1 // Univariate Polynomials.
6 #include "cln/object.h"
8 #include "cln/malloc.h"
9 #include "cln/proplist.h"
10 #include "cln/symbol.h"
16 // To protect against mixing elements of different polynomial rings, every
17 // polynomial carries its ring in itself.
19 class cl_heap_univpoly_ring;
21 class cl_univpoly_ring : public cl_ring {
23 // Default constructor.
25 // Constructor. Takes a cl_heap_univpoly_ring*, increments its refcount.
26 cl_univpoly_ring (cl_heap_univpoly_ring* r);
27 // Private constructor. Doesn't increment the refcount.
28 cl_univpoly_ring (cl_private_thing);
30 cl_univpoly_ring (const cl_univpoly_ring&);
31 // Assignment operator.
32 cl_univpoly_ring& operator= (const cl_univpoly_ring&);
33 // Automatic dereferencing.
34 cl_heap_univpoly_ring* operator-> () const
35 { return (cl_heap_univpoly_ring*)heappointer; }
37 // Copy constructor and assignment operator.
38 CL_DEFINE_COPY_CONSTRUCTOR2(cl_univpoly_ring,cl_ring)
39 CL_DEFINE_ASSIGNMENT_OPERATOR(cl_univpoly_ring,cl_univpoly_ring)
41 // Normal constructor for `cl_univpoly_ring'.
42 inline cl_univpoly_ring::cl_univpoly_ring (cl_heap_univpoly_ring* r)
43 : cl_ring ((cl_private_thing) (cl_inc_pointer_refcount((cl_heap*)r), r)) {}
44 // Private constructor for `cl_univpoly_ring'.
45 inline cl_univpoly_ring::cl_univpoly_ring (cl_private_thing p)
48 // Operations on univariate polynomial rings.
50 inline bool operator== (const cl_univpoly_ring& R1, const cl_univpoly_ring& R2)
51 { return (R1.pointer == R2.pointer); }
52 inline bool operator!= (const cl_univpoly_ring& R1, const cl_univpoly_ring& R2)
53 { return (R1.pointer != R2.pointer); }
54 inline bool operator== (const cl_univpoly_ring& R1, cl_heap_univpoly_ring* R2)
55 { return (R1.pointer == R2); }
56 inline bool operator!= (const cl_univpoly_ring& R1, cl_heap_univpoly_ring* R2)
57 { return (R1.pointer != R2); }
59 // Representation of a univariate polynomial.
61 class _cl_UP /* cf. _cl_ring_element */ {
63 cl_gcpointer rep; // vector of coefficients, a cl_V_any
64 // Default constructor.
68 _cl_UP (const cl_heap_univpoly_ring* R, const cl_V_any& r) : rep (as_cl_private_thing(r)) { (void)R; }
69 _cl_UP (const cl_univpoly_ring& R, const cl_V_any& r) : rep (as_cl_private_thing(r)) { (void)R; }
72 CL_DEFINE_CONVERTER(_cl_ring_element)
73 public: // Ability to place an object at a given address.
74 void* operator new (size_t size) { return malloc_hook(size); }
75 void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
76 void operator delete (void* ptr) { free_hook(ptr); }
79 class cl_UP /* cf. cl_ring_element */ : public _cl_UP {
81 cl_univpoly_ring _ring; // polynomial ring (references the base ring)
83 const cl_univpoly_ring& ring () const { return _ring; }
85 // Default constructor.
89 cl_UP (const cl_univpoly_ring& R, const cl_V_any& r)
90 : _cl_UP (R,r), _ring (R) {}
91 cl_UP (const cl_univpoly_ring& R, const _cl_UP& r)
92 : _cl_UP (r), _ring (R) {}
95 CL_DEFINE_CONVERTER(cl_ring_element)
96 // Destructive modification.
97 void set_coeff (uintL index, const cl_ring_element& y);
100 const cl_ring_element operator() (const cl_ring_element& y) const;
102 void debug_print () const;
103 public: // Ability to place an object at a given address.
