1 /** @file pseries.h
2 *
3 * Interface to class for extended truncated power series. */
4
5 /*
6 * GiNaC Copyright (C) 1999-2008 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
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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 */
22
23 #ifndef __GINAC_SERIES_H__
24 #define __GINAC_SERIES_H__
25
26 #include "basic.h"
27 #include "expairseq.h"
28
29 namespace GiNaC {
30
31 /** This class holds a extended truncated power series (positive and negative
32 * integer powers). It consists of expression coefficients (only non-zero
33 * coefficients are stored), an expansion variable and an expansion point.
34 * Other classes must provide members to convert into this type. */
35 class pseries : public basic
36 {
GINAC_DECLARE_REGISTERED_CLASS(pseries,basic)37 GINAC_DECLARE_REGISTERED_CLASS(pseries, basic)
38
39 friend class ex;
40 // other constructors
41 public:
42 pseries(const ex &rel_, epvector ops_);
43 static ex unarchive(const archive_node &n, lst &sym_lst)
44 {
45 return (new pseries(n, sym_lst))->
46 setflag(status_flags::dynallocated);
47 }
48
49 // functions overriding virtual functions from base classes
50 public:
precedence()51 unsigned precedence() const override {return 38;} // for clarity just below add::precedence
52 size_t nops() const override;
53 const ex op(size_t i) const override;
54 numeric degree(const ex &s) const override;
55 numeric ldegree(const ex &s) const override;
56 ex coeff(const ex &s, const ex & n) const override;
57 ex collect(const ex &s, bool distributed = false) const override;
58 ex eval(int level=0) const override;
59 ex evalf(int level=0, PyObject* parent=nullptr) const override;
60 ex series(const relational & r, int order, unsigned options = 0) const override;
61 ex subs(const exmap & m, unsigned options = 0) const override;
62 ex normal(exmap & repl, exmap & rev_lookup, int level = 0, unsigned options = 0) const override;
63 ex expand(unsigned options = 0) const override;
64 ex conjugate() const override;
65 ex real_part() const override;
66 ex imag_part() const override;
67 protected:
68 ex derivative(const symbol & s) const override;
69
70 // non-virtual functions in this class
71 public:
72 /** Get the expansion variable. */
get_var()73 ex get_var() const {return var;}
74
75 /** Get the expansion point. */
get_point()76 ex get_point() const {return point;}
77
78 /** Convert the pseries object to an ordinary polynomial.
79 *
80 * @param no_order flag: discard higher order terms */
81 ex convert_to_poly(bool no_order = false) const;
82
83 /** Check whether series is compatible to another series (expansion
84 * variable and point are the same. */
is_compatible_to(const pseries & other)85 bool is_compatible_to(const pseries &other) const {return var.is_equal(other.var) && point.is_equal(other.point);}
86
87 /** Check whether series has the value zero. */
is_zero()88 bool is_zero() const {return seq.empty();}
89
90 /** Returns true if there is no order term, i.e. the series terminates and
91 * false otherwise. */
92 bool is_terminating() const;
93
94 /** Get coefficients and exponents. */
95 ex coeffop(size_t i) const;
96 ex exponop(size_t i) const;
97
98 ex add_series(const pseries &other) const;
99 ex mul_const(const numeric &other) const;
100 ex mul_series(const pseries &other) const;
101 ex power_const(const numeric &p, int deg) const;
102 pseries shift_exponents(int deg) const;
103
104 protected:
105 void print_series(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, const char *pow_sym, unsigned level) const;
106 void do_print(const print_context & c, unsigned level) const override;
107 void do_print_latex(const print_latex & c, unsigned level) const;
108 void do_print_tree(const print_tree & c, unsigned level) const override;
109 void do_print_python(const print_python & c, unsigned level) const;
110 void do_print_python_repr(const print_python_repr & c, unsigned level) const override;
111
112 protected:
113 /** Vector of {coefficient, power} pairs */
114 epvector seq;
115
116 /** Series variable (holds a symbol) */
117 ex var;
118
119 /** Expansion point */
120 ex point;
121 };
122
123
124 // utility functions
125
126 /** Convert the pseries object embedded in an expression to an ordinary
127 * polynomial in the expansion variable. The result is undefined if the
128 * expression does not contain a pseries object at its top level.
129 *
130 * @param e expression
131 * @return polynomial expression
132 * @see is_a<>
133 * @see pseries::convert_to_poly */
series_to_poly(const ex & e)134 inline ex series_to_poly(const ex &e)
135 {
136 return (ex_to<pseries>(e).convert_to_poly(true));
137 }
138
is_terminating(const pseries & s)139 inline bool is_terminating(const pseries & s)
140 {
141 return s.is_terminating();
142 }
143
144 } // namespace GiNaC
145
146 #endif // ndef __GINAC_SERIES_H__
147