GiNaC 1.8.4
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6 * GiNaC Copyright (C) 1999-2022 Johannes Gutenberg University Mainz, Germany
7 *
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
12 *
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * GNU General Public License for more details.
17 *
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
21 */
23#ifndef GINAC_BASIC_H
24#define GINAC_BASIC_H
26#include "flags.h"
27#include "ptr.h"
28#include "assertion.h"
29#include "registrar.h"
31#include <cstddef> // for size_t
32#include <map>
33#include <set>
34#include <typeinfo> // for typeid
35#include <vector>
36#include <utility>
38namespace GiNaC {
40class ex;
41struct ex_is_less;
42class symbol;
43class numeric;
44class relational;
45class archive_node;
46class print_context;
48typedef std::vector<ex> exvector;
49typedef std::set<ex, ex_is_less> exset;
50typedef std::map<ex, ex, ex_is_less> exmap;
52// Define this to enable some statistical output for comparisons and hashing
56class compare_statistics_t {
58 compare_statistics_t()
59 : total_compares(0), nontrivial_compares(0), total_basic_compares(0), compare_same_hashvalue(0), compare_same_type(0),
60 total_is_equals(0), nontrivial_is_equals(0), total_basic_is_equals(0), is_equal_same_hashvalue(0), is_equal_same_type(0),
61 total_gethash(0), gethash_cached(0) {}
62 ~compare_statistics_t();
64 unsigned long total_compares;
65 unsigned long nontrivial_compares;
66 unsigned long total_basic_compares;
67 unsigned long compare_same_hashvalue;
68 unsigned long compare_same_type;
70 unsigned long total_is_equals;
71 unsigned long nontrivial_is_equals;
72 unsigned long total_basic_is_equals;
73 unsigned long is_equal_same_hashvalue;
74 unsigned long is_equal_same_type;
76 unsigned long total_gethash;
77 unsigned long gethash_cached;
80extern compare_statistics_t compare_statistics;
86 virtual ~map_function() {}
87 typedef const ex & argument_type;
88 typedef ex result_type;
89 virtual ex operator()(const ex & e) = 0;
97class visitor {
99 virtual ~visitor() {}
104class basic : public refcounted
108 friend class ex;
110 // default constructor, destructor, copy constructor and assignment operator
112 basic() : flags(0) {}
117 virtual ~basic()
118 {
120 }
121 basic(const basic & other);
122 const basic & operator=(const basic & other);
125 // new virtual functions which can be overridden by derived classes
126public: // only const functions please (may break reference counting)
131 virtual basic * duplicate() const
132 {
133 basic * bp = new basic(*this);
135 return bp;
136 }
138 // evaluation
139 virtual ex eval() const;
140 virtual ex evalf() const;
141 virtual ex evalm() const;
142 virtual ex eval_integ() const;
144 virtual ex eval_ncmul(const exvector & v) const;
146 virtual ex eval_indexed(const basic & i) const;
148 // printing
149 virtual void print(const print_context & c, unsigned level = 0) const;
150 virtual void dbgprint() const;
151 virtual void dbgprinttree() const;
152 virtual unsigned precedence() const;
154 // info
155 virtual bool info(unsigned inf) const;
157 // operand access
158 virtual size_t nops() const;
159 virtual ex op(size_t i) const;
160 virtual ex operator[](const ex & index) const;
161 virtual ex operator[](size_t i) const;
162 virtual ex & let_op(size_t i);
163 virtual ex & operator[](const ex & index);
164 virtual ex & operator[](size_t i);
166 // pattern matching
167 virtual bool has(const ex & other, unsigned options = 0) const;
168 virtual bool match(const ex & pattern, exmap & repls) const;
170 virtual bool match_same_type(const basic & other) const;
173 // substitutions
174 virtual ex subs(const exmap & m, unsigned options = 0) const;
176 // function mapping
177 virtual ex map(map_function & f) const;
179 // visitors and tree traversal
180 virtual void accept(GiNaC::visitor & v) const
181 {
182 if (visitor *p = dynamic_cast<visitor *>(&v))
183 p->visit(*this);
184 }
186 // degree/coeff
187 virtual bool is_polynomial(const ex & var) const;
188 virtual int degree(const ex & s) const;
189 virtual int ldegree(const ex & s) const;
190 virtual ex coeff(const ex & s, int n = 1) const;
192 // expand/collect
193 virtual ex expand(unsigned options = 0) const;
194 virtual ex collect(const ex & s, bool distributed = false) const;
196 // differentiation and series expansion
198 virtual ex derivative(const symbol & s) const;
200 virtual ex series(const relational & r, int order, unsigned options = 0) const;