104 void* operator new (size_t size) { return malloc_hook(size); }
105 void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
106 void operator delete (void* ptr) { free_hook(ptr); }
112 struct _cl_univpoly_setops /* cf. _cl_ring_setops */ {
114 void (* fprint) (cl_heap_univpoly_ring* R, std::ostream& stream, const _cl_UP& x);
116 // (Be careful: This is not well-defined for polynomials with
117 // floating-point coefficients.)
118 cl_boolean (* equal) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
120 struct _cl_univpoly_addops /* cf. _cl_ring_addops */ {
122 const _cl_UP (* zero) (cl_heap_univpoly_ring* R);
123 cl_boolean (* zerop) (cl_heap_univpoly_ring* R, const _cl_UP& x);
125 const _cl_UP (* plus) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
127 const _cl_UP (* minus) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
129 const _cl_UP (* uminus) (cl_heap_univpoly_ring* R, const _cl_UP& x);
131 struct _cl_univpoly_mulops /* cf. _cl_ring_mulops */ {
133 const _cl_UP (* one) (cl_heap_univpoly_ring* R);
134 // canonical homomorphism
135 const _cl_UP (* canonhom) (cl_heap_univpoly_ring* R, const cl_I& x);
137 const _cl_UP (* mul) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
139 const _cl_UP (* square) (cl_heap_univpoly_ring* R, const _cl_UP& x);
141 const _cl_UP (* expt_pos) (cl_heap_univpoly_ring* R, const _cl_UP& x, const cl_I& y);
143 struct _cl_univpoly_modulops {
144 // scalar multiplication x*y
145 const _cl_UP (* scalmul) (cl_heap_univpoly_ring* R, const cl_ring_element& x, const _cl_UP& y);
147 struct _cl_univpoly_polyops {
149 sintL (* degree) (cl_heap_univpoly_ring* R, const _cl_UP& x);
151 sintL (* ldegree) (cl_heap_univpoly_ring* R, const _cl_UP& x);
153 const _cl_UP (* monomial) (cl_heap_univpoly_ring* R, const cl_ring_element& x, uintL e);
154 // coefficient (0 if index>degree)
155 const cl_ring_element (* coeff) (cl_heap_univpoly_ring* R, const _cl_UP& x, uintL index);
156 // create new polynomial, bounded degree
157 const _cl_UP (* create) (cl_heap_univpoly_ring* R, sintL deg);
158 // set coefficient in new polynomial
159 void (* set_coeff) (cl_heap_univpoly_ring* R, _cl_UP& x, uintL index, const cl_ring_element& y);
160 // finalize polynomial
161 void (* finalize) (cl_heap_univpoly_ring* R, _cl_UP& x);
162 // evaluate, substitute an element of R
163 const cl_ring_element (* eval) (cl_heap_univpoly_ring* R, const _cl_UP& x, const cl_ring_element& y);
165 typedef const _cl_univpoly_setops cl_univpoly_setops;
166 typedef const _cl_univpoly_addops cl_univpoly_addops;
167 typedef const _cl_univpoly_mulops cl_univpoly_mulops;
168 typedef const _cl_univpoly_modulops cl_univpoly_modulops;
169 typedef const _cl_univpoly_polyops cl_univpoly_polyops;
171 // Representation of a univariate polynomial ring.
173 class cl_heap_univpoly_ring /* cf. cl_heap_ring */ : public cl_heap {
174 SUBCLASS_cl_heap_ring()
176 cl_property_list properties;
178 cl_univpoly_setops* setops;
179 cl_univpoly_addops* addops;
180 cl_univpoly_mulops* mulops;
181 cl_univpoly_modulops* modulops;
182 cl_univpoly_polyops* polyops;
184 cl_ring _basering; // the coefficients are elements of this ring
186 const cl_ring& basering () const { return _basering; }
188 // Low-level operations.
