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							733 lines
						
					
					
						
							24 KiB
						
					
					
				
								// Univariate Polynomials.
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								#ifndef _CL_UNIVPOLY_H
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								#define _CL_UNIVPOLY_H
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								#include "cln/object.h"
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								#include "cln/ring.h"
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								#include "cln/malloc.h"
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								#include "cln/proplist.h"
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								#include "cln/symbol.h"
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								#include "cln/V.h"
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								#include "cln/io.h"
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								namespace cln {
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								// To protect against mixing elements of different polynomial rings, every
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								// polynomial carries its ring in itself.
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								class cl_heap_univpoly_ring;
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								class cl_univpoly_ring : public cl_ring {
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								public:
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									// Default constructor.
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									cl_univpoly_ring ();
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									// Constructor. Takes a cl_heap_univpoly_ring*, increments its refcount.
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									cl_univpoly_ring (cl_heap_univpoly_ring* r);
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									// Private constructor. Doesn't increment the refcount.
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									cl_univpoly_ring (cl_private_thing);
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									// Copy constructor.
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									cl_univpoly_ring (const cl_univpoly_ring&);
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									// Assignment operator.
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									cl_univpoly_ring& operator= (const cl_univpoly_ring&);
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									// Automatic dereferencing.
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									cl_heap_univpoly_ring* operator-> () const
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									{ return (cl_heap_univpoly_ring*)heappointer; }
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								};
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								// Copy constructor and assignment operator.
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								CL_DEFINE_COPY_CONSTRUCTOR2(cl_univpoly_ring,cl_ring)
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								CL_DEFINE_ASSIGNMENT_OPERATOR(cl_univpoly_ring,cl_univpoly_ring)
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								// Normal constructor for `cl_univpoly_ring'.
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								inline cl_univpoly_ring::cl_univpoly_ring (cl_heap_univpoly_ring* r)
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									: cl_ring ((cl_private_thing) (cl_inc_pointer_refcount((cl_heap*)r), r)) {}
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								// Private constructor for `cl_univpoly_ring'.
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								inline cl_univpoly_ring::cl_univpoly_ring (cl_private_thing p)
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									: cl_ring (p) {}
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								// Operations on univariate polynomial rings.
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								inline bool operator== (const cl_univpoly_ring& R1, const cl_univpoly_ring& R2)
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								{ return (R1.pointer == R2.pointer); }
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								inline bool operator!= (const cl_univpoly_ring& R1, const cl_univpoly_ring& R2)
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								{ return (R1.pointer != R2.pointer); }
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								inline bool operator== (const cl_univpoly_ring& R1, cl_heap_univpoly_ring* R2)
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								{ return (R1.pointer == R2); }
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								inline bool operator!= (const cl_univpoly_ring& R1, cl_heap_univpoly_ring* R2)
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								{ return (R1.pointer != R2); }
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								// Representation of a univariate polynomial.
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								class _cl_UP /* cf. _cl_ring_element */ {
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								public:
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									cl_gcpointer rep; // vector of coefficients, a cl_V_any
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									// Default constructor.
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									_cl_UP ();
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								public: /* ugh */
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									// Constructor.
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									_cl_UP (const cl_heap_univpoly_ring* R, const cl_V_any& r) : rep (as_cl_private_thing(r)) { (void)R; }
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									_cl_UP (const cl_univpoly_ring& R, const cl_V_any& r) : rep (as_cl_private_thing(r)) { (void)R; }
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								public:
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									// Conversion.
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									CL_DEFINE_CONVERTER(_cl_ring_element)
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								public:	// Ability to place an object at a given address.
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									void* operator new (size_t size) { return malloc_hook(size); }
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									void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
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									void operator delete (void* ptr) { free_hook(ptr); }
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								};
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								class cl_UP /* cf. cl_ring_element */ : public _cl_UP {
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								protected:
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									cl_univpoly_ring _ring;	// polynomial ring (references the base ring)
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								public:
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									const cl_univpoly_ring& ring () const { return _ring; }
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								private:
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									// Default constructor.
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									cl_UP ();
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								public: /* ugh */
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									// Constructor.
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									cl_UP (const cl_univpoly_ring& R, const cl_V_any& r)
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										: _cl_UP (R,r), _ring (R) {}
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									cl_UP (const cl_univpoly_ring& R, const _cl_UP& r)
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										: _cl_UP (r), _ring (R) {}
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								public:
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									// Conversion.
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									CL_DEFINE_CONVERTER(cl_ring_element)
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									// Destructive modification.
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									void set_coeff (uintL index, const cl_ring_element& y);
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									void finalize();
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									// Evaluation.
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									const cl_ring_element operator() (const cl_ring_element& y) const;
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									// Debugging output.
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									void debug_print () const;
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								public:	// Ability to place an object at a given address.
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									void* operator new (size_t size) { return malloc_hook(size); }
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									void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
