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https://github.com/Z3Prover/z3
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resource-limit related fixes in src/test
This commit is contained in:
Christoph M. Wintersteiger
parent
e91b1e1da4
commit
c2ab9b72dc
11 changed files with 672 additions and 569 deletions
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@ -19,7 +19,7 @@ Notes:
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#include"upolynomial_factorization_int.h"
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#include"timeit.h"
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#include"polynomial.h"
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#include"rlimit.h"
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#if 0
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#include"polynomial_factorization.h"
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#endif
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@ -41,30 +41,30 @@ unsigned knuth_factors[2][11] = {
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// [k,l,i]: how many factors the S_k has over p_i, when i = 0 it's Z, p_1 = 2, for l=0 distinct, for l = 1 total
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unsigned swinnerton_dyer_factors[5][2][11] = {
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// S1 = (x^2) - 2
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// S1 = (x^2) - 2
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{
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// 2, 3, 5, 7,11,13,17,19,23,29, Z
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// 2, 3, 5, 7,11,13,17,19,23,29, Z
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{1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1},
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{2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1}
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},
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// S2 = (x^4) - 10*(x^2) + 1
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// S2 = (x^4) - 10*(x^2) + 1
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{
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{1, 1, 2, 2, 2, 2, 2, 2, 4, 2, 1},
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{4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 1}
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},
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// S3 = (x^8) - 40*(x^6) + 352*(x^4) - 960*(x^2) + 576
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// S3 = (x^8) - 40*(x^6) + 352*(x^4) - 960*(x^2) + 576
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{
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{1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 1},
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{8, 6, 4, 4, 4, 4, 4, 4, 4, 4, 1}
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},
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// S4 = (x^16) - 136*(x^14) + 6476*(x^12) - 141912*(x^10) + 1513334*(x^8) - 7453176*(x^6) + 13950764*(x^4) - 5596840*(x^2) + 46225
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// S4 = (x^16) - 136*(x^14) + 6476*(x^12) - 141912*(x^10) + 1513334*(x^8) - 7453176*(x^6) + 13950764*(x^4) - 5596840*(x^2) + 46225
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{
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{1, 4, 3, 4, 8, 8, 8, 8, 8, 8, 1},
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{16, 12, 10, 8, 8, 8, 8, 8, 8, 8, 1}
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},
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// SA = S1*S2*S3*S4
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{
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//p = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, Z
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//p = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, Z
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{ 2, 6, 3, 6, 15, 11, 16, 15, 18, 15, 1},
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{30, 21, 17, 16, 15, 15, 16, 15, 18, 15, 1}
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}
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@ -176,17 +176,17 @@ int random_polynomial[20][2][11] = {
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#if 0
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static void tst_square_free_finite_1() {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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// example from Knuth, p. 442
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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// polynomials \prod_{i < p} (x - i)^i
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for (unsigned prime_i = 0; prime_i < 5; ++ prime_i)
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for (unsigned prime_i = 0; prime_i < 5; ++ prime_i)
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{
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int p = primes[prime_i];
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// make the polynomial
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polynomial_ref f(pm);
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f = x - 1;
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@ -222,19 +222,19 @@ static void tst_square_free_finite_1() {
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}
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static void tst_factor_finite_1() {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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// example from Knuth, p. 442
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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polynomial_ref K(pm);
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K = (x^8) + (x^6) + 10*(x^4) + 10*(x^3) + 8*(x^2) + 2*x + 8;
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// factor them for all the prime numbers
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for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i)
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{
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for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i)
