3 * Chinese remainder algorithm. */
6 * GiNaC Copyright (C) 1999-2009 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
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14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
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23 #include "operators.h"
24 #include "chinrem_gcd.h"
26 #include "collect_vargs.h"
27 #include "primes_factory.h"
28 #include "divide_in_z_p.h"
31 #include <cln/integer.h>
35 static cln::cl_I extract_integer_content(ex& Apr, const ex& A)
37 static const cln::cl_I n1(1);
38 const numeric icont_ = A.integer_content();
39 const cln::cl_I icont = cln::the<cln::cl_I>(icont_.to_cl_N());
41 Apr = (A/icont_).expand();
49 ex chinrem_gcd(const ex& A_, const ex& B_, const exvector& vars)
52 const cln::cl_I a_icont = extract_integer_content(A, A_);
53 const cln::cl_I b_icont = extract_integer_content(B, B_);
54 const cln::cl_I c = cln::gcd(a_icont, b_icont);
56 const cln::cl_I a_lc = integer_lcoeff(A, vars);
57 const cln::cl_I b_lc = integer_lcoeff(B, vars);
58 const cln::cl_I g_lc = cln::gcd(a_lc, b_lc);
60 const ex& x(vars.back());
61 int n = std::min(A.degree(x), B.degree(x));
62 const cln::cl_I A_max_coeff = to_cl_I(A.max_coefficient());
63 const cln::cl_I B_max_coeff = to_cl_I(B.max_coefficient());
64 const cln::cl_I lcoeff_limit = (cln::cl_I(1) << n)*cln::abs(g_lc)*
65 std::min(A_max_coeff, B_max_coeff);
71 primes_factory pfactory;
73 bool has_primes = pfactory(p, g_lc);
75 throw chinrem_gcd_failed();
77 const numeric pnum(p);
80 ex Cp = pgcd(Ap, Bp, vars, p);
82 const cln::cl_I g_lcp = smod(g_lc, p);
83 const cln::cl_I Cp_lc = integer_lcoeff(Cp, vars);
84 const cln::cl_I nlc = smod(recip(Cp_lc, p)*g_lcp, p);
85 Cp = (Cp*numeric(nlc)).expand().smod(pnum);
86 int cp_deg = Cp.degree(x);
95 ex H_next = chinese_remainder(H, q, Cp, p);
98 } else if (cp_deg < n) {
99 // all previous homomorphisms are unlucky
104 // dp_deg > d_deg: current prime is bad
107 if (q < lcoeff_limit)
108 continue; // don't bother to do division checks
109 ex C, dummy1, dummy2;
110 extract_integer_content(C, H);
111 if (divide_in_z_p(A, C, dummy1, vars, 0) &&
112 divide_in_z_p(B, C, dummy2, vars, 0))
113 return (numeric(c)*C).expand();
114 // else: try more primes