189 void _fprint (std::ostream& stream, const _cl_UP& x)
190 { setops->fprint(this,stream,x); }
191 cl_boolean _equal (const _cl_UP& x, const _cl_UP& y)
192 { return setops->equal(this,x,y); }
193 const _cl_UP _zero ()
194 { return addops->zero(this); }
195 cl_boolean _zerop (const _cl_UP& x)
196 { return addops->zerop(this,x); }
197 const _cl_UP _plus (const _cl_UP& x, const _cl_UP& y)
198 { return addops->plus(this,x,y); }
199 const _cl_UP _minus (const _cl_UP& x, const _cl_UP& y)
200 { return addops->minus(this,x,y); }
201 const _cl_UP _uminus (const _cl_UP& x)
202 { return addops->uminus(this,x); }
204 { return mulops->one(this); }
205 const _cl_UP _canonhom (const cl_I& x)
206 { return mulops->canonhom(this,x); }
207 const _cl_UP _mul (const _cl_UP& x, const _cl_UP& y)
208 { return mulops->mul(this,x,y); }
209 const _cl_UP _square (const _cl_UP& x)
210 { return mulops->square(this,x); }
211 const _cl_UP _expt_pos (const _cl_UP& x, const cl_I& y)
212 { return mulops->expt_pos(this,x,y); }
213 const _cl_UP _scalmul (const cl_ring_element& x, const _cl_UP& y)
214 { return modulops->scalmul(this,x,y); }
215 sintL _degree (const _cl_UP& x)
216 { return polyops->degree(this,x); }
217 sintL _ldegree (const _cl_UP& x)
218 { return polyops->ldegree(this,x); }
219 const _cl_UP _monomial (const cl_ring_element& x, uintL e)
220 { return polyops->monomial(this,x,e); }
221 const cl_ring_element _coeff (const _cl_UP& x, uintL index)
222 { return polyops->coeff(this,x,index); }
223 const _cl_UP _create (sintL deg)
224 { return polyops->create(this,deg); }
225 void _set_coeff (_cl_UP& x, uintL index, const cl_ring_element& y)
226 { polyops->set_coeff(this,x,index,y); }
227 void _finalize (_cl_UP& x)
228 { polyops->finalize(this,x); }
229 const cl_ring_element _eval (const _cl_UP& x, const cl_ring_element& y)
230 { return polyops->eval(this,x,y); }
231 // High-level operations.
232 void fprint (std::ostream& stream, const cl_UP& x)
234 if (!(x.ring() == this)) cl_abort();
237 cl_boolean equal (const cl_UP& x, const cl_UP& y)
239 if (!(x.ring() == this)) cl_abort();
240 if (!(y.ring() == this)) cl_abort();
245 return cl_UP(this,_zero());
247 cl_boolean zerop (const cl_UP& x)
249 if (!(x.ring() == this)) cl_abort();
252 const cl_UP plus (const cl_UP& x, const cl_UP& y)
254 if (!(x.ring() == this)) cl_abort();
255 if (!(y.ring() == this)) cl_abort();
256 return cl_UP(this,_plus(x,y));
258 const cl_UP minus (const cl_UP& x, const cl_UP& y)
260 if (!(x.ring() == this)) cl_abort();
261 if (!(y.ring() == this)) cl_abort();
262 return cl_UP(this,_minus(x,y));
264 const cl_UP uminus (const cl_UP& x)
266 if (!(x.ring() == this)) cl_abort();
267 return cl_UP(this,_uminus(x));
271 return cl_UP(this,_one());
273 const cl_UP canonhom (const cl_I& x)
275 return cl_UP(this,_canonhom(x));
277 const cl_UP mul (const cl_UP& x, const cl_UP& y)
279 if (!(x.ring() == this)) cl_abort();
280 if (!(y.ring() == this)) cl_abort();
281 return cl_UP(this,_mul(x,y));
283 const cl_UP square (const cl_UP& x)
285 if (!(x.ring() == this)) cl_abort();
