1 // Univariate Polynomials over a general ring.
3 #include "cln/SV_ringelt.h"
4 #include "cln/integer.h"
9 // Assume a ring is a ring.
10 inline cl_heap_ring* TheRing (const cl_ring& R)
11 { return (cl_heap_ring*) R.heappointer; }
13 // Normalize a vector: remove leading zero coefficients.
14 // The result vector is known to have length len > 0.
15 static inline void gen_normalize (cl_heap_ring* R, cl_SV_ringelt& result, uintL len)
17 if (R->_zerop(result[len-1])) {
20 if (!R->_zerop(result[len-1]))
24 var cl_SV_ringelt newresult = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(len));
25 for (var sintL i = len-1; i >= 0; i--)
26 init1(_cl_ring_element, newresult[i]) (result[i]);
31 static void gen_fprint (cl_heap_univpoly_ring* UPR, std::ostream& stream, const _cl_UP& x)
33 DeclarePoly(cl_SV_ringelt,x);
34 var cl_heap_ring* R = TheRing(UPR->basering());
35 var sintL xlen = x.length();
39 var cl_string varname = get_varname(UPR);
40 for (var sintL i = xlen-1; i >= 0; i--)
41 if (!R->_zerop(x[i])) {
43 fprint(stream, " + ");
45 R->_fprint(stream, x[i]);
49 fprint(stream, varname);
52 fprintdecimal(stream, i);
59 static cl_boolean gen_equal (cl_heap_univpoly_ring* UPR, const _cl_UP& x, const _cl_UP& y)
61 DeclarePoly(cl_SV_ringelt,x);
62 DeclarePoly(cl_SV_ringelt,y);
63 var cl_heap_ring* R = TheRing(UPR->basering());
64 var sintL xlen = x.length();
65 var sintL ylen = y.length();
68 for (var sintL i = xlen-1; i >= 0; i--)
69 if (!R->_equal(x[i],y[i]))
74 static const _cl_UP gen_zero (cl_heap_univpoly_ring* UPR)
76 return _cl_UP(UPR, cl_null_SV_ringelt);
79 static cl_boolean gen_zerop (cl_heap_univpoly_ring* UPR, const _cl_UP& x)
82 { DeclarePoly(cl_SV_ringelt,x);
83 var sintL xlen = x.length();
90 static const _cl_UP gen_plus (cl_heap_univpoly_ring* UPR, const _cl_UP& x, const _cl_UP& y)
92 DeclarePoly(cl_SV_ringelt,x);
93 DeclarePoly(cl_SV_ringelt,y);
94 var cl_heap_ring* R = TheRing(UPR->basering());
95 var sintL xlen = x.length();
96 var sintL ylen = y.length();
98 return _cl_UP(UPR, y);
100 return _cl_UP(UPR, x);
101 // Now xlen > 0, ylen > 0.
103 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(xlen));
105 for (i = xlen-1; i >= ylen; i--)
106 init1(_cl_ring_element, result[i]) (x[i]);
107 for (i = ylen-1; i >= 0; i--)
108 init1(_cl_ring_element, result[i]) (R->_plus(x[i],y[i]));
109 return _cl_UP(UPR, result);
112 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(ylen));
114 for (i = ylen-1; i >= xlen; i--)
115 init1(_cl_ring_element, result[i]) (y[i]);
116 for (i = xlen-1; i >= 0; i--)
117 init1(_cl_ring_element, result[i]) (R->_plus(x[i],y[i]));
118 return _cl_UP(UPR, result);
120 // Now xlen = ylen > 0. Add and normalize simultaneously.
121 for (var sintL i = xlen-1; i >= 0; i--) {
122 var _cl_ring_element hicoeff = R->_plus(x[i],y[i]);
123 if (!R->_zerop(hicoeff)) {
124 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(i+1));
125 init1(_cl_ring_element, result[i]) (hicoeff);
126 for (i-- ; i >= 0; i--)
127 init1(_cl_ring_element, result[i]) (R->_plus(x[i],y[i]));
128 return _cl_UP(UPR, result);
131 return _cl_UP(UPR, cl_null_SV_ringelt);
134 static const _cl_UP gen_uminus (cl_heap_univpoly_ring* UPR, const _cl_UP& x)
136 DeclarePoly(cl_SV_ringelt,x);
137 var cl_heap_ring* R = TheRing(UPR->basering());
138 var sintL xlen = x.length();
140 return _cl_UP(UPR, x);
142 // Negate. No normalization necessary, since the degree doesn't change.
