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726 lines
24 KiB
726 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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cl_boolean (* 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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cl_boolean (* 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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cl_boolean _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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cl_boolean _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)) cl_abort();
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_fprint(stream,x);
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}
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cl_boolean equal (const cl_UP& x, const cl_UP& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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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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}
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cl_boolean zerop (const cl_UP& x)
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{
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if (!(x.ring() == this)) cl_abort();
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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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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return cl_UP(this,_plus(x,y));
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}
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const cl_UP minus (const cl_UP& x, const cl_UP& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return cl_UP(this,_minus(x,y));
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}
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const cl_UP uminus (const cl_UP& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_UP(this,_uminus(x));
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}
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const cl_UP one ()
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{
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return cl_UP(this,_one());
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}
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const cl_UP canonhom (const cl_I& x)
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{
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return cl_UP(this,_canonhom(x));
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}
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const cl_UP mul (const cl_UP& x, const cl_UP& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return cl_UP(this,_mul(x,y));
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}
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const cl_UP square (const cl_UP& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_UP(this,_square(x));
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}
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const cl_UP expt_pos (const cl_UP& x, const cl_I& y)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_UP(this,_expt_pos(x,y));
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}
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const cl_UP scalmul (const cl_ring_element& x, const cl_UP& y)
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{
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if (!(y.ring() == this)) cl_abort();
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return cl_UP(this,_scalmul(x,y));
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}
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sintL degree (const cl_UP& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return _degree(x);
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}
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sintL ldegree (const cl_UP& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return _ldegree(x);
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}
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const cl_UP monomial (const cl_ring_element& x, uintL e)
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{
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return cl_UP(this,_monomial(x,e));
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}
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const cl_ring_element coeff (const cl_UP& x, uintL index)
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{
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if (!(x.ring() == this)) cl_abort();
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return _coeff(x,index);
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}
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const cl_UP create (sintL deg)
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{
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return cl_UP(this,_create(deg));
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}
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void set_coeff (cl_UP& x, uintL index, const cl_ring_element& y)
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{
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if (!(x.ring() == this)) cl_abort();
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_set_coeff(x,index,y);
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}
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void finalize (cl_UP& x)
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{
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if (!(x.ring() == this)) cl_abort();
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_finalize(x);
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}
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const cl_ring_element eval (const cl_UP& x, const cl_ring_element& y)
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{
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if (!(x.ring() == this)) cl_abort();
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return _eval(x,y);
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}
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// Property operations.
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cl_property* get_property (const cl_symbol& key)
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{ return properties.get_property(key); }
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void add_property (cl_property* new_property)
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{ properties.add_property(new_property); }
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// Constructor.
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cl_heap_univpoly_ring (const cl_ring& r, cl_univpoly_setops*, cl_univpoly_addops*, cl_univpoly_mulops*, cl_univpoly_modulops*, cl_univpoly_polyops*);
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// This class is intented to be subclassable, hence needs a virtual destructor.
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virtual ~cl_heap_univpoly_ring () {}
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private:
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virtual void dummy ();
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};
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#define SUBCLASS_cl_heap_univpoly_ring() \
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SUBCLASS_cl_heap_ring()
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// Lookup or create the "standard" univariate polynomial ring over a ring r.
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extern const cl_univpoly_ring find_univpoly_ring (const cl_ring& r);
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//CL_REQUIRE(cl_UP_unnamed)
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// Lookup or create a univariate polynomial ring with a named variable over r.
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extern const cl_univpoly_ring find_univpoly_ring (const cl_ring& r, const cl_symbol& varname);
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//CL_REQUIRE(cl_UP_named)
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CL_REQUIRE(cl_UP)
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// Runtime typing support.
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extern cl_class cl_class_univpoly_ring;
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// Operations on polynomials.
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// Output.
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inline void fprint (std::ostream& stream, const cl_UP& x)
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{ x.ring()->fprint(stream,x); }
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CL_DEFINE_PRINT_OPERATOR(cl_UP)
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// Add.
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inline const cl_UP operator+ (const cl_UP& x, const cl_UP& y)
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{ return x.ring()->plus(x,y); }
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// Negate.
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inline const cl_UP operator- (const cl_UP& x)
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{ return x.ring()->uminus(x); }
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// Subtract.
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inline const cl_UP operator- (const cl_UP& x, const cl_UP& y)
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{ return x.ring()->minus(x,y); }
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// Equality.
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inline bool operator== (const cl_UP& x, const cl_UP& y)
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{ return x.ring()->equal(x,y); }
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inline bool operator!= (const cl_UP& x, const cl_UP& y)
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{ return !x.ring()->equal(x,y); }
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// Compare against 0.
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inline cl_boolean zerop (const cl_UP& x)
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{ return x.ring()->zerop(x); }
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// Multiply.
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inline const cl_UP operator* (const cl_UP& x, const cl_UP& y)
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{ return x.ring()->mul(x,y); }
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// Squaring.
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inline const cl_UP square (const cl_UP& x)
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{ return x.ring()->square(x); }
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// Exponentiation x^y, where y > 0.
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inline const cl_UP expt_pos (const cl_UP& x, const cl_I& y)
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{ return x.ring()->expt_pos(x,y); }
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// Scalar multiplication.
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#if 0 // less efficient
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inline const cl_UP operator* (const cl_I& x, const cl_UP& y)
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{ return y.ring()->mul(y.ring()->canonhom(x),y); }
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inline const cl_UP operator* (const cl_UP& x, const cl_I& y)
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{ return x.ring()->mul(x.ring()->canonhom(y),x); }
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#endif
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inline const cl_UP operator* (const cl_I& x, const cl_UP& y)
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{ return y.ring()->scalmul(y.ring()->basering()->canonhom(x),y); }
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inline const cl_UP operator* (const cl_UP& x, const cl_I& y)
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{ return x.ring()->scalmul(x.ring()->basering()->canonhom(y),x); }
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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); }
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|
|
|
// Degree.
|
|
inline sintL degree (const cl_UP& x)
|
|
{ return x.ring()->degree(x); }
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|
|
|
// 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);
|
|
|
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|
|
// Ring of uninitialized elements.
|
|
// Any operation results in a run-time error.
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|
|
|
extern const cl_univpoly_ring cl_no_univpoly_ring;
|
|
extern cl_class cl_class_no_univpoly_ring;
|
|
CL_REQUIRE(cl_UP_no_ring)
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|
|
|
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);
|
|
}
|
|
cl_boolean 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());
|
|
}
|
|
cl_boolean 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
|