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									void operator delete (void* ptr) { free_hook(ptr); }
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								};
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								// Ring operations.
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								struct _cl_univpoly_setops /* cf. _cl_ring_setops */ {
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									// print
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									void (* fprint) (cl_heap_univpoly_ring* R, std::ostream& stream, const _cl_UP& x);
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									// equality
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									// (Be careful: This is not well-defined for polynomials with
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									// floating-point coefficients.)
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									bool (* equal) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
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								};
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								struct _cl_univpoly_addops /* cf. _cl_ring_addops */ {
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									// 0
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									const _cl_UP (* zero) (cl_heap_univpoly_ring* R);
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									bool (* zerop) (cl_heap_univpoly_ring* R, const _cl_UP& x);
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									// x+y
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									const _cl_UP (* plus) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
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									// x-y
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									const _cl_UP (* minus) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
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									// -x
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									const _cl_UP (* uminus) (cl_heap_univpoly_ring* R, const _cl_UP& x);
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								};
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								struct _cl_univpoly_mulops /* cf. _cl_ring_mulops */ {
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									// 1
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									const _cl_UP (* one) (cl_heap_univpoly_ring* R);
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									// canonical homomorphism
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									const _cl_UP (* canonhom) (cl_heap_univpoly_ring* R, const cl_I& x);
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									// x*y
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									const _cl_UP (* mul) (cl_heap_univpoly_ring* R, const _cl_UP& x, const _cl_UP& y);
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									// x^2
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									const _cl_UP (* square) (cl_heap_univpoly_ring* R, const _cl_UP& x);
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									// x^y, y Integer >0
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									const _cl_UP (* expt_pos) (cl_heap_univpoly_ring* R, const _cl_UP& x, const cl_I& y);
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								};
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								struct _cl_univpoly_modulops {
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									// scalar multiplication x*y
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									const _cl_UP (* scalmul) (cl_heap_univpoly_ring* R, const cl_ring_element& x, const _cl_UP& y);
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								};
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								struct _cl_univpoly_polyops {
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									// degree
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									sintL (* degree) (cl_heap_univpoly_ring* R, const _cl_UP& x);
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									// low degree
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									sintL (* ldegree) (cl_heap_univpoly_ring* R, const _cl_UP& x);
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									// monomial
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									const _cl_UP (* monomial) (cl_heap_univpoly_ring* R, const cl_ring_element& x, uintL e);
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									// coefficient (0 if index>degree)
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									const cl_ring_element (* coeff) (cl_heap_univpoly_ring* R, const _cl_UP& x, uintL index);
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									// create new polynomial, bounded degree
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									const _cl_UP (* create) (cl_heap_univpoly_ring* R, sintL deg);
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									// set coefficient in new polynomial
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									void (* set_coeff) (cl_heap_univpoly_ring* R, _cl_UP& x, uintL index, const cl_ring_element& y);
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									// finalize polynomial
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									void (* finalize) (cl_heap_univpoly_ring* R, _cl_UP& x);
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									// evaluate, substitute an element of R
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									const cl_ring_element (* eval) (cl_heap_univpoly_ring* R, const _cl_UP& x, const cl_ring_element& y);
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								};
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								  typedef const _cl_univpoly_setops  cl_univpoly_setops;
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								  typedef const _cl_univpoly_addops  cl_univpoly_addops;
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								  typedef const _cl_univpoly_mulops  cl_univpoly_mulops;
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								  typedef const _cl_univpoly_modulops  cl_univpoly_modulops;
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								  typedef const _cl_univpoly_polyops  cl_univpoly_polyops;
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								// Representation of a univariate polynomial ring.
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								class cl_heap_univpoly_ring /* cf. cl_heap_ring */ : public cl_heap {
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									SUBCLASS_cl_heap_ring()
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								private:
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									cl_property_list properties;
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								protected:
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									cl_univpoly_setops* setops;
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									cl_univpoly_addops* addops;
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									cl_univpoly_mulops* mulops;
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									cl_univpoly_modulops* modulops;
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									cl_univpoly_polyops* polyops;
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								protected:
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									cl_ring _basering;	// the coefficients are elements of this ring
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								public:
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									const cl_ring& basering () const { return _basering; }
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								public:
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									// Low-level operations.
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									void _fprint (std::ostream& stream, const _cl_UP& x)
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										{ setops->fprint(this,stream,x); }
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									bool _equal (const _cl_UP& x, const _cl_UP& y)
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										{ return setops->equal(this,x,y); }
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									const _cl_UP _zero ()
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										{ return addops->zero(this); }
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									bool _zerop (const _cl_UP& x)
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										{ return addops->zerop(this,x); }
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									const _cl_UP _plus (const _cl_UP& x, const _cl_UP& y)
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										{ return addops->plus(this,x,y); }
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									const _cl_UP _minus (const _cl_UP& x, const _cl_UP& y)
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										{ return addops->minus(this,x,y); }
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									const _cl_UP _uminus (const _cl_UP& x)
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										{ return addops->uminus(this,x); }
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									const _cl_UP _one ()