286 return cl_UP(this,_square(x));
288 const cl_UP expt_pos (const cl_UP& x, const cl_I& y)
290 if (!(x.ring() == this)) cl_abort();
291 return cl_UP(this,_expt_pos(x,y));
293 const cl_UP scalmul (const cl_ring_element& x, const cl_UP& y)
295 if (!(y.ring() == this)) cl_abort();
296 return cl_UP(this,_scalmul(x,y));
298 sintL degree (const cl_UP& x)
300 if (!(x.ring() == this)) cl_abort();
303 sintL ldegree (const cl_UP& x)
305 if (!(x.ring() == this)) cl_abort();
308 const cl_UP monomial (const cl_ring_element& x, uintL e)
310 return cl_UP(this,_monomial(x,e));
312 const cl_ring_element coeff (const cl_UP& x, uintL index)
314 if (!(x.ring() == this)) cl_abort();
315 return _coeff(x,index);
317 const cl_UP create (sintL deg)
319 return cl_UP(this,_create(deg));
321 void set_coeff (cl_UP& x, uintL index, const cl_ring_element& y)
323 if (!(x.ring() == this)) cl_abort();
324 _set_coeff(x,index,y);
326 void finalize (cl_UP& x)
328 if (!(x.ring() == this)) cl_abort();
331 const cl_ring_element eval (const cl_UP& x, const cl_ring_element& y)
333 if (!(x.ring() == this)) cl_abort();
336 // Property operations.
337 cl_property* get_property (const cl_symbol& key)
338 { return properties.get_property(key); }
339 void add_property (cl_property* new_property)
340 { properties.add_property(new_property); }
342 cl_heap_univpoly_ring (const cl_ring& r, cl_univpoly_setops*, cl_univpoly_addops*, cl_univpoly_mulops*, cl_univpoly_modulops*, cl_univpoly_polyops*);
343 ~cl_heap_univpoly_ring () {}
345 #define SUBCLASS_cl_heap_univpoly_ring() \
346 SUBCLASS_cl_heap_ring()
349 // Lookup or create the "standard" univariate polynomial ring over a ring r.
350 extern const cl_univpoly_ring find_univpoly_ring (const cl_ring& r);
351 //CL_REQUIRE(cl_UP_unnamed)
353 // Lookup or create a univariate polynomial ring with a named variable over r.
354 extern const cl_univpoly_ring find_univpoly_ring (const cl_ring& r, const cl_symbol& varname);
355 //CL_REQUIRE(cl_UP_named)
360 // Operations on polynomials.
363 inline void fprint (std::ostream& stream, const cl_UP& x)
364 { x.ring()->fprint(stream,x); }
365 CL_DEFINE_PRINT_OPERATOR(cl_UP)
368 inline const cl_UP operator+ (const cl_UP& x, const cl_UP& y)
369 { return x.ring()->plus(x,y); }
372 inline const cl_UP operator- (const cl_UP& x)
373 { return x.ring()->uminus(x); }
376 inline const cl_UP operator- (const cl_UP& x, const cl_UP& y)
377 { return x.ring()->minus(x,y); }
380 inline bool operator== (const cl_UP& x, const cl_UP& y)
381 { return x.ring()->equal(x,y); }
382 inline bool operator!= (const cl_UP& x, const cl_UP& y)
383 { return !x.ring()->equal(x,y); }
385 // Compare against 0.
386 inline cl_boolean zerop (const cl_UP& x)
387 { return x.ring()->zerop(x); }
390 inline const cl_UP operator* (const cl_UP& x, const cl_UP& y)
391 { return x.ring()->mul(x,y); }
394 inline const cl_UP square (const cl_UP& x)
395 { return x.ring()->square(x); }
397 // Exponentiation x^y, where y > 0.
398 inline const cl_UP expt_pos (const cl_UP& x, const cl_I& y)
399 { return x.ring()->expt_pos(x,y); }
401 // Scalar multiplication.