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{
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// make the Z_p
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unsigned prime = primes[prime_i];
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upolynomial::zp_manager upm(nm);
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@ -246,35 +246,35 @@ static void tst_factor_finite_1() {
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cout << "Factoring " << K << "("; upm.display(cout, K_u); cout << ") in Z_" << prime << endl;
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cout << "Expecting " << knuth_factors[0][prime_i] << " distinct factors, " << knuth_factors[1][prime_i] << " total" << endl;
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// factor it
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upolynomial::zp_factors factors(upm);
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upolynomial::zp_factors factors(upm);
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/* bool factorized = */ upolynomial::zp_factor(upm, K_u, factors);
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// check the result
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unsigned distinct = factors.distinct_factors();
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unsigned total = factors.total_factors();
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unsigned total = factors.total_factors();
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cout << "Got " << factors << endl;
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cout << "Thats " << distinct << " distinct factors, " << total << " total" << endl;
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SASSERT(knuth_factors[0][prime_i] == distinct);
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SASSERT(knuth_factors[1][prime_i] == total);
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upolynomial::numeral_vector multiplied;
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factors.multiply(multiplied);
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SASSERT(upm.eq(K_u, multiplied));
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upm.reset(multiplied);
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// remove the temp
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upm.reset(K_u);
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}
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}
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}
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static void tst_factor_finite_2() {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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@ -284,7 +284,7 @@ static void tst_factor_finite_2() {
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polynomial_ref S2 = (x^4) - 10*(x^2) + 1;
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polynomial_ref S3 = (x^8) - 40*(x^6) + 352*(x^4) - 960*(x^2) + 576;
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polynomial_ref S4 = (x^16) - 136*(x^14) + 6476*(x^12) - 141912*(x^10) + 1513334*(x^8) - 7453176*(x^6) + 13950764*(x^4) - 5596840*(x^2) + 46225;
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vector<polynomial_ref> S;
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S.push_back(S1);
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S.push_back(S2);
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@ -294,9 +294,9 @@ static void tst_factor_finite_2() {
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// factor all the S_i them for all the prime numbers
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for (unsigned S_i = 0; S_i < S.size(); ++ S_i) {
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for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i) {
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unsigned prime = primes[prime_i];
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for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i) {
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unsigned prime = primes[prime_i];
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upolynomial::zp_manager upm(nm);
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upm.set_zp(prime);
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@ -308,22 +308,22 @@ static void tst_factor_finite_2() {
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upolynomial::zp_factors factors(upm);
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upolynomial::zp_factor(upm, S_i_u, factors);
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// check the result
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unsigned distinct = factors.distinct_factors();
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unsigned total = factors.total_factors();
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unsigned total = factors.total_factors();
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cout << "Got " << factors << endl;
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cout << "Thats " << distinct << " distinct factors, " << total << " total" << endl;
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SASSERT(swinnerton_dyer_factors[S_i][0][prime_i] == distinct);
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SASSERT(swinnerton_dyer_factors[S_i][1][prime_i] == total);
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upolynomial::numeral_vector multiplied;
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factors.multiply(multiplied);
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SASSERT(upm.eq(S_i_u, multiplied));
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upm.reset(multiplied);
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// remove the temp
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upm.reset(S_i_u);
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}
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@ -331,9 +331,9 @@ static void tst_factor_finite_2() {
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}
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static void tst_factor_finite_3() {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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@ -360,15 +360,15 @@ static void tst_factor_finite_3() {
