3 * Interface to class for extended truncated power series. */
6 * GiNaC Copyright (C) 1999-2001 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 void print(const print_context & c, unsigned level = 0) const;
46 unsigned precedence(void) const {return 38;} // for clarity just below add::precedence
47 unsigned nops(void) const;
50 int degree(const ex &s) const;
51 int ldegree(const ex &s) const;
52 ex coeff(const ex &s, int n = 1) const;
53 ex collect(const ex &s, bool distributed = false) const;
54 ex eval(int level=0) const;
55 ex evalf(int level=0) const;
56 ex series(const relational & r, int order, unsigned options = 0) const;
57 ex subs(const lst & ls, const lst & lr, bool no_pattern = false) const;
58 ex normal(lst &sym_lst, lst &repl_lst, int level = 0) const;
59 ex expand(unsigned options = 0) const;
61 ex derivative(const symbol & s) const;
63 // non-virtual functions in this class
65 /** Get the expansion variable. */
66 ex get_var(void) const {return var;}
68 /** Get the expansion point. */
69 ex get_point(void) const {return point;}
71 /** Convert the pseries object to an ordinary polynomial.
73 * @param no_order flag: discard higher order terms */
74 ex convert_to_poly(bool no_order = false) const;
76 /** Check whether series is compatible to another series (expansion
77 * variable and point are the same. */
78 bool is_compatible_to(const pseries &other) const {return var.is_equal(other.var) && point.is_equal(other.point);}
80 /** Check whether series has the value zero. */
81 bool is_zero(void) const {return seq.size() == 0;}
83 /** Returns true if there is no order term, i.e. the series terminates and
85 bool is_terminating(void) const;
87 ex add_series(const pseries &other) const;
88 ex mul_const(const numeric &other) const;
89 ex mul_series(const pseries &other) const;
90 ex power_const(const numeric &p, int deg) const;
91 pseries shift_exponents(int deg) const;
94 /** Vector of {coefficient, power} pairs */
97 /** Series variable (holds a symbol) */
100 /** Expansion point */
104 /** Return a reference to the pseries object embedded in an expression.
105 * The result is undefined if the expression does not contain a pseries
106 * object at its top level.
108 * @param e expression
109 * @return reference to pseries object
110 * @see is_ex_of_type */
111 inline const pseries &ex_to_pseries(const ex &e)
113 return static_cast<const pseries &>(*e.bp);
116 /** Convert the pseries object embedded in an expression to an ordinary
117 * polynomial in the expansion variable. The result is undefined if the
118 * expression does not contain a pseries object at its top level.
120 * @param e expression
121 * @return polynomial expression
123 * @see pseries::convert_to_poly */
124 inline ex series_to_poly(const ex &e)
126 return (static_cast<const pseries &>(*e.bp).convert_to_poly(true));
129 inline bool is_terminating(const pseries & s)
131 return s.is_terminating();
136 #endif // ndef __GINAC_SERIES_H__