1 | // -*- c++ -*- |
---|
2 | //***************************************************************************** |
---|
3 | /** @file facAlgExt.cc |
---|
4 | * |
---|
5 | * @author Martin Lee |
---|
6 | * @date |
---|
7 | * |
---|
8 | * Univariate factorization over algebraic extension of Q using Trager's |
---|
9 | * algorithm |
---|
10 | * |
---|
11 | * @par Copyright: |
---|
12 | * (c) by The SINGULAR Team, see LICENSE file |
---|
13 | * |
---|
14 | **/ |
---|
15 | //***************************************************************************** |
---|
16 | |
---|
17 | #include "config.h" |
---|
18 | |
---|
19 | #include "cf_assert.h" |
---|
20 | #include "debug.h" |
---|
21 | #include "timing.h" |
---|
22 | |
---|
23 | #include "canonicalform.h" |
---|
24 | #include "cf_random.h" |
---|
25 | #include "cf_algorithm.h" |
---|
26 | #include "facFqBivarUtil.h" |
---|
27 | #include "facAlgExt.h" |
---|
28 | #include "cfModResultant.h" |
---|
29 | #include "fac_sqrfree.h" |
---|
30 | |
---|
31 | TIMING_DEFINE_PRINT(fac_alg_resultant) |
---|
32 | TIMING_DEFINE_PRINT(fac_alg_norm) |
---|
33 | TIMING_DEFINE_PRINT(fac_alg_factor_norm) |
---|
34 | TIMING_DEFINE_PRINT(fac_alg_gcd) |
---|
35 | TIMING_DEFINE_PRINT(fac_alg_sqrf) |
---|
36 | TIMING_DEFINE_PRINT(fac_alg_factor_sqrf) |
---|
37 | TIMING_DEFINE_PRINT(fac_alg_time_shift) |
---|
38 | |
---|
39 | // squarefree part of F |
---|
40 | CanonicalForm |
---|
41 | uniSqrfPart (const CanonicalForm& F) |
---|
42 | { |
---|
43 | ASSERT (F.isUnivariate(), "univariate input expected"); |
---|
44 | ASSERT (getCharacteristic() == 0, "characteristic 0 expected"); |
---|
45 | CanonicalForm G= deriv (F, F.mvar()); |
---|
46 | G= gcd (F, G); |
---|
47 | return F/G; |
---|
48 | } |
---|
49 | |
---|
50 | // i is an integer such that Norm (F (x-i*alpha)) is squarefree |
---|
51 | CanonicalForm sqrfNorm (const CanonicalForm& F, const Variable& alpha, int& i) |
---|
52 | { |
---|
53 | Variable x= Variable (F.level() + 1); |
---|
54 | Variable y= F.mvar(); |
---|
55 | CanonicalForm g= F (x, alpha); |
---|
56 | CanonicalForm mipo= getMipo (alpha); |
---|
57 | mipo= mipo (x, alpha); |
---|
58 | mipo *= bCommonDen (mipo); |
---|
59 | |
---|
60 | int degg= degree (g); |
---|
61 | int degmipo= degree (mipo); |
---|
62 | CanonicalForm norm; |
---|
63 | TIMING_START (fac_alg_resultant); |
---|
64 | if (degg >= 8 || degmipo >= 8) |
---|
65 | norm= resultantZ (g, mipo, x); |
---|
66 | else |
---|
67 | norm= resultant (g, mipo, x); |
---|
68 | TIMING_END_AND_PRINT (fac_alg_resultant, "time to compute resultant0: "); |
---|
69 | |
---|
70 | i= 0; |
---|
71 | int k; |
---|
72 | if (degree (gcd (deriv (norm, y), norm)) <= 0) |
---|
73 | return norm; |
---|
74 | i= 1; |
---|
75 | do |
---|
76 | { |
---|
77 | k= 1; |
---|
78 | while (k < 3) |
---|
79 | { |
---|
80 | if (k == 1) |
---|
81 | { |
---|