402 #if 0 // less efficient
403 inline const cl_UP operator* (const cl_I& x, const cl_UP& y)
404 { return y.ring()->mul(y.ring()->canonhom(x),y); }
405 inline const cl_UP operator* (const cl_UP& x, const cl_I& y)
406 { return x.ring()->mul(x.ring()->canonhom(y),x); }
408 inline const cl_UP operator* (const cl_I& x, const cl_UP& y)
409 { return y.ring()->scalmul(y.ring()->basering()->canonhom(x),y); }
410 inline const cl_UP operator* (const cl_UP& x, const cl_I& y)
411 { return x.ring()->scalmul(x.ring()->basering()->canonhom(y),x); }
412 inline const cl_UP operator* (const cl_ring_element& x, const cl_UP& y)
413 { return y.ring()->scalmul(x,y); }
414 inline const cl_UP operator* (const cl_UP& x, const cl_ring_element& y)
415 { return x.ring()->scalmul(y,x); }
418 inline sintL degree (const cl_UP& x)
419 { return x.ring()->degree(x); }
422 inline sintL ldegree (const cl_UP& x)
423 { return x.ring()->ldegree(x); }
426 inline const cl_ring_element coeff (const cl_UP& x, uintL index)
427 { return x.ring()->coeff(x,index); }
429 // Destructive modification.
430 inline void set_coeff (cl_UP& x, uintL index, const cl_ring_element& y)
431 { x.ring()->set_coeff(x,index,y); }
432 inline void finalize (cl_UP& x)
433 { x.ring()->finalize(x); }
434 inline void cl_UP::set_coeff (uintL index, const cl_ring_element& y)
435 { ring()->set_coeff(*this,index,y); }
436 inline void cl_UP::finalize ()
437 { ring()->finalize(*this); }
439 // Evaluation. (No extension of the base ring allowed here for now.)
440 inline const cl_ring_element cl_UP::operator() (const cl_ring_element& y) const
442 return ring()->eval(*this,y);
446 extern const cl_UP deriv (const cl_UP& x);
449 // Ring of uninitialized elements.
450 // Any operation results in a run-time error.
452 extern const cl_univpoly_ring cl_no_univpoly_ring;
453 extern cl_class cl_class_no_univpoly_ring;
454 CL_REQUIRE(cl_UP_no_ring)
456 inline cl_univpoly_ring::cl_univpoly_ring ()
457 : cl_ring (as_cl_private_thing(cl_no_univpoly_ring)) {}
458 inline _cl_UP::_cl_UP ()
459 : rep ((cl_private_thing) cl_combine(cl_FN_tag,0)) {}
460 inline cl_UP::cl_UP ()
461 : _cl_UP (), _ring () {}
464 // Debugging support.
466 extern int cl_UP_debug_module;
467 CL_FORCE_LINK(cl_UP_debug_dummy, cl_UP_debug_module)
472 #endif /* _CL_UNIVPOLY_H */
476 // Templates for univariate polynomials of complex/real/rational/integers.
479 // Unfortunately, this is not usable now, because of gcc-2.7 bugs:
480 // - A template inline function is not inline in the first function that
482 // - Argument matching bug: User-defined conversions are not tried (or
483 // tried with too low priority) for template functions w.r.t. normal
484 // functions. For example, a call expt_pos(cl_UP_specialized<cl_N>,int)
485 // is compiled as expt_pos(const cl_UP&, const cl_I&) instead of
486 // expt_pos(const cl_UP_specialized<cl_N>&, const cl_I&).
487 // It will, however, be usable when gcc-2.8 is released.
489 #if defined(_CL_UNIVPOLY_COMPLEX_H) || defined(_CL_UNIVPOLY_REAL_H) || defined(_CL_UNIVPOLY_RATIONAL_H) || defined(_CL_UNIVPOLY_INTEGER_H)
490 #ifndef _CL_UNIVPOLY_AUX_H
492 // Normal univariate polynomials with stricter static typing:
493 // `class T' instead of `cl_ring_element'.