202 // rational functions
203 virtual ex normal(exmap & repl, exmap & rev_lookup, lst & modifier) const;
204 virtual ex to_rational(exmap & repl) const;
205 virtual ex to_polynomial(exmap & repl) const;
207 // polynomial algorithms
208 virtual numeric integer_content() const;
209 virtual ex smod(const numeric &xi) const;
210 virtual numeric max_coefficient() const;
212 // indexed objects
213 virtual exvector get_free_indices() const;
214 virtual ex add_indexed(const ex & self, const ex & other) const;
215 virtual ex scalar_mul_indexed(const ex & self, const numeric & other) const;
216 virtual bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
218 // noncommutativity
219 virtual unsigned return_type() const;
220 virtual return_type_t return_type_tinfo() const;
222 // functions for complex expressions
223 virtual ex conjugate() const;
224 virtual ex real_part() const;
225 virtual ex imag_part() const;
227 // functions that should be called from class ex only
229 virtual int compare_same_type(const basic & other) const;
230 virtual bool is_equal_same_type(const basic & other) const;
232 virtual unsigned calchash() const;
234 // non-virtual functions in this class
241 template <class T>
242 void print_dispatch(const print_context & c, unsigned level) const
243 {
244 print_dispatch(T::get_class_info_static(), c, level);
245 }
247 void print_dispatch(const registered_class_info & ri, const print_context & c, unsigned level) const;
255 virtual void archive(archive_node& n) const;
264 virtual void read_archive(const archive_node& n, lst& syms); // no const
266 ex subs_one_level(const exmap & m, unsigned options) const;
267 ex diff(const symbol & s, unsigned nth = 1) const;
268 int compare(const basic & other) const;
269 bool is_equal(const basic & other) const;
270 const basic & hold() const;
272 unsigned gethash() const
273 {
275 compare_statistics.total_gethash++;
279 compare_statistics.gethash_cached++;
281 return hashvalue;
282 } else {
283 return calchash();
284 }
285 }
288 const basic & setflag(unsigned f) const {flags |= f; return *this;}
291 const basic & clearflag(unsigned f) const {flags &= ~f; return *this;}
294 void ensure_if_modifiable() const;
296 void do_print(const print_context & c, unsigned level) const;
297 void do_print_tree(const print_tree & c, unsigned level) const;
298 void do_print_python_repr(const print_python_repr & c, unsigned level) const;
300 // member variables
302 mutable unsigned flags;
303 mutable unsigned hashvalue;
306// global variables
309// convenience type checker template functions
312template <class T>
313inline bool is_a(const basic &obj)
315 return dynamic_cast<const T *>(&obj) != nullptr;
319template <class T>
320inline bool is_exactly_a(const basic & obj)
322 return typeid(T) == typeid(obj);
333template<class B, typename... Args>
334inline B & dynallocate(Args &&... args)
336 return const_cast<B &>(static_cast<const B &>((new B(std::forward<Args>(args)...))->setflag(status_flags::dynallocated)));
344template<class B>
345inline B & dynallocate(std::initializer_list<ex> il)
347 return const_cast<B &>(static_cast<const B &>((new B(il))->setflag(status_flags::dynallocated)));
350} // namespace GiNaC
352#endif // ndef GINAC_BASIC_H
Assertion macro definition.
Assertion macro for checking invariances.
Definition: assertion.h:33
This class stores all properties needed to record/retrieve the state of one object of class basic (or...
Definition: archive.h:49
This class is the ABC (abstract base class) of GiNaC's class hierarchy.
Definition: basic.h:105
virtual return_type_t return_type_tinfo() const
Definition: basic.cpp:756
virtual size_t nops() const
Number of operands/members.
Definition: basic.cpp:229
unsigned gethash() const
Definition: basic.h:272
virtual ex eval_integ() const
Evaluate integrals, if result is known.
Definition: basic.cpp:455
const basic & clearflag(unsigned f) const
Clear some status_flags.
Definition: basic.h:291
virtual bool match_same_type(const basic &other) const
Returns true if the attributes of two objects are similar enough for a match.
Definition: basic.cpp:744
virtual bool match(const ex &pattern, exmap &repls) const
Check whether the expression matches a given pattern.
Definition: basic.cpp:519
virtual void dbgprinttree() const
Little wrapper around printtree to be called within a debugger.
Definition: basic.cpp:208
void print_dispatch(const print_context &c, unsigned level) const
Like print(), but dispatch to the specified class.