82 | g= F (y - i*alpha, y); |
---|
83 | g *= bCommonDen (g); |
---|
84 | TIMING_START (fac_alg_resultant); |
---|
85 | if (degg >= 8 || degmipo >= 8) |
---|
86 | norm= resultantZ (g (x, alpha), mipo, x); |
---|
87 | else |
---|
88 | norm= resultant (g (x, alpha), mipo, x); |
---|
89 | TIMING_END_AND_PRINT (fac_alg_resultant,"time to compute resultant1: "); |
---|
90 | } |
---|
91 | else |
---|
92 | { |
---|
93 | g= F (y + i*alpha, y); |
---|
94 | g *= bCommonDen (g); |
---|
95 | TIMING_START (fac_alg_resultant); |
---|
96 | if (degg >= 8 || degmipo >= 8) |
---|
97 | norm= resultantZ (g (x, alpha), mipo, x); |
---|
98 | else |
---|
99 | norm= resultant (g (x, alpha), mipo, x); |
---|
100 | TIMING_END_AND_PRINT (fac_alg_resultant,"time to compute resultant2: "); |
---|
101 | } |
---|
102 | if (degree (gcd (deriv (norm, y), norm)) <= 0) |
---|
103 | { |
---|
104 | if (k == 2) |
---|
105 | i= -i; |
---|
106 | return norm; |
---|
107 | } |
---|
108 | k++; |
---|
109 | } |
---|
110 | i++; |
---|
111 | } while (1); |
---|
112 | } |
---|
113 | |
---|
114 | CFList |
---|
115 | AlgExtSqrfFactorize (const CanonicalForm& F, const Variable& alpha) |
---|
116 | { |
---|
117 | ASSERT (F.isUnivariate(), "univariate input expected"); |
---|
118 | ASSERT (getCharacteristic() == 0, "characteristic 0 expected"); |
---|
119 | |
---|
120 | bool save_rat=!isOn (SW_RATIONAL); |
---|
121 | On (SW_RATIONAL); |
---|
122 | CanonicalForm f= F*bCommonDen (F); |
---|
123 | int shift; |
---|
124 | TIMING_START (fac_alg_norm); |
---|
125 | CanonicalForm norm= sqrfNorm (f, alpha, shift); |
---|
126 | TIMING_END_AND_PRINT (fac_alg_norm, "time to compute sqrf norm: "); |
---|
127 | ASSERT (degree (norm, alpha) <= 0, "wrong norm computed"); |
---|
128 | TIMING_START (fac_alg_factor_norm); |
---|
129 | bool save_sort= !isOn (SW_USE_NTL_SORT); |
---|
130 | On (SW_USE_NTL_SORT); |
---|
131 | CFFList normFactors= factorize (norm); |
---|
132 | if (save_sort) |
---|
133 | Off (SW_USE_NTL_SORT); |
---|
134 | TIMING_END_AND_PRINT (fac_alg_factor_norm, "time to factor norm: "); |
---|
135 | CFList factors; |
---|
136 | if (normFactors.length() <= 2) |
---|
137 | { |
---|
138 | if (save_rat) Off(SW_RATIONAL); |
---|
139 | return CFList (F); |
---|
140 | } |
---|
141 | |
---|
142 | normFactors.removeFirst(); |
---|
143 | CFFListIterator i= normFactors; |
---|
144 | CanonicalForm buf; |
---|
145 | bool shiftBuf= false; |
---|
146 | if (!(normFactors.length() == 2 && degree (i.getItem().factor()) <= degree (f))) |
---|
147 | { |
---|
148 | TIMING_START (fac_alg_time_shift); |
---|
149 | if (shift != 0) |
---|
150 | buf= f (f.mvar() - shift*alpha, f.mvar()); |
---|
151 | else |
---|
152 | buf= f; |
---|
153 | shiftBuf= true; |
---|
154 | TIMING_END_AND_PRINT (fac_alg_time_shift, "time to shift: "); |
---|
155 | } |
---|
156 | else |
---|
157 | buf= f; |
