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added ox_ntl

install `NTL'
   % make install-ntl

install ox_ntl
   % make install

EX.
  [1028] load("ntl.rr")$
  [1040] F=ntl.ex_data(4);
  x^16-136*x^14+6476*x^12-141912*x^10+1513334*x^8-7453176*x^6+13950764*x^4-5596840*x^2+46225
  [1041] F=F*subst(F,x,x+1)$
  [1042] ntl.factor(PID,F);
  [[1,1],[x^16+16*x^15-16*x^14-1344*x^13-4080*x^12+32576*x^11+157376*x^10-255232*x^9-2062624*x^8-249088*x^7+10702080*x^6+9126912*x^5-18643712*x^4-24167424*x^3+2712576*x^2+10653696*x+2324736,1],[x^16-136*x^14+6476*x^12-141912*x^10+1513334*x^8-7453176*x^6+13950764*x^4-5596840*x^2+46225,1]]

/* $OpenXM: OpenXM/src/ox_ntl/ntl.cpp,v 1.1 2003/11/03 03:11:21 iwane Exp $ */

#include <NTL/ZZXFactoring.h>
#include <NTL/ZZ_pXFactoring.h>

#include <iostream>
#include <strstream>

#include "ntl.h"


/*==========================================================================*
 * Check string format
 *==========================================================================*/

#define NtlIsSpace(c)  ((c) == ' ' || (c) == '\t')
#define NtlIsDigit(c)  ((c) >= '0' && (c) <= '9')

/****************************************************************************
 *
 * test for string format of integer
 *
 * PARAM : I : str    : string
 *       : O : endptr :
 * RETURN: !0         : the string tests true
 *       :  0         : the string tests false
 *
 ****************************************************************************/
static int
ntl_isZZstr_(const char *str, char const **endptr)
{
	while (NtlIsSpace(*str))
		str++;

	/* NTL reject "+999"  */
	if (*str == '-')
		str++;

	if (!NtlIsDigit(*str))
		return (0);

	str++;

	while (NtlIsDigit(*str))
		str++;

	*endptr = str;

	return (!0);

}

static int
ntl_isZZstr(const char *str)
{
	const char *ptr;
	int ret = ntl_isZZstr_(str, &ptr);
	if (!ret)
		return (ret);

	while (NtlIsSpace(*ptr))
		ptr++;

	return (*ptr == '\0');
}


/****************************************************************************
 *
 * test for string format of univariate polynomials with integer coefficients
 * in NTL style.
 *
 * PARAM : I : str    : string
 *       : O : endptr :
 * RETURN: !0         : the string tests true
 *       :  0         : the string tests false
 *
 ****************************************************************************/
static int
ntl_isZZXstr_(const char *str, char const **endptr)
{
	const char *s;

	while (NtlIsSpace(*str))
		str++;

	if (*str != '[')
		return (0);

	str++;

	while (*str != ']' && *str != '\0') {

		if (!ntl_isZZstr_(str, &s))
			return (0);
		str = s;

		while (NtlIsSpace(*str))
			str++;
	}

	while (NtlIsSpace(*str))
		str++;

	if (*str != ']')
		return (0);

	str++;
	*endptr = str;
	return (!0);
}

static int
ntl_isZZXstr(const char *str)
{
	const char *ptr;
	int ret = ntl_isZZXstr_(str, &ptr);
	if (!ret)
		return (ret);

	while (NtlIsSpace(*ptr))
		ptr++;

	return (*ptr == '\0');
}


/*==========================================================================*
 * Convert
 *==========================================================================*/
static cmo_zz *
ZZ_to_cmo_zz(const ZZ &z)
{
	cmo_zz *c;

	ostrstream sout;
	sout << z << '\0';

	c = new_cmo_zz_set_string(sout.str());

	return (c);
}


static int
cmo_to_ZZ(ZZ &z, cmo *c)
{
	int ret = NTL_SUCCESS;
	char *str;

	switch (c->tag) {
	case CMO_ZERO:
		z = to_ZZ(0);
		break;
	case CMO_ZZ:
	{
		str = new_string_set_cmo(c);
		istrstream sin(str, strlen(str));
		sin >> z;
		break;
	}
	case CMO_INT32:
		z = to_ZZ(((cmo_int32 *)c)->i);
		break;
	case CMO_STRING:
	{
		str = ((cmo_string *)c)->s;
		if (!ntl_isZZstr(str))
			return (NTL_FAILURE);

		istrstream sin(str, strlen(str));
		sin >> z;
		break;
	}
	default:
		ret = NTL_FAILURE;
		break;
	}

	return (ret);
}


static int
cmo_to_ZZX(ZZX &f, cmo *m, cmo_indeterminate *&x)
{
	char *str;
	int ret;

	switch (m->tag) {
	case CMO_STRING:   /* [ 3 4 7 ] ==> 3+4*x+7*x^2 */
		str = ((cmo_string *)m)->s;
		ret = 0; //ntl_isZZXstr(str);