Definition: basic.h:242
virtual ex imag_part() const
Definition: basic.cpp:681
virtual void archive(archive_node &n) const
Save (serialize) the object into archive node.
Definition: basic.cpp:100
virtual ex eval() const
Perform automatic non-interruptive term rewriting rules.
Definition: basic.cpp:413
virtual numeric integer_content() const
Definition: normal.cpp:323
const basic & setflag(unsigned f) const
Set some status_flags.
Definition: basic.h:288
virtual bool info(unsigned inf) const
Information about the object.
Definition: basic.cpp:222
virtual bool contract_with(exvector::iterator self, exvector::iterator other, exvector &v) const
Try to contract two indexed expressions that appear in the same product.
Definition: basic.cpp:510
ex diff(const symbol &s, unsigned nth=1) const
Default interface of nth derivative ex::diff(s, n).
Definition: basic.cpp:646
virtual ex scalar_mul_indexed(const ex &self, const numeric &other) const
Multiply an indexed expression with a scalar.
Definition: basic.cpp:493
virtual numeric max_coefficient() const
Implementation ex::max_coefficient().
Definition: normal.cpp:1161
unsigned hashvalue
hash value
Definition: basic.h:303
void ensure_if_modifiable() const
Ensure the object may be modified without hurting others, throws if this is not the case.
Definition: basic.cpp:894
virtual bool is_equal_same_type(const basic &other) const
Returns true if two objects of same type are equal.
Definition: basic.cpp:729
virtual bool has(const ex &other, unsigned options=0) const
Test for occurrence of a pattern.
Definition: basic.cpp:280
virtual ex evalm() const
Evaluate sums, products and integer powers of matrices.
Definition: basic.cpp:441
virtual ex eval_indexed(const basic &i) const
Perform automatic symbolic evaluations on indexed expression that contains this object as the base ex...
Definition: basic.cpp:465
virtual int degree(const ex &s) const
Return degree of highest power in object s.
Definition: basic.cpp:325
virtual ex conjugate() const
Definition: basic.cpp:671
virtual unsigned precedence() const
Return relative operator precedence (for parenthezing output).
Definition: basic.cpp:214
virtual ex op(size_t i) const
Return operand/member at position i.
Definition: basic.cpp:238
unsigned flags
of type status_flags
Definition: basic.h:302
virtual ex add_indexed(const ex &self, const ex &other) const
Add two indexed expressions.
Definition: basic.cpp:481
const basic & operator=(const basic &other)
basic assignment operator: the other object might be of a derived class.
Definition: basic.cpp:64
virtual void print(const print_context &c, unsigned level=0) const
Output to stream.
Definition: basic.cpp:116
void do_print(const print_context &c, unsigned level) const
Default output to stream.
Definition: basic.cpp:169
virtual void read_archive(const archive_node &n, lst &syms)
Load (deserialize) the object from an archive node.
Definition: basic.cpp:96
ex subs_one_level(const exmap &m, unsigned options) const
Helper function for subs().
Definition: basic.cpp:585
const basic & hold() const
Stop further evaluation.
Definition: basic.cpp:887
virtual ex series(const relational &r, int order, unsigned options=0) const
Default implementation of ex::series().
Definition: pseries.cpp:612
virtual void accept(GiNaC::visitor &v) const
Definition: basic.h:180
bool is_equal(const basic &other) const
Test for syntactic equality.
Definition: basic.cpp:863
virtual ex collect(const ex &s, bool distributed=false) const
Sort expanded expression in terms of powers of some object(s).
Definition: basic.cpp:348
virtual ex to_polynomial(exmap &repl) const
Definition: normal.cpp:2643
virtual ex subs(const exmap &m, unsigned options=0) const
Substitute a set of objects by arbitrary expressions.
Definition: basic.cpp:607
virtual ex real_part() const
Definition: basic.cpp:676
virtual int compare_same_type(const basic &other) const
Returns order relation between two objects of same type.
Definition: basic.cpp:719
virtual ex & let_op(size_t i)
Return modifiable operand/member at position i.
Definition: basic.cpp:244
virtual basic * duplicate() const
Create a clone of this object on the heap.
Definition: basic.h:131
virtual void dbgprint() const
Little wrapper around print to be called within a debugger.
Definition: basic.cpp:199
virtual ex to_rational(exmap &repl) const
Default implementation of ex::to_rational().
Definition: normal.cpp:2638
void do_print_tree(const print_tree &c, unsigned level) const
Tree output to stream.
Definition: basic.cpp:175
virtual ex coeff(const ex &s, int n=1) const
Return coefficient of degree n in object s.