495 template <class T> class cl_univpoly_specialized_ring;
496 template <class T> class cl_UP_specialized;
497 template <class T> class cl_heap_univpoly_specialized_ring;
500 class cl_univpoly_specialized_ring : public cl_univpoly_ring {
502 // Default constructor.
503 cl_univpoly_specialized_ring () : cl_univpoly_ring () {}
505 cl_univpoly_specialized_ring (const cl_univpoly_specialized_ring&);
506 // Assignment operator.
507 cl_univpoly_specialized_ring& operator= (const cl_univpoly_specialized_ring&);
508 // Automatic dereferencing.
509 cl_heap_univpoly_specialized_ring<T>* operator-> () const
510 { return (cl_heap_univpoly_specialized_ring<T>*)heappointer; }
512 // Copy constructor and assignment operator.
514 _CL_DEFINE_COPY_CONSTRUCTOR2(cl_univpoly_specialized_ring<T>,cl_univpoly_specialized_ring,cl_univpoly_ring)
516 CL_DEFINE_ASSIGNMENT_OPERATOR(cl_univpoly_specialized_ring<T>,cl_univpoly_specialized_ring<T>)
519 class cl_UP_specialized : public cl_UP {
521 const cl_univpoly_specialized_ring<T>& ring () const { return The(cl_univpoly_specialized_ring<T>)(_ring); }
523 CL_DEFINE_CONVERTER(cl_ring_element)
524 // Destructive modification.
525 void set_coeff (uintL index, const T& y);
528 const T operator() (const T& y) const;
529 public: // Ability to place an object at a given address.
530 void* operator new (size_t size) { return malloc_hook(size); }
531 void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
532 void operator delete (void* ptr) { free_hook(ptr); }
536 class cl_heap_univpoly_specialized_ring : public cl_heap_univpoly_ring {
537 SUBCLASS_cl_heap_univpoly_ring()
538 // High-level operations.
539 void fprint (std::ostream& stream, const cl_UP_specialized<T>& x)
541 cl_heap_univpoly_ring::fprint(stream,x);
543 cl_boolean equal (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
545 return cl_heap_univpoly_ring::equal(x,y);
547 const cl_UP_specialized<T> zero ()
549 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::zero());
551 cl_boolean zerop (const cl_UP_specialized<T>& x)
553 return cl_heap_univpoly_ring::zerop(x);
555 const cl_UP_specialized<T> plus (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
557 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::plus(x,y));
559 const cl_UP_specialized<T> minus (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
561 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::minus(x,y));
563 const cl_UP_specialized<T> uminus (const cl_UP_specialized<T>& x)
565 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::uminus(x));
567 const cl_UP_specialized<T> one ()
569 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::one());
571 const cl_UP_specialized<T> canonhom (const cl_I& x)
573 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::canonhom(x));
575 const cl_UP_specialized<T> mul (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
577 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::mul(x,y));
579 const cl_UP_specialized<T> square (const cl_UP_specialized<T>& x)
581 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::square(x));
583 const cl_UP_specialized<T> expt_pos (const cl_UP_specialized<T>& x, const cl_I& y)
585 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::expt_pos(x,y));
587 const cl_UP_specialized<T> scalmul (const T& x, const cl_UP_specialized<T>& y)
589 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::scalmul(x,y));
591 sintL degree (const cl_UP_specialized<T>& x)
593 return cl_heap_univpoly_ring::degree(x);
595 sintL ldegree (const cl_UP_specialized<T>& x)
597 return cl_heap_univpoly_ring::ldegree(x);
599 const cl_UP_specialized<T> monomial (const T& x, uintL e)
601 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::monomial(cl_ring_element(cl_C_ring??,x),e));
603 const T coeff (const cl_UP_specialized<T>& x, uintL index)
605 return The(T)(cl_heap_univpoly_ring::coeff(x,index));
607 const cl_UP_specialized<T> create (sintL deg)
609 return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::create(deg));
611 void set_coeff (cl_UP_specialized<T>& x, uintL index, const T& y)
613 cl_heap_univpoly_ring::set_coeff(x,index,cl_ring_element(cl_C_ring??,y));
615 void finalize (cl_UP_specialized<T>& x)
617 cl_heap_univpoly_ring::finalize(x);
619 const T eval (const cl_UP_specialized<T>& x, const T& y)
621 return The(T)(cl_heap_univpoly_ring::eval(x,cl_ring_element(cl_C_ring??,y)));
624 // No need for any constructors.