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										{ return mulops->one(this); }
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									const _cl_UP _canonhom (const cl_I& x)
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										{ return mulops->canonhom(this,x); }
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									const _cl_UP _mul (const _cl_UP& x, const _cl_UP& y)
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										{ return mulops->mul(this,x,y); }
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									const _cl_UP _square (const _cl_UP& x)
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										{ return mulops->square(this,x); }
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									const _cl_UP _expt_pos (const _cl_UP& x, const cl_I& y)
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										{ return mulops->expt_pos(this,x,y); }
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									const _cl_UP _scalmul (const cl_ring_element& x, const _cl_UP& y)
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										{ return modulops->scalmul(this,x,y); }
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									sintL _degree (const _cl_UP& x)
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										{ return polyops->degree(this,x); }
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									sintL _ldegree (const _cl_UP& x)
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										{ return polyops->ldegree(this,x); }
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									const _cl_UP _monomial (const cl_ring_element& x, uintL e)
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										{ return polyops->monomial(this,x,e); }
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									const cl_ring_element _coeff (const _cl_UP& x, uintL index)
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										{ return polyops->coeff(this,x,index); }
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									const _cl_UP _create (sintL deg)
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										{ return polyops->create(this,deg); }
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									void _set_coeff (_cl_UP& x, uintL index, const cl_ring_element& y)
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										{ polyops->set_coeff(this,x,index,y); }
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									void _finalize (_cl_UP& x)
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										{ polyops->finalize(this,x); }
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									const cl_ring_element _eval (const _cl_UP& x, const cl_ring_element& y)
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										{ return polyops->eval(this,x,y); }
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									// High-level operations.
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									void fprint (std::ostream& stream, const cl_UP& x)
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									{
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										if (!(x.ring() == this)) throw runtime_exception();
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										_fprint(stream,x);
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									}
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									bool equal (const cl_UP& x, const cl_UP& y)
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									{
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										if (!(x.ring() == this)) throw runtime_exception();
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										if (!(y.ring() == this)) throw runtime_exception();
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										return _equal(x,y);
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									}
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									const cl_UP zero ()
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									{
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										return cl_UP(this,_zero());
							 | 
						|
									}
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									bool zerop (const cl_UP& x)
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						|
									{
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										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return _zerop(x);
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						|
									}
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						|
									const cl_UP plus (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{
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						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										if (!(y.ring() == this)) throw runtime_exception();
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						|
										return cl_UP(this,_plus(x,y));
							 | 
						|
									}
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						|
									const cl_UP minus (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										if (!(y.ring() == this)) throw runtime_exception();
							 | 
						|
										return cl_UP(this,_minus(x,y));
							 | 
						|
									}
							 | 
						|
									const cl_UP uminus (const cl_UP& x)
							 | 
						|
									{
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						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return cl_UP(this,_uminus(x));
							 | 
						|
									}
							 | 
						|
									const cl_UP one ()
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						|
									{
							 | 
						|
										return cl_UP(this,_one());
							 | 
						|
									}
							 | 
						|
									const cl_UP canonhom (const cl_I& x)
							 | 
						|
									{
							 | 
						|
										return cl_UP(this,_canonhom(x));
							 | 
						|
									}
							 | 
						|
									const cl_UP mul (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										if (!(y.ring() == this)) throw runtime_exception();
							 | 
						|
										return cl_UP(this,_mul(x,y));
							 | 
						|
									}
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						|
									const cl_UP square (const cl_UP& x)
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						|
									{
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						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return cl_UP(this,_square(x));
							 | 
						|
									}
							 | 
						|
									const cl_UP expt_pos (const cl_UP& x, const cl_I& y)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return cl_UP(this,_expt_pos(x,y));
							 | 
						|
									}
							 | 
						|
									const cl_UP scalmul (const cl_ring_element& x, const cl_UP& y)
							 | 
						|
									{
							 | 
						|
										if (!(y.ring() == this)) throw runtime_exception();
							 | 
						|
										return cl_UP(this,_scalmul(x,y));
							 | 
						|
									}
							 | 
						|
									sintL degree (const cl_UP& x)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return _degree(x);
							 | 
						|
									}
							 | 
						|
									sintL ldegree (const cl_UP& x)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return _ldegree(x);
							 | 
						|
									}
							 | 
						|
									const cl_UP monomial (const cl_ring_element& x, uintL e)
							 | 
						|
									{
							 | 
						|
										return cl_UP(this,_monomial(x,e));
							 | 
						|
									}
							 | 
						|
									const cl_ring_element coeff (const cl_UP& x, uintL index)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return _coeff(x,index);
							 | 
						|
									}
							 | 
						|
									const cl_UP create (sintL deg)
							 | 
						|
									{
							 | 
						|
										return cl_UP(this,_create(deg));
							 | 
						|
									}
							 | 
						|
									void set_coeff (cl_UP& x, uintL index, const cl_ring_element& y)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										_set_coeff(x,index,y);
							 | 
						|
									}
							 | 
						|
									void finalize (cl_UP& x)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										_finalize(x);
							 | 
						|
									}
							 | 
						|
									const cl_ring_element eval (const cl_UP& x, const cl_ring_element& y)
							 | 
						|
									{
							 | 
						|
										if (!(x.ring() == this)) throw runtime_exception();
							 | 
						|
										return _eval(x,y);
							 | 
						|
									}
							 | 
						|
									// Property operations.
							 | 
						|
									cl_property* get_property (const cl_symbol& key)
							 | 
						|
										{ return properties.get_property(key); }
							 | 
						|
									void add_property (cl_property* new_property)
							 | 
						|
										{ properties.add_property(new_property); }
							 | 
						|
								// Constructor.
							 | 
						|
									cl_heap_univpoly_ring (const cl_ring& r, cl_univpoly_setops*, cl_univpoly_addops*, cl_univpoly_mulops*, cl_univpoly_modulops*, cl_univpoly_polyops*);
							 | 
						|
									~cl_heap_univpoly_ring () {}
							 | 
						|
								};
							 | 
						|
								#define SUBCLASS_cl_heap_univpoly_ring() \
							 | 
						|
								  SUBCLASS_cl_heap_ring()
							 | 
						|
								
