X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;ds=sidebyside;f=ginac%2Fpseries.cpp;h=0602ddd74f26df5a1e00bbe70aa249b9439ef6f3;hb=eaaba68453c2863a12244a532db4455d1fc41a7a;hp=9dc0921ed3317a299ee15533b11789a16d6ad130;hpb=9e2d60e206395fc9908e1f9025e50c76b3d7c182;p=ginac.git diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 9dc0921e..0602ddd7 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -4,7 +4,7 @@ * methods for series expansion. */ /* - * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -25,51 +25,29 @@ #include "pseries.h" #include "add.h" -#include "inifcns.h" +#include "inifcns.h" // for Order function #include "lst.h" #include "mul.h" #include "power.h" #include "relational.h" #include "symbol.h" +#include "print.h" #include "archive.h" #include "utils.h" #include "debugmsg.h" -#ifndef NO_NAMESPACE_GINAC namespace GiNaC { -#endif // ndef NO_NAMESPACE_GINAC GINAC_IMPLEMENT_REGISTERED_CLASS(pseries, basic) + /* - * Default constructor, destructor, copy constructor, assignment operator and helpers + * Default ctor, dtor, copy ctor, assignment operator and helpers */ pseries::pseries() : basic(TINFO_pseries) { - debugmsg("pseries default constructor", LOGLEVEL_CONSTRUCT); -} - -pseries::~pseries() -{ - debugmsg("pseries destructor", LOGLEVEL_DESTRUCT); - destroy(false); -} - -pseries::pseries(const pseries &other) -{ - debugmsg("pseries copy constructor", LOGLEVEL_CONSTRUCT); - copy(other); -} - -const pseries &pseries::operator=(const pseries & other) -{ - debugmsg("pseries operator=", LOGLEVEL_ASSIGNMENT); - if (this != &other) { - destroy(true); - copy(other); - } - return *this; + debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT); } void pseries::copy(const pseries &other) @@ -80,15 +58,11 @@ void pseries::copy(const pseries &other) point = other.point; } -void pseries::destroy(bool call_parent) -{ - if (call_parent) - inherited::destroy(call_parent); -} +DEFAULT_DESTROY(pseries) /* - * Other constructors + * Other ctors */ /** Construct pseries from a vector of coefficients and powers. @@ -102,7 +76,7 @@ void pseries::destroy(bool call_parent) * @return newly constructed pseries */ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_) { - debugmsg("pseries constructor from ex,epvector", LOGLEVEL_CONSTRUCT); + debugmsg("pseries ctor from ex,epvector", LOGLEVEL_CONSTRUCT); GINAC_ASSERT(is_ex_exactly_of_type(rel_, relational)); GINAC_ASSERT(is_ex_exactly_of_type(rel_.lhs(),symbol)); point = rel_.rhs(); @@ -114,10 +88,9 @@ pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), s * Archiving */ -/** Construct object from archive_node. */ pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("pseries constructor from archive_node", LOGLEVEL_CONSTRUCT); + debugmsg("pseries ctor from archive_node", LOGLEVEL_CONSTRUCT); for (unsigned int i=0; true; ++i) { ex rest; ex coeff; @@ -130,13 +103,6 @@ pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_l n.find_ex("point", point, sym_lst); } -/** Unarchive the object. */ -ex pseries::unarchive(const archive_node &n, const lst &sym_lst) -{ - return (new pseries(n, sym_lst))->setflag(status_flags::dynallocated); -} - -/** Archive the object. */ void pseries::archive(archive_node &n) const { inherited::archive(n); @@ -150,81 +116,127 @@ void pseries::archive(archive_node &n) const n.add_ex("point", point); } +DEFAULT_UNARCHIVE(pseries) + ////////// // functions overriding virtual functions from bases classes ////////// -basic *pseries::duplicate() const -{ - debugmsg("pseries duplicate", LOGLEVEL_DUPLICATE); - return new pseries(*this); -} - -void pseries::print(std::ostream &os, unsigned upper_precedence) const +void pseries::print(const print_context & c, unsigned level) const { debugmsg("pseries print", LOGLEVEL_PRINT); - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { - // omit zero terms - if (i->rest.is_zero()) - continue; - // print a sign, if needed - if (i!=seq.begin()) - os << '+'; - if (!is_order_function(i->rest)) { - // print 'rest', i.e. the expansion coefficient - if (i->rest.info(info_flags::numeric) && - i->rest.info(info_flags::positive)) { - os << i->rest; - } else - os << "(" << i->rest << ')'; - // print 'coeff', something like (x-1)^42 - if (!i->coeff.is_zero()) { - os << '*'; - if (!point.is_zero()) - os << '(' << var-point << ')'; - else - os << var; - if (i->coeff.compare(_ex1())) { - os << '^'; - if (i->coeff.info(info_flags::negative)) - os << '(' << i->coeff << ')'; + + if (is_a(c)) { + + c.s << std::string(level, ' ') << class_name() + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << std::endl; + unsigned delta_indent = static_cast(c).delta_indent; + unsigned num = seq.size(); + for (unsigned i=0; i(c) ? "{(" : "("; + std::string par_close = is_a(c) ? ")}" : ")"; + + // objects of type pseries must not have any zero entries, so the + // trivial (zero) pseries needs a special treatment here: + if (seq.empty()) + c.s << '0'; + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + // print a sign, if needed + if (i != seq.begin()) + c.s << '+'; + if (!is_order_function(i->rest)) { + // print 