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random_p.push_back( 3*(x^10) + 2*(x^8) + 1*(x^7) + 1*(x^6) + 3*(x^4) + 3*(x^3) + 4*(x^2) + 3*x + 0 );
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random_p.push_back( 1*(x^10) + 2*(x^9) + 2*(x^6) + 4*(x^3) + 4*(x^2) + 0 );
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random_p.push_back( 1*(x^10) + 2*(x^9) + 2*(x^8) + 4*(x^7) + 4*(x^6) + 1*(x^5) + 1*(x^3) + 1*(x^2) + 3*x + 0 );
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// factor all the randoms them for all the prime numbers
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for (unsigned random_i = 0; random_i < random_p.size(); ++ random_i) {
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for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i) {
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unsigned prime = primes[prime_i];
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for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i) {
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unsigned prime = primes[prime_i];
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upolynomial::zp_manager upm(nm);
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upm.set_zp(prime);
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upolynomial::numeral_vector poly;
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upm.to_numeral_vector(random_p[random_i], poly);
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@ -377,24 +377,24 @@ static void tst_factor_finite_3() {
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upolynomial::zp_factors factors(upm);
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upolynomial::zp_factor(upm, poly, factors);
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// check the result
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unsigned distinct = factors.distinct_factors();
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unsigned total = factors.total_factors();
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unsigned total = factors.total_factors();
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cout << "Got " << factors << endl;
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cout << "Thats " << distinct << " distinct factors, " << total << " total" << endl;
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// SASSERT(random_polynomial[random_i][0][prime_i] == distinct);
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// SASSERT(random_polynomial[random_i][1][prime_i] == total);
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upolynomial::numeral_vector multiplied;
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factors.multiply(multiplied);
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bool equal = upm.eq(poly, multiplied);
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cout << (equal ? "equal" : "not equal") << endl;
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SASSERT(equal);
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upm.reset(multiplied);
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// remove the temp
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upm.reset(poly);
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}
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@ -403,11 +403,11 @@ static void tst_factor_finite_3() {
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static void tst_factor_enumeration() {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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vector<polynomial_ref> factors;
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for (int i = 0; i < 5; ++ i) {
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polynomial_ref factor(pm);
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@ -419,12 +419,12 @@ static void tst_factor_enumeration() {
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upolynomial::zp_manager upm_13(nm);
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upm_13.set_zp(13);
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upolynomial::zp_factors factors_13(upm_13);
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upolynomial::zp_factors factors_13(upm_13);
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upolynomial::numeral constant;
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nm.set(constant, 10);
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factors_13.set_constant(constant);
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for (unsigned i = 0; i < 5; ++ i) {
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upolynomial::numeral_vector ufactor;
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upm_13.to_numeral_vector(factors[i], ufactor);
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@ -463,7 +463,7 @@ static void tst_factor_enumeration() {
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factors_13.set_degree(i, factors_13.get_degree(i) + i);
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}
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cout << "Different: " << factors_13 << " of degree " << factors_13.get_degree() << endl;
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upolynomial::factorization_degree_set degrees1(factors_13);
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upolynomial::factorization_degree_set degrees1(factors_13);
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degrees1.display(cout); cout << endl; // [0, ..., 15]
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polynomial_ref tmp1 = (x^3) + 1;
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@ -482,15 +482,15 @@ static void tst_factor_enumeration() {
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upm_13.reset(up3);
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cout << "Different: " << tmp << " of degree " << tmp.get_degree() << endl;
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upolynomial::factorization_degree_set degrees2(tmp);
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degrees2.display(cout); cout << endl;
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upolynomial::factorization_degree_set degrees2(tmp);
