynome_sort().

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monome_colin()

bool monome_colin	(	Pmonome	pm1,
		Pmonome	pm2
	)

bool monome_colin(Pmonome pm1, Pmonome pm2) PRIVATE returns true if the two monomials are "colinear": same variables, same exponents.

We consider that MONOME_UNDEFINED is only colinear to MONOME_UNDEFINED. [???]

Parameters

pm1	m1
pm2	m2

Definition at line 77 of file pnome-private.c.

{
    if (MONOME_UNDEFINED_P(pm1) || MONOME_UNDEFINED_P(pm2)
        ||    MONOME_NUL_P(pm1) || MONOME_NUL_P(pm2))
        return(pm1 == pm2);    
    else 
        return(vect_equal(monome_term(pm1), monome_term(pm2)));
}

References MONOME_NUL_P, monome_term, MONOME_UNDEFINED_P, and vect_equal().

Referenced by polynome_check(), polynome_monome_add(), and polynome_monome_addition().

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monome_del_var()

Pmonome monome_del_var	(	Pmonome	pm,
		Variable	var
	)

Pmonome monome_del_var(Pmonome pm, Variable var) PRIVATE returns a copy of monomial pm, where variable var is deleted.

pnome-private.c

is it the only variable

now it is a constant term

Parameters

pm	m
var	ar

Definition at line 47 of file pnome-private.c.

{
    if (MONOME_UNDEFINED_P(pm)) 
        return (MONOME_UNDEFINED);
    else if (MONOME_NUL_P(pm)) 
        return (MONOME_NUL);
    else {
        Pmonome newpm = new_monome();
 
        monome_coeff(newpm) = monome_coeff(pm);
        monome_term(newpm)  = vect_del_var(monome_term(pm), var);
        if (VECTEUR_NUL_P(monome_term(newpm))) {
            /* is it the only variable */
            monome_term(newpm) = vect_new(TCST, VALUE_ONE); 
            /* now it is a constant term   */
        }
    
        return(newpm);
    }
}

References monome_coeff, MONOME_NUL, MONOME_NUL_P, monome_term, MONOME_UNDEFINED, MONOME_UNDEFINED_P, new_monome(), TCST, VALUE_ONE, vect_del_var(), vect_new(), and VECTEUR_NUL_P.

Referenced by polynome_factorize(), and polynome_var_subst().

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monome_equal()

bool monome_equal	(	Pmonome	pm1,
		Pmonome	pm2
	)

bool monome_equal(Pmonome pm1, Pmonome pm2) PRIVATE returns true if the two monomials are equal same coeff., same variables, same exponents.

Parameters

pm1	m1
pm2	m2

Definition at line 93 of file pnome-private.c.

{
    if (MONOME_UNDEFINED_P(pm1) || MONOME_UNDEFINED_P(pm2)
        ||    MONOME_NUL_P(pm1) || MONOME_NUL_P(pm2))
        return(pm1 == pm2);    
    else 
        return(vect_equal(monome_term(pm1), monome_term(pm2))
               && ((monome_coeff(pm1) == monome_coeff(pm2))));
}

References monome_coeff, MONOME_NUL_P, monome_term, MONOME_UNDEFINED_P, and vect_equal().

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