143 var sintL i = xlen-1;
144 var _cl_ring_element hicoeff = R->_uminus(x[i]);
145 if (R->_zerop(hicoeff)) cl_abort();
146 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(xlen));
147 init1(_cl_ring_element, result[i]) (hicoeff);
148 for (i-- ; i >= 0; i--)
149 init1(_cl_ring_element, result[i]) (R->_uminus(x[i]));
150 return _cl_UP(UPR, result);
153 static const _cl_UP gen_minus (cl_heap_univpoly_ring* UPR, const _cl_UP& x, const _cl_UP& y)
155 DeclarePoly(cl_SV_ringelt,x);
156 DeclarePoly(cl_SV_ringelt,y);
157 var cl_heap_ring* R = TheRing(UPR->basering());
158 var sintL xlen = x.length();
159 var sintL ylen = y.length();
161 return _cl_UP(UPR, x);
163 return gen_uminus(UPR,_cl_UP(UPR, y));
164 // Now xlen > 0, ylen > 0.
166 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(xlen));
168 for (i = xlen-1; i >= ylen; i--)
169 init1(_cl_ring_element, result[i]) (x[i]);
170 for (i = ylen-1; i >= 0; i--)
171 init1(_cl_ring_element, result[i]) (R->_minus(x[i],y[i]));
172 return _cl_UP(UPR, result);
175 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(ylen));
177 for (i = ylen-1; i >= xlen; i--)
178 init1(_cl_ring_element, result[i]) (R->_uminus(y[i]));
179 for (i = xlen-1; i >= 0; i--)
180 init1(_cl_ring_element, result[i]) (R->_minus(x[i],y[i]));
181 return _cl_UP(UPR, result);
183 // Now xlen = ylen > 0. Add and normalize simultaneously.
184 for (var sintL i = xlen-1; i >= 0; i--) {
185 var _cl_ring_element hicoeff = R->_minus(x[i],y[i]);
186 if (!R->_zerop(hicoeff)) {
187 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(i+1));
188 init1(_cl_ring_element, result[i]) (hicoeff);
189 for (i-- ; i >= 0; i--)
190 init1(_cl_ring_element, result[i]) (R->_minus(x[i],y[i]));
191 return _cl_UP(UPR, result);
194 return _cl_UP(UPR, cl_null_SV_ringelt);
197 static const _cl_UP gen_one (cl_heap_univpoly_ring* UPR)
199 var cl_heap_ring* R = TheRing(UPR->basering());
200 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(1));
201 init1(_cl_ring_element, result[0]) (R->_one());
202 return _cl_UP(UPR, result);
205 static const _cl_UP gen_canonhom (cl_heap_univpoly_ring* UPR, const cl_I& x)
207 var cl_heap_ring* R = TheRing(UPR->basering());
208 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(1));
209 init1(_cl_ring_element, result[0]) (R->_canonhom(x));
210 return _cl_UP(UPR, result);
213 static const _cl_UP gen_mul (cl_heap_univpoly_ring* UPR, const _cl_UP& x, const _cl_UP& y)
215 DeclarePoly(cl_SV_ringelt,x);
216 DeclarePoly(cl_SV_ringelt,y);
217 var cl_heap_ring* R = TheRing(UPR->basering());
218 var sintL xlen = x.length();
219 var sintL ylen = y.length();
221 return _cl_UP(UPR, x);
223 return _cl_UP(UPR, y);
225 var sintL len = xlen + ylen - 1;
226 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(len));
229 var sintL i = xlen-1;
230 var _cl_ring_element xi = x[i];
231 for (sintL j = ylen-1; j >= 0; j--)
232 init1(_cl_ring_element, result[i+j]) (R->_mul(xi,y[j]));
234 for (sintL i = xlen-2; i >= 0; i--) {
235 var _cl_ring_element xi = x[i];
236 for (sintL j = ylen-1; j > 0; j--)
237 result[i+j] = R->_plus(result[i+j],R->_mul(xi,y[j]));
238 /* j=0 */ init1(_cl_ring_element, result[i]) (R->_mul(xi,y[0]));
242 var sintL j = ylen-1;
243 var _cl_ring_element yj = y[j];
244 for (sintL i = xlen-1; i >= 0; i--)
245 init1(_cl_ring_element, result[i+j]) (R->_mul(x[i],yj));
247 for (sintL j = ylen-2; j >= 0; j--) {
248 var _cl_ring_element yj = y[j];
249 for (sintL i = xlen-1; i > 0; i--)
250 result[i+j] = R->_plus(result[i+j],R->_mul(x[i],yj));
251 /* i=0 */ init1(_cl_ring_element, result[j]) (R->_mul(x[0],yj));
254 // Normalize (not necessary in integral domains).