		if (!ret) {
			/* format error */
			return (NTL_FAILURE);
		}

		{
			istrstream sin(str, strlen(str));
			sin >> f;
		}
		break;
	case CMO_RECURSIVE_POLYNOMIAL:
	{
		cmo_recursive_polynomial *rec = (cmo_recursive_polynomial *)m;
		cmo_polynomial_in_one_variable *poly = (cmo_polynomial_in_one_variable *)rec->coef;
		cell *el;
		int len;

		if (poly->tag != CMO_POLYNOMIAL_IN_ONE_VARIABLE) {
			return (NTL_FAILURE);
		}

		el = list_first((cmo_list *)poly);
		len = list_length((cmo_list *)poly);

		f = 0;

		while (!list_endof((cmo_list *)poly, el)) {
			ZZ c;
			ostrstream sout;
			cmo *coef = el->cmo;
			int exp = el->exp;

			ret = cmo_to_ZZ(c, coef);
			if (ret != NTL_SUCCESS) {
				return (NTL_FAILURE);
			}

			SetCoeff(f, exp, c);

			el = list_next(el);			
		}


		el = list_first(rec->ringdef);
		x = (cmo_indeterminate *)el->cmo;

		break;	
	}
	default:
		break;
	}
	return (NTL_SUCCESS);
}

/****************************************************************************
 *
 * 
 *
 * PARAM : I : arg  : polynomial
 *       : I : argc :
 * RETURN: [[num, 1],[factor1,multiplicity1],[factor2,multiplicity2],...]
 *
 * EX    : 
 *
 ****************************************************************************/
static cmo_recursive_polynomial *
ZZX_to_cmo(ZZX &factor, cmo_indeterminate *x)
{
	cmo_recursive_polynomial *rec;
	cmo_polynomial_in_one_variable *poly;

	cmo_list *ringdef;
	int i;
	cmo *coef;

	ringdef = new_cmo_list();
	list_append(ringdef, (cmo *)x);

	poly = new_cmo_polynomial_in_one_variable(0);
	for (i = deg(factor); i >= 0; i--) {
		if (coeff(factor, i) == 0)
			continue;

		coef = (cmo *)ZZ_to_cmo_zz(coeff(factor, i));
		list_append_monomial((cmo_list *)poly, coef, i);
	}

	rec = new_cmo_recursive_polynomial(ringdef, (cmo *)poly);
	return (rec);
}


static cmo_list *
new_cmo_pair_ZZX_int(ZZX &factors, int d, cmo_indeterminate *x)
{
	cmo_recursive_polynomial *poly;
	cmo_int32 *deg;
	cmo_list *list;

	poly = ZZX_to_cmo(factors, x);
	deg = new_cmo_int32(d);

	list = list_appendl(NULL, poly, deg, NULL);

	return (list);
}


/****************************************************************************
 *
 * convert vec_pair_ZZX_long(list of factor and multiplicity) to cmo_list
 *
 * PARAM : I : factors : list of factor and multiplicity 
 *       :   :         :  [[factor1,multiplicity1][factor2,multiplicity2]...]
 *       : I : x       : indeterminate
 * RETURN: 
 *
 ****************************************************************************/
static cmo_list *
factors_to_cmo(vec_pair_ZZX_long &factors, cmo_indeterminate *x)
{
	int i;
	cmo_list *list = new_cmo_list();
	cmo_list *factor;

	for (i = 0; i < factors.length(); i++) {
		factor = new_cmo_pair_ZZX_int(factors[i].a, factors[i].b, x);
		list_append(list, (cmo *)factor);
	}

	return (list);
}


/****************************************************************************
 *
 * Factorize polynomial over the integers.
 *
 * PARAM : I : arg  : polynomial
 *       : I : argc :
 * RETURN: [num,[[factor1,multiplicity1],[factor2,multiplicity2],...]]
 *
 * EX    : ntl_fctr([2*x^11+4*x^8-2*x^6+2*x^5-4*x^3-2],1) ==>
         : [2,[[x-1,1],[x^4+x^3+x^2+x+1,1],[x+1,2],[x^2-x+1,2]]]
 *
 ****************************************************************************/
cmo *
ntl_fctr(cmo **arg, int argc)
{
	cmo *poly = arg[0];
	cmo_indeterminate *x;
	ZZX f;
	ZZ c;

	int ret;

	vec_pair_ZZX_long factors;

	cmo_list *ans;
	cmo *fcts;

	if (argc != 1) {
		return ((cmo *)new_cmo_error2((cmo *)new_cmo_string("Invalid Parameter(#)")));
	}

	ret = cmo_to_ZZX(f, poly, x);
	if (ret != NTL_SUCCESS) {
		/* format error */
		return ((cmo *)new_cmo_error2((cmo *)new_cmo_string("Invalid Parameter(type)")));
	}

	factor(c, factors, f);

	cmo_zz *zz = ZZ_to_cmo_zz(c);

	ans = new_cmo_list();

	fcts = (cmo *)factors_to_cmo(factors, x);

	list_appendl(ans, zz, (cmo *)fcts, NULL);

	return ((cmo *)ans);
}