							 | 
						|
								
							 | 
						|
								// Lookup or create the "standard" univariate polynomial ring over a ring r.
							 | 
						|
								extern const cl_univpoly_ring find_univpoly_ring (const cl_ring& r);
							 | 
						|
								
							 | 
						|
								// Lookup or create a univariate polynomial ring with a named variable over r.
							 | 
						|
								extern const cl_univpoly_ring find_univpoly_ring (const cl_ring& r, const cl_symbol& varname);
							 | 
						|
								
							 | 
						|
								class cl_UP_init_helper
							 | 
						|
								{
							 | 
						|
									static int count;
							 | 
						|
								public:
							 | 
						|
									cl_UP_init_helper();
							 | 
						|
									~cl_UP_init_helper();
							 | 
						|
								};
							 | 
						|
								static cl_UP_init_helper cl_UP_init_helper_instance;
							 | 
						|
								
							 | 
						|
								
							 | 
						|
								// Operations on polynomials.
							 | 
						|
								
							 | 
						|
								// Output.
							 | 
						|
								inline void fprint (std::ostream& stream, const cl_UP& x)
							 | 
						|
									{ x.ring()->fprint(stream,x); }
							 | 
						|
								CL_DEFINE_PRINT_OPERATOR(cl_UP)
							 | 
						|
								
							 | 
						|
								// Add.
							 | 
						|
								inline const cl_UP operator+ (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{ return x.ring()->plus(x,y); }
							 | 
						|
								
							 | 
						|
								// Negate.
							 | 
						|
								inline const cl_UP operator- (const cl_UP& x)
							 | 
						|
									{ return x.ring()->uminus(x); }
							 | 
						|
								
							 | 
						|
								// Subtract.
							 | 
						|
								inline const cl_UP operator- (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{ return x.ring()->minus(x,y); }
							 | 
						|
								
							 | 
						|
								// Equality.
							 | 
						|
								inline bool operator== (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{ return x.ring()->equal(x,y); }
							 | 
						|
								inline bool operator!= (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{ return !x.ring()->equal(x,y); }
							 | 
						|
								
							 | 
						|
								// Compare against 0.
							 | 
						|
								inline bool zerop (const cl_UP& x)
							 | 
						|
									{ return x.ring()->zerop(x); }
							 | 
						|
								
							 | 
						|
								// Multiply.
							 | 
						|
								inline const cl_UP operator* (const cl_UP& x, const cl_UP& y)
							 | 
						|
									{ return x.ring()->mul(x,y); }
							 | 
						|
								
							 | 
						|
								// Squaring.
							 | 
						|
								inline const cl_UP square (const cl_UP& x)
							 | 
						|
									{ return x.ring()->square(x); }
							 | 
						|
								
							 | 
						|
								// Exponentiation x^y, where y > 0.
							 | 
						|
								inline const cl_UP expt_pos (const cl_UP& x, const cl_I& y)
							 | 
						|
									{ return x.ring()->expt_pos(x,y); }
							 | 
						|
								
							 | 
						|
								// Scalar multiplication.
							 | 
						|
								#if 0 // less efficient
							 | 
						|
								inline const cl_UP operator* (const cl_I& x, const cl_UP& y)
							 | 
						|
									{ return y.ring()->mul(y.ring()->canonhom(x),y); }
							 | 
						|
								inline const cl_UP operator* (const cl_UP& x, const cl_I& y)
							 | 
						|
									{ return x.ring()->mul(x.ring()->canonhom(y),x); }
							 | 
						|
								#endif
							 | 
						|
								inline const cl_UP operator* (const cl_I& x, const cl_UP& y)
							 | 
						|
									{ return y.ring()->scalmul(y.ring()->basering()->canonhom(x),y); }
							 | 
						|
								inline const cl_UP operator* (const cl_UP& x, const cl_I& y)
							 | 
						|
									{ return x.ring()->scalmul(x.ring()->basering()->canonhom(y),x); }
							 | 
						|
								inline const cl_UP operator* (const cl_ring_element& x, const cl_UP& y)
							 | 
						|
									{ return y.ring()->scalmul(x,y); }
							 | 
						|
								inline const cl_UP operator* (const cl_UP& x, const cl_ring_element& y)
							 | 
						|
									{ return x.ring()->scalmul(y,x); }
							 | 
						|
								
							 | 
						|
								// Degree.
							 | 
						|
								inline sintL degree (const cl_UP& x)
							 | 
						|
									{ return x.ring()->degree(x); }
							 | 
						|
								
							 | 
						|
								// Low degree.
							 | 
						|
								inline sintL ldegree (const cl_UP& x)
							 | 
						|
									{ return x.ring()->ldegree(x); }
							 | 
						|
								
							 | 
						|
								// Coefficient.
							 | 
						|
								inline const cl_ring_element coeff (const cl_UP& x, uintL index)
							 | 
						|
									{ return x.ring()->coeff(x,index); }
							 | 
						|
								
							 | 
						|
								// Destructive modification.
							 | 
						|
								inline void set_coeff (cl_UP& x, uintL index, const cl_ring_element& y)
							 | 
						|
									{ x.ring()->set_coeff(x,index,y); }
							 | 
						|
								inline void finalize (cl_UP& x)
							 | 
						|
									{ x.ring()->finalize(x); }
							 | 
						|
								inline void cl_UP::set_coeff (uintL index, const cl_ring_element& y)
							 | 
						|
									{ ring()->set_coeff(*this,index,y); }
							 | 
						|
								inline void cl_UP::finalize ()
							 | 
						|
									{ ring()->finalize(*this); }
							 | 
						|
								
							 | 
						|
								// Evaluation. (No extension of the base ring allowed here for now.)
							 | 
						|
								inline const cl_ring_element cl_UP::operator() (const cl_ring_element& y) const
							 | 
						|
								{
							 | 
						|
									return ring()->eval(*this,y);
							 | 
						|
								}
							 | 
						|
								
							 | 
						|
								// Derivative.
							 | 
						|
								extern const cl_UP deriv (const cl_UP& x);
							 | 
						|
								
							 | 
						|
								
							 | 
						|
								// Ring of uninitialized elements.
							 | 
						|
								// Any operation results in a run-time error.
							 | 
						|
								
							 | 
						|
								extern const cl_univpoly_ring cl_no_univpoly_ring;
							 | 
						|
								extern cl_class cl_class_no_univpoly_ring;
							 | 
						|
								
							 | 
						|
								class cl_UP_no_ring_init_helper
							 | 
						|
								{
							 | 
						|
									static int count;
							 | 
						|
								public:
							 | 
						|
									cl_UP_no_ring_init_helper();
							 | 
						|
									~cl_UP_no_ring_init_helper();
							 | 
						|
								};
							 | 
						|
								static cl_UP_no_ring_init_helper cl_UP_no_ring_init_helper_instance;
							 | 
						|
								
							 | 
						|
								inline cl_univpoly_ring::cl_univpoly_ring ()
							 | 
						|
									: cl_ring (as_cl_private_thing(cl_no_univpoly_ring)) {}
							 | 
						|
								inline _cl_UP::_cl_UP ()
							 | 
						|
									: rep ((cl_private_thing) cl_combine(cl_FN_tag,0)) {}
							 | 
						|
								inline cl_UP::cl_UP ()
							 | 
						|
									: _cl_UP (), _ring () {}
							 | 
						|
								
							 | 
						|
								
							 | 
						|
								// Debugging support.
							 | 
						|
								#ifdef CL_DEBUG
							 | 
						|
								extern int cl_UP_debug_module;
							 | 
						|
								CL_FORCE_LINK(cl_UP_debug_dummy, cl_UP_debug_module)
							 | 
						|
								#endif
							 | 
						|
								
							 | 
						|
								}  // namespace cln
							 | 
						|
								
							 | 
						|
								#endif /* _CL_UNIVPOLY_H */
							 | 
						|
								
							 | 
						|
								namespace cln {
							 | 
						|
								
							 | 
						|
								// Templates for univariate polynomials of complex/real/rational/integers.
							 | 
						|
								
							 | 
						|
								#ifdef notyet
							 | 
						|
								// Unfortunately, this is not usable now, because of gcc-2.7 bugs:
							 | 
						|
								// - A template inline function is not inline in the first function that
							 | 
						|
								//   uses it.
							 | 
						|
								// - Argument matching bug: User-defined conversions are not tried (or
							 | 
						|
								//   tried with too low priority) for template functions w.r.t. normal
							 | 
						|
								//   functions. For example, a call expt_pos(cl_UP_specialized<cl_N>,int)
							 | 
						|
								//   is compiled as expt_pos(const cl_UP&, const cl_I&) instead of
							 | 
						|
								//   expt_pos(const cl_UP_specialized<cl_N>&, const cl_I&).
							 | 
						|
								// It will, however, be usable when gcc-2.8 is released.
							 | 
						|
								
							 | 
						|
								#if defined(_CL_UNIVPOLY_COMPLEX_H) || defined(_CL_UNIVPOLY_REAL_H) || defined(_CL_UNIVPOLY_RATIONAL_H) || defined(_CL_UNIVPOLY_INTEGER_H)
							 | 
						|
								#ifndef _CL_UNIVPOLY_AUX_H
							 | 
						|
								
							 | 
						|
								// Normal univariate polynomials with stricter static typing:
							 | 
						|
								// `class T' instead of `cl_ring_element'.
							 | 
						|
								
							 | 
						|
								template <class T> class cl_univpoly_specialized_ring;
							 | 
						|
								template <class T> class cl_UP_specialized;
							 | 
						|
								template <class T> class cl_heap_univpoly_specialized_ring;
							 | 
						|
								
							 | 
						|
								template <class T>
							 | 
						|
								class cl_univpoly_specialized_ring : public cl_univpoly_ring {
							 | 
						|
								public:
							 | 
						|
									// Default constructor.
							 | 
						|
									cl_univpoly_specialized_ring () : cl_univpoly_ring () {}
							 | 
						|
									// Copy constructor.
							 | 
						|
									cl_univpoly_specialized_ring (const cl_univpoly_specialized_ring&);
							 | 
						|
									// Assignment operator.
							 | 
						|
									cl_univpoly_specialized_ring& operator= (const cl_univpoly_specialized_ring&);
							 | 
						|
									// Automatic dereferencing.
							 | 
						|
									cl_heap_univpoly_specialized_ring<T>* operator-> () const
							 | 
						|
									{ return (cl_heap_univpoly_specialized_ring<T>*)heappointer; }
							 | 
						|
								};
							 | 
						|
								// Copy constructor and assignment operator.
							 | 
						|
								template <class T>
							 | 
						|
								_CL_DEFINE_COPY_CONSTRUCTOR2(cl_univpoly_specialized_ring<T>,cl_univpoly_specialized_ring,cl_univpoly_ring)
							 | 
						|
								template <class T>
							 | 
						|
								CL_DEFINE_ASSIGNMENT_OPERATOR(cl_univpoly_specialized_ring<T>,cl_univpoly_specialized_ring<T>)
							 | 
						|
								
