3 * Interface to class for extended truncated power series. */
6 * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
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.
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.
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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 #ifndef __GINAC_SERIES_H__
24 #define __GINAC_SERIES_H__
27 #include "expairseq.h"
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
37 GINAC_DECLARE_REGISTERED_CLASS(pseries, basic)
41 pseries(const ex &rel_, const epvector &ops_);
43 // functions overriding virtual functions from base classes
45 unsigned precedence() const {return 38;} // for clarity just below add::precedence
47 ex op(size_t i) const;
48 int degree(const ex &s) const;
49 int ldegree(const ex &s) const;
50 ex coeff(const ex &s, int n = 1) const;
51 ex collect(const ex &s, bool distributed = false) const;
52 ex eval(int level=0) const;
53 ex evalf(int level=0) const;
54 ex series(const relational & r, int order, unsigned options = 0) const;
55 ex subs(const exmap & m, unsigned options = 0) const;
56 ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
57 ex expand(unsigned options = 0) const;
60 ex derivative(const symbol & s) const;
62 // non-virtual functions in this class
64 /** Get the expansion variable. */
65 ex get_var() const {return var;}
67 /** Get the expansion point. */
68 ex get_point() const {return point;}
70 /** Convert the pseries object to an ordinary polynomial.
72 * @param no_order flag: discard higher order terms */
73 ex convert_to_poly(bool no_order = false) const;
75 /** Check whether series is compatible to another series (expansion
76 * variable and point are the same. */
77 bool is_compatible_to(const pseries &other) const {return var.is_equal(other.var) && point.is_equal(other.point);}
79 /** Check whether series has the value zero. */
80 bool is_zero() const {return seq.size() == 0;}
82 /** Returns true if there is no order term, i.e. the series terminates and
84 bool is_terminating() const;
86 ex add_series(const pseries &other) const;
87 ex mul_const(const numeric &other) const;
88 ex mul_series(const pseries &other) const;
89 ex power_const(const numeric &p, int deg) const;
90 pseries shift_exponents(int deg) const;
93 void print_series(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, const char *pow_sym, unsigned level) const;
94 void do_print(const print_context & c, unsigned level) const;
95 void do_print_latex(const print_latex & c, unsigned level) const;
96 void do_print_tree(const print_tree & c, unsigned level) const;
97 void do_print_python(const print_python & c, unsigned level) const;
98 void do_print_python_repr(const print_python_repr & c, unsigned level) const;
101 /** Vector of {coefficient, power} pairs */
104 /** Series variable (holds a symbol) */
107 /** Expansion point */
114 /** Specialization of is_exactly_a<pseries>(obj) for pseries objects. */
115 template<> inline bool is_exactly_a<pseries>(const basic & obj)
117 return obj.tinfo()==TINFO_pseries;
120 /** Convert the pseries object embedded in an expression to an ordinary
121 * polynomial in the expansion variable. The result is undefined if the
122 * expression does not contain a pseries object at its top level.
124 * @param e expression
125 * @return polynomial expression
127 * @see pseries::convert_to_poly */
128 inline ex series_to_poly(const ex &e)
130 return (ex_to<pseries>(e).convert_to_poly(true));
133 inline bool is_terminating(const pseries & s)
135 return s.is_terminating();
140 #endif // ndef __GINAC_SERIES_H__