255 //gen_normalize(R,result,len);
256 if (R->_zerop(result[len-1])) cl_abort();
257 return _cl_UP(UPR, result);
260 static const _cl_UP gen_square (cl_heap_univpoly_ring* UPR, const _cl_UP& x)
262 DeclarePoly(cl_SV_ringelt,x);
263 var cl_heap_ring* R = TheRing(UPR->basering());
264 var sintL xlen = x.length();
266 return cl_UP(UPR, x);
267 var sintL len = 2*xlen-1;
268 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(len));
270 // Loop through all 0 <= j < i <= xlen-1.
272 var sintL i = xlen-1;
273 var _cl_ring_element xi = x[i];
274 for (sintL j = i-1; j >= 0; j--)
275 init1(_cl_ring_element, result[i+j]) (R->_mul(xi,x[j]));
277 {for (sintL i = xlen-2; i >= 1; i--) {
278 var _cl_ring_element xi = x[i];
279 for (sintL j = i-1; j >= 1; j--)
280 result[i+j] = R->_plus(result[i+j],R->_mul(xi,x[j]));
281 /* j=0 */ init1(_cl_ring_element, result[i]) (R->_mul(xi,x[0]));
284 {for (sintL i = len-2; i >= 1; i--)
285 result[i] = R->_plus(result[i],result[i]);
288 init1(_cl_ring_element, result[2*(xlen-1)]) (R->_square(x[xlen-1]));
289 for (sintL i = xlen-2; i >= 1; i--)
290 result[2*i] = R->_plus(result[2*i],R->_square(x[i]));
292 init1(_cl_ring_element, result[0]) (R->_square(x[0]));
293 // Normalize (not necessary in integral domains).
294 //gen_normalize(R,result,len);
295 if (R->_zerop(result[len-1])) cl_abort();
296 return _cl_UP(UPR, result);
299 static const _cl_UP gen_exptpos (cl_heap_univpoly_ring* UPR, const _cl_UP& x, const cl_I& y)
303 while (!oddp(b)) { a = UPR->_square(a); b = b >> 1; }
308 if (oddp(b)) { c = UPR->_mul(a,c); }
313 static const _cl_UP gen_scalmul (cl_heap_univpoly_ring* UPR, const cl_ring_element& x, const _cl_UP& y)
315 if (!(UPR->basering() == x.ring())) cl_abort();
317 DeclarePoly(cl_SV_ringelt,y);
318 var cl_heap_ring* R = TheRing(UPR->basering());
319 var sintL ylen = y.length();
321 return _cl_UP(UPR, y);
323 return _cl_UP(UPR, cl_null_SV_ringelt);
324 var cl_SV_ringelt result = cl_SV_ringelt(cl_make_heap_SV_ringelt_uninit(ylen));
325 for (sintL i = ylen-1; i >= 0; i--)
326 init1(_cl_ring_element, result[i]) (R->_mul(x,y[i]));
327 // Normalize (not necessary in integral domains).