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degrees2.display(cout); cout << endl;
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tmp1 = (x^2) + 1;
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tmp2 = (x^10) + 2;
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tmp3 = x + 3;
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tmp3 = x + 3;
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upm_13.to_numeral_vector(tmp1, up1);
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upm_13.to_numeral_vector(tmp2, up2);
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upm_13.to_numeral_vector(tmp3, up3);
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upm_13.to_numeral_vector(tmp3, up3);
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tmp.clear();
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tmp.push_back(up1, 2);
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tmp.push_back(up2, 1);
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@ -499,23 +499,23 @@ static void tst_factor_enumeration() {
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upm_13.reset(up1);
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upm_13.reset(up2);
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upm_13.reset(up3);
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upolynomial::factorization_degree_set degrees3(tmp);
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degrees3.display(cout); cout << endl;
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upolynomial::factorization_degree_set degrees3(tmp);
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degrees3.display(cout); cout << endl;
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degrees1.intersect(degrees3);
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degrees1.display(cout); cout << endl;
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}
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static void tst_factor_square_free_univariate_1(unsigned max_length) {
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polynomial::numeral_manager nm;
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polynomial::numeral_manager nm;
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upolynomial::numeral test;
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upolynomial::numeral p;
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nm.set(test, -9);
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nm.set(p, 5);
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nm.mod(test, p, test);
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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@ -527,8 +527,8 @@ static void tst_factor_square_free_univariate_1(unsigned max_length) {
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for(unsigned length = 1; length < max_length; ++ length) {
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// starting from prime_i going for length
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for(unsigned start_i = 0; start_i < n_primes; ++ start_i) {
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for(unsigned start_i = 0; start_i < n_primes; ++ start_i) {
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polynomial_ref f(pm);
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bool first = true;
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@ -541,18 +541,18 @@ static void tst_factor_square_free_univariate_1(unsigned max_length) {
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} else {
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f = f*(p1*(x^p2) - p2);
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}
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}
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}
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upolynomial::manager upm(nm);
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scoped_mpz_vector f_u(nm);
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upm.to_numeral_vector(f, f_u);
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cout << "factoring "; upm.display(cout, f_u); cout << endl;
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cout << "expecting " << length << " factors ";
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upolynomial::factors factors(upm);
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/* bool ok = */ upolynomial::factor_square_free(upm, f_u, factors);
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/* bool ok = */ upolynomial::factor_square_free(upm, f_u, factors);
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cout << "got " << factors << endl;
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SASSERT(factors.distinct_factors() == length);
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}
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}
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@ -560,7 +560,7 @@ static void tst_factor_square_free_univariate_1(unsigned max_length) {
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static void tst_factor_square_free_univariate_2() {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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reslimit rl; polynomial::manager pm(rl, nm);
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polynomial_ref x(pm);
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x = pm.mk_polynomial(pm.mk_var());
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@ -570,7 +570,7 @@ static void tst_factor_square_free_univariate_2() {
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polynomial_ref S2 = (x^4) - 10*(x^2) + 1;
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polynomial_ref S3 = (x^8) - 40*(x^6) + 352*(x^4) - 960*(x^2) + 576;
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polynomial_ref S4 = (x^16) - 136*(x^14) + 6476*(x^12) - 141912*(x^10) + 1513334*(x^8) - 7453176*(x^6) + 13950764*(x^4) - 5596840*(x^2) + 46225;
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vector<polynomial_ref> S;
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S.push_back(S1);
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S.push_back(S2);
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@ -580,17 +580,17 @@ static void tst_factor_square_free_univariate_2() {