625 cl_heap_univpoly_specialized_ring ();
628 // Lookup of polynomial rings.
630 inline const cl_univpoly_specialized_ring<T> find_univpoly_ring (const cl_specialized_number_ring<T>& r)
631 { return The(cl_univpoly_specialized_ring<T>) (find_univpoly_ring((const cl_ring&)r)); }
633 inline const cl_univpoly_specialized_ring<T> find_univpoly_ring (const cl_specialized_number_ring<T>& r, const cl_symbol& varname)
634 { return The(cl_univpoly_specialized_ring<T>) (find_univpoly_ring((const cl_ring&)r,varname)); }
636 // Operations on polynomials.
640 inline const cl_UP_specialized<T> operator+ (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
641 { return x.ring()->plus(x,y); }
645 inline const cl_UP_specialized<T> operator- (const cl_UP_specialized<T>& x)
646 { return x.ring()->uminus(x); }
650 inline const cl_UP_specialized<T> operator- (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
651 { return x.ring()->minus(x,y); }
655 inline const cl_UP_specialized<T> operator* (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
656 { return x.ring()->mul(x,y); }
660 inline const cl_UP_specialized<T> square (const cl_UP_specialized<T>& x)
661 { return x.ring()->square(x); }
663 // Exponentiation x^y, where y > 0.
665 inline const cl_UP_specialized<T> expt_pos (const cl_UP_specialized<T>& x, const cl_I& y)
666 { return x.ring()->expt_pos(x,y); }
668 // Scalar multiplication.
669 // Need more discrimination on T ??
671 inline const cl_UP_specialized<T> operator* (const cl_I& x, const cl_UP_specialized<T>& y)
672 { return y.ring()->mul(y.ring()->canonhom(x),y); }
674 inline const cl_UP_specialized<T> operator* (const cl_UP_specialized<T>& x, const cl_I& y)
675 { return x.ring()->mul(x.ring()->canonhom(y),x); }
677 inline const cl_UP_specialized<T> operator* (const T& x, const cl_UP_specialized<T>& y)
678 { return y.ring()->scalmul(x,y); }
680 inline const cl_UP_specialized<T> operator* (const cl_UP_specialized<T>& x, const T& y)
681 { return x.ring()->scalmul(y,x); }
685 inline const T coeff (const cl_UP_specialized<T>& x, uintL index)
686 { return x.ring()->coeff(x,index); }
688 // Destructive modification.
690 inline void set_coeff (cl_UP_specialized<T>& x, uintL index, const T& y)
691 { x.ring()->set_coeff(x,index,y); }
693 inline void finalize (cl_UP_specialized<T>& x)
694 { x.ring()->finalize(x); }
696 inline void cl_UP_specialized<T>::set_coeff (uintL index, const T& y)
697 { ring()->set_coeff(*this,index,y); }
699 inline void cl_UP_specialized<T>::finalize ()
700 { ring()->finalize(*this); }
702 // Evaluation. (No extension of the base ring allowed here for now.)
704 inline const T cl_UP_specialized<T>::operator() (const T& y) const
706 return ring()->eval(*this,y);
711 inline const cl_UP_specialized<T> deriv (const cl_UP_specialized<T>& x)
712 { return The(cl_UP_specialized<T>)(deriv((const cl_UP&)x)); }
715 #endif /* _CL_UNIVPOLY_AUX_H */