							 | 
						|
								template <class T>
							 | 
						|
								class cl_UP_specialized : public cl_UP {
							 | 
						|
								public:
							 | 
						|
									const cl_univpoly_specialized_ring<T>& ring () const { return The(cl_univpoly_specialized_ring<T>)(_ring); }
							 | 
						|
									// Conversion.
							 | 
						|
									CL_DEFINE_CONVERTER(cl_ring_element)
							 | 
						|
									// Destructive modification.
							 | 
						|
									void set_coeff (uintL index, const T& y);
							 | 
						|
									void finalize();
							 | 
						|
									// Evaluation.
							 | 
						|
									const T operator() (const T& y) const;
							 | 
						|
								public:	// Ability to place an object at a given address.
							 | 
						|
									void* operator new (size_t size) { return malloc_hook(size); }
							 | 
						|
									void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
							 | 
						|
									void operator delete (void* ptr) { free_hook(ptr); }
							 | 
						|
								};
							 | 
						|
								
							 | 
						|
								template <class T>
							 | 
						|
								class cl_heap_univpoly_specialized_ring : public cl_heap_univpoly_ring {
							 | 
						|
									SUBCLASS_cl_heap_univpoly_ring()
							 | 
						|
									// High-level operations.
							 | 
						|
									void fprint (std::ostream& stream, const cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										cl_heap_univpoly_ring::fprint(stream,x);
							 | 
						|
									}
							 | 
						|
									bool equal (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{
							 | 
						|
										return cl_heap_univpoly_ring::equal(x,y);
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> zero ()
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::zero());
							 | 
						|
									}
							 | 
						|
									bool zerop (const cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										return cl_heap_univpoly_ring::zerop(x);
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> plus (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::plus(x,y));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> minus (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::minus(x,y));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> uminus (const cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::uminus(x));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> one ()
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::one());
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> canonhom (const cl_I& x)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::canonhom(x));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> mul (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::mul(x,y));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> square (const cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::square(x));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> expt_pos (const cl_UP_specialized<T>& x, const cl_I& y)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::expt_pos(x,y));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> scalmul (const T& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::scalmul(x,y));
							 | 
						|
									}
							 | 
						|
									sintL degree (const cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										return cl_heap_univpoly_ring::degree(x);
							 | 
						|
									}
							 | 
						|
									sintL ldegree (const cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										return cl_heap_univpoly_ring::ldegree(x);
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> monomial (const T& x, uintL e)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::monomial(cl_ring_element(cl_C_ring??,x),e));
							 | 
						|
									}
							 | 
						|
									const T coeff (const cl_UP_specialized<T>& x, uintL index)
							 | 
						|
									{
							 | 
						|
										return The(T)(cl_heap_univpoly_ring::coeff(x,index));
							 | 
						|
									}
							 | 
						|
									const cl_UP_specialized<T> create (sintL deg)
							 | 
						|
									{
							 | 
						|
										return The2(cl_UP_specialized<T>)(cl_heap_univpoly_ring::create(deg));
							 | 
						|
									}
							 | 
						|
									void set_coeff (cl_UP_specialized<T>& x, uintL index, const T& y)
							 | 
						|
									{
							 | 
						|
										cl_heap_univpoly_ring::set_coeff(x,index,cl_ring_element(cl_C_ring??,y));
							 | 
						|
									}
							 | 
						|
									void finalize (cl_UP_specialized<T>& x)
							 | 
						|
									{
							 | 
						|
										cl_heap_univpoly_ring::finalize(x);
							 | 
						|
									}
							 | 
						|
									const T eval (const cl_UP_specialized<T>& x, const T& y)
							 | 
						|
									{
							 | 
						|
										return The(T)(cl_heap_univpoly_ring::eval(x,cl_ring_element(cl_C_ring??,y)));
							 | 
						|
									}
							 | 
						|
								private:
							 | 
						|
									// No need for any constructors.
							 | 
						|
									cl_heap_univpoly_specialized_ring ();
							 | 
						|
								};
							 | 
						|
								