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upolynomial::manager upm(nm);
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// factor all the S_i them for all the prime numbers
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for (unsigned S_i = 0; S_i < S.size(); ++ S_i) {
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for (unsigned S_i = 0; S_i < S.size(); ++ S_i) {
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upolynomial::numeral_vector S_i_u;
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upm.to_numeral_vector(S[S_i], S_i_u);
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||||
|
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cout << "Factoring "; upm.display(cout, S_i_u); cout << " over Z " << endl;
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upolynomial::factors factors(upm);
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upolynomial::factor_square_free(upm, S_i_u, factors);
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||||
|
||||
|
||||
// check the result
|
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cout << "Got " << factors << endl;
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||||
|
||||
|
||||
// remove the temp
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upm.reset(S_i_u);
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||||
}
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||||
|
|
@ -598,31 +598,31 @@ static void tst_factor_square_free_univariate_2() {
|
|||
|
||||
static void tst_factor_square_free_univariate_3() {
|
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polynomial::numeral_manager nm;
|
||||
polynomial::manager pm(nm);
|
||||
reslimit rl; polynomial::manager pm(rl, nm);
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||||
|
||||
polynomial_ref x(pm);
|
||||
x = pm.mk_polynomial(pm.mk_var());
|
||||
|
||||
polynomial_ref deg70 = (x^70) - 6*(x^65) - (x^60) + 60*(x^55) - 54*(x^50) - 230*(x^45) + 274*(x^40) + 542*(x^35) - 615*(x^30) - 1120*(x^25) + 1500*(x^20) - 160*(x^15) - 395*(x^10) + 76*(x^5) + 34;
|
||||
|
||||
|
||||
upolynomial::manager upm(nm);
|
||||
upolynomial::numeral_vector deg70_u;
|
||||
|
||||
|
||||
upm.to_numeral_vector(deg70, deg70_u);
|
||||
|
||||
cout << "Factoring "; upm.display(cout, deg70_u); cout << " over Z " << endl;
|
||||
upolynomial::factors factors(upm);
|
||||
upolynomial::factor_square_free(upm, deg70_u, factors);
|
||||
|
||||
|
||||
cout << "Got " << factors << endl;
|
||||
|
||||
|
||||
upm.reset(deg70_u);
|
||||
}
|
||||
#endif
|
||||
|
||||
void tst_factor_swinnerton_dyer_big(unsigned max) {
|
||||
polynomial::numeral_manager nm;
|
||||
polynomial::manager pm(nm);
|
||||
reslimit rl; polynomial::manager pm(rl, nm);
|
||||
|
||||
polynomial_ref x(pm);
|
||||
x = pm.mk_polynomial(pm.mk_var());
|
||||
|
|
@ -631,8 +631,8 @@ void tst_factor_swinnerton_dyer_big(unsigned max) {
|
|||
vector<polynomial::var> vars;
|
||||
|
||||
unsigned n = std::min(max, static_cast<unsigned>(sizeof(primes)/sizeof(unsigned)));
|
||||
for(unsigned prime_i = 0; prime_i < n; ++ prime_i) {
|
||||
|
||||
for(unsigned prime_i = 0; prime_i < n; ++ prime_i) {
|
||||
|
||||
int prime = primes[prime_i];
|
||||
|
||||
cout << "Computing Swinnerton-Dyer[" << prime_i + 1 << "]" << endl;
|
||||
|
|
@ -643,7 +643,7 @@ void tst_factor_swinnerton_dyer_big(unsigned max) {
|
|||
|
||||
polynomial_ref p(pm);
|
||||
p = (y^2) - prime;
|
||||
roots.push_back(p);
|
||||
roots.push_back(p);
|
||||
|
||||
polynomial_ref computation = x;
|
||||
for (unsigned i = 0; i < roots.size(); ++ i) {
|
||||
|
|
@ -663,17 +663,18 @@ void tst_factor_swinnerton_dyer_big(unsigned max) {
|
|||
}
|
||||
|
||||
cout << "Computed Swinnerton-Dyer[" << prime_i + 1 << "], degree = " << pm.total_degree(computation) << ", size = " << pm.size(computation) << endl;
|
||||
|
||||
|
||||
cout << "Starting factoring " << endl;
|
||||
|
||||
|
||||
{
|
||||
timeit timer(true, "factoring swinnerton-dyer");
|
||||
|
||||
upolynomial::manager upm(nm);
|
||||
scoped_mpz_vector sd_u(nm);
|
||||
upm.to_numeral_vector(computation, sd_u);
|
||||
reslimit rl;
|
||||
upolynomial::manager upm(rl, nm);
|
||||
scoped_mpz_vector sd_u(nm);
|
||||
upm.to_numeral_vector(computation, sd_u);
|
||||
upolynomial::factors factors(upm);
|
||||
upolynomial::factor_square_free(upm, sd_u, factors);
|
||||
upolynomial::factor_square_free(upm, sd_u, factors);
|
||||
cout << "Got " << factors.distinct_factors() << " factors" << endl;
|
||||
}
|
||||
|
||||
|
|
@ -681,16 +682,16 @@ void tst_factor_swinnerton_dyer_big(unsigned max) {
|
|||
}
|
||||
|
||||
static void tst_factor_square_free_multivariate_1(unsigned max_n) {
|
||||
#if 0
|
||||
polynomial::numeral_manager nm;
|
||||
#if 0
|
||||
polynomial::numeral_manager nm;
|
||||
upolynomial::numeral test;
|
||||
upolynomial::numeral p;
|
||||
nm.set(test, -9);
|
||||
nm.set(p, 5);
|
||||
nm.mod(test, p, test);
|
||||
|
||||
polynomial::manager pm(nm);
|
||||
|
||||
reslimit rl; polynomial::manager pm(rl, nm);
|
||||
|
||||
polynomial_ref x(pm);
|
||||
x = pm.mk_polynomial(pm.mk_var());
|
||||
|
||||
|
|
@ -700,7 +701,7 @@ static void tst_factor_square_free_multivariate_1(unsigned max_n) {
|
|||
// lets start simple x^n - y^n
|
||||
for (unsigned prime_i = 0; prime_i < sizeof(primes)/sizeof(unsigned); ++ prime_i) {
|
||||
unsigned prime = primes[prime_i];
|
||||
|
||||
|
||||
if (prime > max_n) {
|
||||
break;
|
||||
}
|
||||
|
|
@ -719,7 +720,7 @@ static void tst_factor_square_free_multivariate_1(unsigned max_n) {
|
|||
|
||||
|
||||
void tst_polynomial_factorization() {
|
||||
|
||||
|
||||
enable_trace("polynomial::factorization");
|
||||
// enable_trace("polynomial::factorization::bughunt");
|
||||
enable_trace("polynomial::factorization::multivariate");
|
||||
|
|
@ -727,12 +728,12 @@ void tst_polynomial_factorization() {
|
|||
|
||||
// Z_p square-free factorization tests
|
||||
// tst_square_free_finite_1();
|
||||
|
||||
|
||||
// Z_p factorization tests
|
||||
// tst_factor_finite_1();
|
||||
// tst_factor_finite_2();
|
||||
// tst_factor_finite_3();
|
||||
|
||||
|
||||
// Z factorization
|
||||
// tst_factor_enumeration();
|
||||
// tst_factor_square_free_univariate_1(3);
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue