1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id: rintegers.cc,v 1.12 2008-04-18 13:32:53 wienand Exp $ */ |
---|
5 | /* |
---|
6 | * ABSTRACT: numbers modulo n |
---|
7 | */ |
---|
8 | |
---|
9 | #include <string.h> |
---|
10 | #include "mod2.h" |
---|
11 | #include <mylimits.h> |
---|
12 | #include "structs.h" |
---|
13 | #include "febase.h" |
---|
14 | #include "omalloc.h" |
---|
15 | #include "numbers.h" |
---|
16 | #include "longrat.h" |
---|
17 | #include "mpr_complex.h" |
---|
18 | #include "ring.h" |
---|
19 | #include "rintegers.h" |
---|
20 | #include "gmp.h" |
---|
21 | |
---|
22 | #ifdef HAVE_RINGZ |
---|
23 | |
---|
24 | typedef MP_INT *int_number; |
---|
25 | omBin gmp_nrz_bin = omGetSpecBin(sizeof(MP_INT)); |
---|
26 | |
---|
27 | /* |
---|
28 | * Multiply two numbers |
---|
29 | */ |
---|
30 | number nrzMult (number a, number b) |
---|
31 | { |
---|
32 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
33 | mpz_init(erg); |
---|
34 | mpz_mul(erg, (int_number) a, (int_number) b); |
---|
35 | return (number) erg; |
---|
36 | } |
---|
37 | |
---|
38 | /* |
---|
39 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
---|
40 | */ |
---|
41 | number nrzLcm (number a,number b,ring r) |
---|
42 | { |
---|
43 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
44 | mpz_init(erg); |
---|
45 | mpz_lcm(erg, (int_number) a, (int_number) b); |
---|
46 | return (number) erg; |
---|
47 | } |
---|
48 | |
---|
49 | /* |
---|
50 | * Give the largest non unit k, such that a = x * k, b = y * k has |
---|
51 | * a solution. |
---|
52 | */ |
---|
53 | number nrzGcd (number a,number b,ring r) |
---|
54 | { |
---|
55 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
56 | mpz_init(erg); |
---|
57 | mpz_gcd(erg, (int_number) a, (int_number) b); |
---|
58 | return (number) erg; |
---|
59 | } |
---|
60 | |
---|
61 | /* |
---|
62 | * Give the largest non unit k, such that a = x * k, b = y * k has |
---|
63 | * a solution and r, s, s.t. k = s*a + t*b |
---|
64 | */ |
---|
65 | number nrzExtGcd (number a, number b, number *s, number *t) |
---|
66 | { |
---|
67 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
68 | int_number bs = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
69 | int_number bt = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
70 | mpz_init(erg); |
---|
71 | mpz_init(bs); |
---|
72 | mpz_init(bt); |
---|
73 | mpz_gcdext(erg, bs, bt, (int_number) a, (int_number) b); |
---|
74 | *s = (number) bs; |
---|
75 | *t = (number) bt; |
---|
76 | return (number) erg; |
---|
77 | } |
---|
78 | |
---|
79 | void nrzPower (number a, int i, number * result) |
---|
80 | { |
---|
81 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
82 | mpz_init(erg); |
---|
83 | mpz_pow_ui(erg, (int_number) a, i); |
---|
84 | *result = (number) erg; |
---|
85 | } |
---|
86 | |
---|
87 | /* |
---|
88 | * create a number from int |
---|
89 | */ |
---|
90 | number nrzInit (int i) |
---|
91 | { |
---|
92 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
93 | mpz_init_set_si(erg, i); |
---|
94 | return (number) erg; |
---|
95 | } |
---|
96 | |
---|
97 | void nrzDelete(number *a, const ring r) |
---|
98 | { |
---|
99 | if (*a == NULL) return; |
---|
100 | mpz_clear((int_number) *a); |
---|
101 | omFreeBin((ADDRESS) *a, gmp_nrz_bin); |
---|
102 | *a = NULL; |
---|
103 | } |
---|
104 | |
---|
105 | number nrzCopy(number a) |
---|
106 | { |
---|
107 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
108 | mpz_init_set(erg, (int_number) a); |
---|
109 | return (number) erg; |
---|
110 | } |
---|
111 | |
---|
112 | number cfrzCopy(number a, const ring r) |
---|
113 | { |
---|
114 | return nrzCopy(a); |
---|
115 | } |
---|
116 | |
---|
117 | int nrzSize(number a) |
---|
118 | { |
---|
119 | if (a == NULL) return 0; |
---|
120 | return sizeof(MP_INT); |
---|
121 | } |
---|
122 | |
---|
123 | /* |
---|
124 | * convert a number to int (-p/2 .. p/2) |
---|
125 | */ |
---|
126 | int nrzInt(number &n) |
---|
127 | { |
---|
128 | return (int) mpz_get_si( (int_number) &n); |
---|
129 | } |
---|
130 | |
---|
131 | number nrzAdd (number a, number b) |
---|
132 | { |
---|
133 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
134 | mpz_init(erg); |
---|
135 | mpz_add(erg, (int_number) a, (int_number) b); |
---|
136 | return (number) erg; |
---|
137 | } |
---|
138 | |
---|
139 | number nrzSub (number a, number b) |
---|
140 | { |
---|
141 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
142 | mpz_init(erg); |
---|
143 | mpz_sub(erg, (int_number) a, (int_number) b); |
---|
144 | return (number) erg; |
---|
145 | } |
---|
146 | |
---|
147 | number nrzGetUnit (number a) |
---|
148 | { |
---|
149 | return nrzInit(1); |
---|
150 | } |
---|
151 | |
---|
152 | BOOLEAN nrzIsUnit (number a) |
---|
153 | { |
---|
154 | return 0 == mpz_cmpabs_ui((int_number) a, 1); |
---|
155 | } |
---|
156 | |
---|
157 | BOOLEAN nrzIsZero (number a) |
---|
158 | { |
---|
159 | return 0 == mpz_cmpabs_ui((int_number) a, 0); |
---|
160 | } |
---|
161 | |
---|
162 | BOOLEAN nrzIsOne (number a) |
---|
163 | { |
---|
164 | return 0 == mpz_cmp_si((int_number) a, 1); |
---|
165 | } |
---|
166 | |
---|
167 | BOOLEAN nrzIsMOne (number a) |
---|
168 | { |
---|
169 | return 0 == mpz_cmp_si((int_number) a, -1); |
---|
170 | } |
---|
171 | |
---|
172 | BOOLEAN nrzEqual (number a,number b) |
---|
173 | { |
---|
174 | return 0 == mpz_cmp((int_number) a, (int_number) b); |
---|
175 | } |
---|
176 | |
---|
177 | BOOLEAN nrzGreater (number a,number b) |
---|
178 | { |
---|
179 | return 0 < mpz_cmp((int_number) a, (int_number) b); |
---|
180 | } |
---|
181 | |
---|
182 | BOOLEAN nrzGreaterZero (number k) |
---|
183 | { |
---|
184 | return 0 <= mpz_cmp_si((int_number) k, 0); |
---|
185 | } |
---|
186 | |
---|
187 | int nrzComp(number a, number b) |
---|
188 | { |
---|
189 | if (nrzEqual(a, b)) return 0; |
---|
190 | if (nrzDivBy(a, b)) return -1; |
---|
191 | if (nrzDivBy(b, a)) return 1; |
---|
192 | return 2; |
---|
193 | } |
---|
194 | |
---|
195 | BOOLEAN nrzDivBy (number a,number b) |
---|
196 | { |
---|
197 | return mpz_divisible_p((int_number) a, (int_number) b) != 0; |
---|
198 | } |
---|
199 | |
---|
200 | number nrzDiv (number a,number b) |
---|
201 | { |
---|
202 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
203 | int_number r = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
204 | mpz_init(erg); |
---|
205 | mpz_tdiv_qr(erg, r, (int_number) a, (int_number) b); |
---|
206 | if (!nrzIsZero((number) r)) |
---|
207 | { |
---|
208 | WarnS("Division by non divisible element."); |
---|
209 | WarnS("Result is without remainder."); |
---|
210 | } |
---|
211 | mpz_clear(r); |
---|
212 | omFreeBin(r, gmp_nrz_bin); |
---|
213 | return (number) erg; |
---|
214 | } |
---|
215 | |
---|
216 | number nrzIntDiv (number a,number b) |
---|
217 | { |
---|
218 | int_number erg = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
219 | mpz_init(erg); |
---|
220 | mpz_tdiv_q(erg, (int_number) a, (int_number) b); |
---|
221 | return (number) erg; |
---|
222 | } |
---|
223 | |
---|
224 | number nrzInvers (number c) |
---|
225 | { |
---|
226 | if (!nrzIsUnit((number) c)) |
---|
227 | { |
---|
228 | WarnS("Non invertible element."); |
---|
229 | return (number)0; //TODO |
---|
230 | } |
---|
231 | return c; |
---|
232 | } |
---|
233 | |
---|
234 | number nrzNeg (number c) |
---|
235 | { |
---|
236 | // nNeg inplace !!! TODO |
---|
237 | // int_number erg = (int_number) omAllocBin(gmp_nrn_bin); // evtl. spaeter mit bin |
---|
238 | // mpz_init(erg); |
---|
239 | mpz_mul_si((int_number) c, (int_number) c, -1); |
---|
240 | return c; |
---|
241 | } |
---|
242 | |
---|
243 | nMapFunc nrzSetMap(ring src, ring dst) |
---|
244 | { |
---|
245 | return NULL; /* default */ |
---|
246 | } |
---|
247 | |
---|
248 | |
---|
249 | /* |
---|
250 | * set the exponent (allocate and init tables) (TODO) |
---|
251 | */ |
---|
252 | |
---|
253 | void nrzSetExp(int m, ring r) |
---|
254 | { |
---|
255 | } |
---|
256 | |
---|
257 | void nrzInitExp(int m, ring r) |
---|
258 | { |
---|
259 | } |
---|
260 | |
---|
261 | #ifdef LDEBUG |
---|
262 | //BOOLEAN nrzDBTest (number a, const char *f, const int l) |
---|
263 | //{ |
---|
264 | // return TRUE;//TODO |
---|
265 | //} |
---|
266 | #endif |
---|
267 | |
---|
268 | void nrzWrite (number &a) |
---|
269 | { |
---|
270 | char *s,*z; |
---|
271 | if (a==NULL) |
---|
272 | { |
---|
273 | StringAppendS("o"); |
---|
274 | } |
---|
275 | else |
---|
276 | { |
---|
277 | int l=mpz_sizeinbase((int_number) a, 10); |
---|
278 | if (a->s<2) l=si_max(l,mpz_sizeinbase((int_number) a,10)); |
---|
279 | l+=2; |
---|
280 | s=(char*)omAlloc(l); |
---|
281 | z=mpz_get_str(s,10,(int_number) a); |
---|
282 | StringAppendS(z); |
---|
283 | omFreeSize((ADDRESS)s,l); |
---|
284 | } |
---|
285 | } |
---|
286 | |
---|
287 | /*2 |
---|
288 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
289 | */ |
---|
290 | static const char * nlEatLongC(char *s, MP_INT *i) |
---|
291 | { |
---|
292 | const char * start=s; |
---|
293 | |
---|
294 | while (*s >= '0' && *s <= '9') s++; |
---|
295 | if (*s=='\0') |
---|
296 | { |
---|
297 | mpz_set_str(i,start,10); |
---|
298 | } |
---|
299 | else |
---|
300 | { |
---|
301 | char c=*s; |
---|
302 | *s='\0'; |
---|
303 | mpz_set_str(i,start,10); |
---|
304 | *s=c; |
---|
305 | } |
---|
306 | return s; |
---|
307 | } |
---|
308 | |
---|
309 | const char * nrzRead (const char *s, number *a) |
---|
310 | { |
---|
311 | int_number z = (int_number) omAllocBin(gmp_nrz_bin); // evtl. spaeter mit bin |
---|
312 | { |
---|
313 | mpz_init(z); |
---|
314 | s = nlEatLongC((char *) s, z); |
---|
315 | } |
---|
316 | *a = (number) z; |
---|
317 | return s; |
---|
318 | } |
---|
319 | #endif |
---|