Definition: basic.cpp:337
virtual unsigned return_type() const
Definition: basic.cpp:751
virtual ex eval_ncmul(const exvector &v) const
Definition: basic.cpp:686
void do_print_python_repr(const print_python_repr &c, unsigned level) const
Python parsable output to stream.
Definition: basic.cpp:187
virtual ex derivative(const symbol &s) const
Default implementation of ex::diff().
Definition: basic.cpp:704
virtual int ldegree(const ex &s) const
Return degree of lowest power in object s.
Definition: basic.cpp:331
virtual ex smod(const numeric &xi) const
Apply symmetric modular homomorphism to an expanded multivariate polynomial.
Definition: normal.cpp:1203
virtual ex expand(unsigned options=0) const
Expand expression, i.e.
Definition: basic.cpp:796
virtual ex normal(exmap &repl, exmap &rev_lookup, lst &modifier) const
Default implementation of ex::normal().
Definition: normal.cpp:2217
basic(const basic &other)
int compare(const basic &other) const
Compare objects syntactically to establish canonical ordering.
Definition: basic.cpp:816
virtual ~basic()
basic destructor, virtual because class ex will delete objects of derived classes via a basic*.
Definition: basic.h:117
virtual ex evalf() const
Evaluate object numerically.
Definition: basic.cpp:425
virtual ex operator[](const ex &index) const
Definition: basic.cpp:250
virtual unsigned calchash() const
Compute the hash value of an object and if it makes sense to store it in the objects status_flags,...
Definition: basic.cpp:770
virtual exvector get_free_indices() const
Return a vector containing the free indices of an expression.
Definition: basic.cpp:666
virtual bool is_polynomial(const ex &var) const
Check whether this is a polynomial in the given variables.
Definition: basic.cpp:319
virtual ex map(map_function &f) const
Construct new expression by applying the specified function to all sub-expressions (one level only,...
Definition: basic.cpp:294
Wrapper template for making GiNaC classes out of STL containers.
Definition: container.h:73
Lightweight wrapper for GiNaC's symbolic objects.
Definition: ex.h:72
This class is a wrapper around CLN-numbers within the GiNaC class hierarchy.
Definition: numeric.h:82
Base class for print_contexts.
Definition: print.h:103
Context for python-parsable output.
Definition: print.h:139
Context for tree-like output for debugging.
Definition: print.h:147
Base class for reference-counted objects.
Definition: ptr.h:35
unsigned int get_refcount() const noexcept
Definition: ptr.h:41
This class holds a relation consisting of two expressions and a logical relation between them.
Definition: relational.h:35
@ dynallocated
heap-allocated (i.e. created by new if we want to be clever and bypass the stack,
Definition: flags.h:202
@ hash_calculated
.calchash() has already done its job
Definition: flags.h:205
Basic CAS symbol.
Definition: symbol.h:39
Degenerate base class for visitors.
Definition: basic.h:97
virtual ~visitor()
Definition: basic.h:99
unsigned options
Definition: factor.cpp:2480
size_t n
Definition: factor.cpp:1463
size_t c
Definition: factor.cpp:770
size_t r
Definition: factor.cpp:770
exset syms
Definition: factor.cpp:2434
mvec m
Definition: factor.cpp:771
Collection of all flags used through the GiNaC framework.
int order
Definition: add.cpp:38
std::map< ex, ex, ex_is_less > exmap
Definition: basic.h:50
std::set< ex, ex_is_less > exset
Definition: basic.h:49
B & dynallocate(Args &&... args)
Constructs a new (class basic or derived) B object on the heap.
Definition: basic.h:334
bool is_a(const basic &obj)
Check if obj is a T, including base classes.
Definition: basic.h:313
bool is_exactly_a(const basic &obj)
Check if obj is a T, not including base classes.
Definition: basic.h:320
std::vector< ex > exvector
Definition: basic.h:48
Reference-counted pointer template.
GiNaC's class registrar (for class basic and all classes derived from it).
#define GINAC_DECLARE_REGISTERED_CLASS_NO_CTORS(classname, supername)
Primary macro for inclusion in the declaration of each registered class.
Definition: registrar.h:141
Function object for map().
Definition: basic.h:85
virtual ~map_function()
Definition: basic.h:86
virtual ex operator()(const ex &e)=0
const ex & argument_type
Definition: basic.h:87
To distinguish between different kinds of non-commutative objects.
Definition: registrar.h:44

This page is part of the GiNaC developer's reference. It was generated automatically by doxygen. For an introduction, see the tutorial.