---|
158 | CanonicalForm factor; |
---|
159 | int count= 0; |
---|
160 | for (; i.hasItem(); i++) |
---|
161 | { |
---|
162 | ASSERT (i.getItem().exp() == 1, "norm not squarefree"); |
---|
163 | TIMING_START (fac_alg_gcd); |
---|
164 | if (shiftBuf) |
---|
165 | factor= gcd (buf, i.getItem().factor()); |
---|
166 | else |
---|
167 | { |
---|
168 | if (shift == 0) |
---|
169 | factor= gcd (buf, i.getItem().factor()); |
---|
170 | else |
---|
171 | factor= gcd (buf, i.getItem().factor() (f.mvar() + shift*alpha, f.mvar())); |
---|
172 | } |
---|
173 | buf /= factor; |
---|
174 | if (shiftBuf) |
---|
175 | { |
---|
176 | if (shift != 0) |
---|
177 | factor= factor (f.mvar() + shift*alpha, f.mvar()); |
---|
178 | } |
---|
179 | TIMING_END_AND_PRINT (fac_alg_gcd, "time to recover factors: "); |
---|
180 | factors.append (factor); |
---|
181 | count++; |
---|
182 | if (normFactors.length() - 1 == count) |
---|
183 | { |
---|
184 | if (shiftBuf) |
---|
185 | factors.append (buf (f.mvar() + shift*alpha, f.mvar())); |
---|
186 | else |
---|
187 | factors.append (buf); |
---|
188 | buf= 1; |
---|
189 | break; |
---|
190 | } |
---|
191 | } |
---|
192 | ASSERT (degree (buf) <= 0, "incomplete factorization"); |
---|
193 | if (save_rat) Off(SW_RATIONAL); |
---|
194 | return factors; |
---|
195 | } |
---|
196 | |
---|
197 | CFFList |
---|
198 | AlgExtFactorize (const CanonicalForm& F, const Variable& alpha) |
---|
199 | { |
---|
200 | ASSERT (F.isUnivariate(), "univariate input expected"); |
---|
201 | ASSERT (getCharacteristic() == 0, "characteristic 0 expected"); |
---|
202 | |
---|
203 | |
---|
204 | if (F.inCoeffDomain()) |
---|
205 | return CFFList (CFFactor (F, 1)); |
---|
206 | |
---|
207 | bool save_rat=!isOn (SW_RATIONAL); |
---|
208 | On (SW_RATIONAL); |
---|
209 | TIMING_START (fac_alg_sqrf); |
---|
210 | CFFList sqrf= sqrFreeZ (F); |
---|
211 | TIMING_END_AND_PRINT (fac_alg_sqrf, "time for sqrf factors in Q(a)[x]: "); |
---|
212 | CFList factorsSqrf; |
---|
213 | CFFList factors; |
---|
214 | CFListIterator j; |
---|
215 | |
---|
216 | CanonicalForm lcinv; |
---|
217 | for (CFFListIterator i= sqrf; i.hasItem(); i++) |
---|
218 | { |
---|
219 | if (i.getItem().factor().inCoeffDomain()) continue; |
---|
220 | TIMING_START (fac_alg_factor_sqrf); |
---|
221 | factorsSqrf= AlgExtSqrfFactorize (i.getItem().factor(), alpha); |
---|
222 | TIMING_END_AND_PRINT (fac_alg_factor_sqrf, |
---|
223 | "time to factor sqrf factors in Q(a)[x]: "); |
---|
224 | for (j= factorsSqrf; j.hasItem(); j++) |
---|
225 | { |
---|
226 | lcinv= 1/Lc (j.getItem()); |
---|
227 | factors.append (CFFactor (j.getItem()*lcinv, i.getItem().exp())); |
---|
228 | } |
---|
229 | } |
---|
230 | |
---|
231 | factors.insert (CFFactor (Lc(F), 1)); |
---|
232 | if (save_rat) Off(SW_RATIONAL); |
---|
233 | return factors; |
---|
234 | } |
---|
235 | |
---|