328 //gen_normalize(R,result,ylen);
329 if (R->_zerop(result[ylen-1])) cl_abort();
330 return _cl_UP(UPR, result);
333 static sintL gen_degree (cl_heap_univpoly_ring* UPR, const _cl_UP& x)
336 { DeclarePoly(cl_SV_ringelt,x);
337 return (sintL) x.length() - 1;
340 static sintL gen_ldegree (cl_heap_univpoly_ring* UPR, const _cl_UP& x)
341 {{ DeclarePoly(cl_SV_ringelt,x);
342 var cl_heap_ring* R = TheRing(UPR->basering());
343 var sintL xlen = x.length();
344 for (sintL i = 0; i < xlen; i++) {
345 if (!R->_zerop(x[i]))
351 static const _cl_UP gen_monomial (cl_heap_univpoly_ring* UPR, const cl_ring_element& x, uintL e)
353 if (!(UPR->basering() == x.ring())) cl_abort();
354 var cl_heap_ring* R = TheRing(UPR->basering());
356 return _cl_UP(UPR, cl_null_SV_ringelt);
359 var cl_SV_ringelt result = cl_SV_ringelt(len);
361 return _cl_UP(UPR, result);
365 static const cl_ring_element gen_coeff (cl_heap_univpoly_ring* UPR, const _cl_UP& x, uintL index)
367 DeclarePoly(cl_SV_ringelt,x);
368 var cl_heap_ring* R = TheRing(UPR->basering());
369 if (index < x.length())
370 return cl_ring_element(R, x[index]);
375 static const _cl_UP gen_create (cl_heap_univpoly_ring* UPR, sintL deg)
378 return _cl_UP(UPR, cl_null_SV_ringelt);
380 var sintL len = deg+1;
381 return _cl_UP(UPR, cl_SV_ringelt(len));
385 static void gen_set_coeff (cl_heap_univpoly_ring* UPR, _cl_UP& x, uintL index, const cl_ring_element& y)
387 DeclareMutablePoly(cl_SV_ringelt,x);
388 if (!(UPR->basering() == y.ring())) cl_abort();
389 if (!(index < x.length())) cl_abort();
393 static void gen_finalize (cl_heap_univpoly_ring* UPR, _cl_UP& x)
395 DeclareMutablePoly(cl_SV_ringelt,x); // NB: x is modified by reference!
396 var cl_heap_ring* R = TheRing(UPR->basering());
397 var uintL len = x.length();
399 gen_normalize(R,x,len);
402 static const cl_ring_element gen_eval (cl_heap_univpoly_ring* UPR, const _cl_UP& x, const cl_ring_element& y)
405 // If x = 0, return 0.
406 // If y = 0, return x[0].
407 // Else compute (...(x[len-1]*y+x[len-2])*y ...)*y + x[0].
408 DeclarePoly(cl_SV_ringelt,x);
409 var cl_heap_ring* R = TheRing(UPR->basering());
410 if (!(y.ring() == R)) cl_abort();
411 var uintL len = x.length();
415 return cl_ring_element(R, x[0]);
417 var _cl_ring_element z = x[i];
419 z = R->_plus(R->_mul(z,y),x[i]);
420 return cl_ring_element(R, z);
423 static cl_univpoly_setops gen_setops = {
428 static cl_univpoly_addops gen_addops = {
436 static cl_univpoly_mulops gen_mulops = {
444 static cl_univpoly_modulops gen_modulops = {
448 static cl_univpoly_polyops gen_polyops = {
459 class cl_heap_gen_univpoly_ring : public cl_heap_univpoly_ring {
460 SUBCLASS_cl_heap_univpoly_ring()
463 cl_heap_gen_univpoly_ring (const cl_ring& r);
465 ~cl_heap_gen_univpoly_ring () {}
468 static void cl_heap_gen_univpoly_ring_destructor (cl_heap* pointer)
470 (*(cl_heap_gen_univpoly_ring*)pointer).~cl_heap_gen_univpoly_ring();
473 cl_class cl_class_gen_univpoly_ring = {
474 cl_heap_gen_univpoly_ring_destructor,
475 cl_class_flags_univpoly_ring
479 inline cl_heap_gen_univpoly_ring::cl_heap_gen_univpoly_ring (const cl_ring& r)
480 : cl_heap_univpoly_ring (r, &gen_setops, &gen_addops, &gen_mulops, &gen_modulops, &gen_polyops)
482 type = &cl_class_gen_univpoly_ring;