							 | 
						|
								// Lookup of polynomial rings.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_univpoly_specialized_ring<T> find_univpoly_ring (const cl_specialized_number_ring<T>& r)
							 | 
						|
								{ return The(cl_univpoly_specialized_ring<T>) (find_univpoly_ring((const cl_ring&)r)); }
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_univpoly_specialized_ring<T> find_univpoly_ring (const cl_specialized_number_ring<T>& r, const cl_symbol& varname)
							 | 
						|
								{ return The(cl_univpoly_specialized_ring<T>) (find_univpoly_ring((const cl_ring&)r,varname)); }
							 | 
						|
								
							 | 
						|
								// Operations on polynomials.
							 | 
						|
								
							 | 
						|
								// Add.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator+ (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{ return x.ring()->plus(x,y); }
							 | 
						|
								
							 | 
						|
								// Negate.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator- (const cl_UP_specialized<T>& x)
							 | 
						|
									{ return x.ring()->uminus(x); }
							 | 
						|
								
							 | 
						|
								// Subtract.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator- (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{ return x.ring()->minus(x,y); }
							 | 
						|
								
							 | 
						|
								// Multiply.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator* (const cl_UP_specialized<T>& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{ return x.ring()->mul(x,y); }
							 | 
						|
								
							 | 
						|
								// Squaring.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> square (const cl_UP_specialized<T>& x)
							 | 
						|
									{ return x.ring()->square(x); }
							 | 
						|
								
							 | 
						|
								// Exponentiation x^y, where y > 0.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> expt_pos (const cl_UP_specialized<T>& x, const cl_I& y)
							 | 
						|
									{ return x.ring()->expt_pos(x,y); }
							 | 
						|
								
							 | 
						|
								// Scalar multiplication.
							 | 
						|
								// Need more discrimination on T ??
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator* (const cl_I& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{ return y.ring()->mul(y.ring()->canonhom(x),y); }
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator* (const cl_UP_specialized<T>& x, const cl_I& y)
							 | 
						|
									{ return x.ring()->mul(x.ring()->canonhom(y),x); }
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator* (const T& x, const cl_UP_specialized<T>& y)
							 | 
						|
									{ return y.ring()->scalmul(x,y); }
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> operator* (const cl_UP_specialized<T>& x, const T& y)
							 | 
						|
									{ return x.ring()->scalmul(y,x); }
							 | 
						|
								
							 | 
						|
								// Coefficient.
							 | 
						|
								template <class T>
							 | 
						|
								inline const T coeff (const cl_UP_specialized<T>& x, uintL index)
							 | 
						|
									{ return x.ring()->coeff(x,index); }
							 | 
						|
								
							 | 
						|
								// Destructive modification.
							 | 
						|
								template <class T>
							 | 
						|
								inline void set_coeff (cl_UP_specialized<T>& x, uintL index, const T& y)
							 | 
						|
									{ x.ring()->set_coeff(x,index,y); }
							 | 
						|
								template <class T>
							 | 
						|
								inline void finalize (cl_UP_specialized<T>& x)
							 | 
						|
									{ x.ring()->finalize(x); }
							 | 
						|
								template <class T>
							 | 
						|
								inline void cl_UP_specialized<T>::set_coeff (uintL index, const T& y)
							 | 
						|
									{ ring()->set_coeff(*this,index,y); }
							 | 
						|
								template <class T>
							 | 
						|
								inline void cl_UP_specialized<T>::finalize ()
							 | 
						|
									{ ring()->finalize(*this); }
							 | 
						|
								
							 | 
						|
								// Evaluation. (No extension of the base ring allowed here for now.)
							 | 
						|
								template <class T>
							 | 
						|
								inline const T cl_UP_specialized<T>::operator() (const T& y) const
							 | 
						|
								{
							 | 
						|
									return ring()->eval(*this,y);
							 | 
						|
								}
							 | 
						|
								
							 | 
						|
								// Derivative.
							 | 
						|
								template <class T>
							 | 
						|
								inline const cl_UP_specialized<T> deriv (const cl_UP_specialized<T>& x)
							 | 
						|
									{ return The(cl_UP_specialized<T>)(deriv((const cl_UP&)x)); }
							 | 
						|
								
							 | 
						|
								
							 | 
						|
								#endif /* _CL_UNIVPOLY_AUX_H */
							 | 
						|
								#endif
							 | 
						|
								
							 | 
						|
								#endif /* notyet */
							 | 
						|
								
							 | 
						|
								}  // namespace cln
							 |