'rest', i.e. the expansion coefficient + if (i->rest.info(info_flags::numeric) && + i->rest.info(info_flags::positive)) { + i->rest.print(c); + } else { + c.s << par_open; + i->rest.print(c); + c.s << par_close; + } + // print 'coeff', something like (x-1)^42 + if (!i->coeff.is_zero()) { + if (is_a(c)) + c.s << ' '; else - os << i->coeff; + c.s << '*'; + if (!point.is_zero()) { + c.s << par_open; + (var-point).print(c); + c.s << par_close; + } else + var.print(c); + if (i->coeff.compare(_ex1())) { + c.s << '^'; + if (i->coeff.info(info_flags::negative)) { + c.s << par_open; + i->coeff.print(c); + c.s << par_close; + } else { + if (is_a(c)) { + c.s << '{'; + i->coeff.print(c); + c.s << '}'; + } else + i->coeff.print(c); + } + } } - } - } else { - os << Order(power(var-point,i->coeff)); + } else + Order(power(var-point,i->coeff)).print(c); + ++i; } - } -} - -void pseries::printraw(std::ostream &os) const -{ - debugmsg("pseries printraw", LOGLEVEL_PRINT); - os << "pseries(" << var << ";" << point << ";"; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { - os << "(" << (*i).rest << "," << (*i).coeff << "),"; + if (precedence() <= level) + c.s << ")"; } - os << ")"; } - -void pseries::printtree(std::ostream & os, unsigned indent) const +int pseries::compare_same_type(const basic & other) const { - debugmsg("pseries printtree",LOGLEVEL_PRINT); - os << std::string(indent,' ') << "pseries " - << ", hash=" << hashvalue - << " (0x" << std::hex << hashvalue << std::dec << ")" - << ", flags=" << flags << std::endl; - for (unsigned i=0; i(other); + + // first compare the lengths of the series... + if (seq.size()>o.seq.size()) + return 1; + if (seq.size()compare(*o_it); + if (cmpval) + return cmpval; + ++it; + ++o_it; } - var.printtree(os, indent+delta_indent); - point.printtree(os, indent+delta_indent); + + // so they are equal. + return 0; } /** Return the number of operands including a possible order term. */ @@ -233,7 +245,6 @@ unsigned pseries::nops(void) const return seq.size(); } - /** Return the ith term in the series when represented as a sum. */ ex pseries::op(int i) const { @@ -242,22 +253,20 @@ ex pseries::op(int i) const return seq[i].rest * power(var - point, seq[i].coeff); } - ex &pseries::let_op(int i) { throw (std::logic_error("let_op not defined for pseries")); } - /** Return degree of highest power of the series. This is usually the exponent * of the Order term. If s is not the expansion variable of the series, the * series is examined termwise. */ -int pseries::degree(const symbol &s) const +int pseries::degree(const ex &s) const { if (var.is_equal(s)) { // Return last exponent if (seq.size()) - return ex_to_numeric((*(seq.end() - 1)).coeff).to_int(); + return ex_to((*(seq.end() - 1)).coeff).to_int(); else return 0; } else { @@ -280,12 +289,12 @@ int pseries::degree(const symbol &s) const * series is examined termwise. If s is the expansion variable but the * expansion point is not zero the series is not expanded to find the degree. * I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */ -int pseries::ldegree(const symbol &s) const +int pseries::ldegree(const ex &s) const { if (var.is_equal(s)) { // Return first exponent if (seq.size()) - return ex_to_numeric((*(seq.begin())).coeff).to_int(); + return ex_to((*(seq.begin())).coeff).to_int(); else return 0; } else { @@ -303,10 +312,17 @@ int pseries::ldegree(const symbol &s) const } } -ex pseries::coeff(const symbol &s, int n) const +/** Return coefficient of degree n in power series if s is the expansion + * variable. If the expansion point is nonzero, by definition the n=1 + * coefficient in s of a+b*(s-z)+c*(s-z)^2+Order((s-z)^3) is b (assuming + * the expansion took place in the s in the first place). + * If s is not the expansion variable, an attempt is made to convert the + * series to a polynomial and return the corresponding coefficient from + * there. */ +ex pseries::coeff(const ex &s, int n) const { if (var.is_equal(s)) { - if (seq.size() == 0) + if (seq.empty()) return _ex0(); // Binary search in sequence for given power @@ -315,7 +331,7 @@ ex pseries::coeff(const symbol &s, int n) const while (lo <= hi) { int mid = (lo + hi) / 2; GINAC_ASSERT(is_ex_exactly_of_type(seq[mid].coeff, numeric)); - int cmp = ex_to_numeric(seq[mid].coeff).compare(looking_for); + int cmp = ex_to(seq[mid].coeff).compare(looking_for); switch (cmp) { case -1: lo = mid + 1; @@ -334,13 +350,12 @@ ex pseries::coeff(const symbol &s, int n) const return convert_to_poly().coeff(s, n); } - -ex pseries::collect(const symbol &s) const +/** Does nothing. */ +ex pseries::collect(const ex &s, bool distributed) const { return *this; } - /** Evaluate coefficients. */ ex pseries::eval(int level) const { @@ -361,7 +376,6 @@ ex pseries::eval(int level) const return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); } - /** Evaluate coefficients numerically. */ ex pseries::evalf(int level) const { @@ -382,14 +396,13 @@ ex pseries::evalf(int level) const return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated); } - -ex pseries::subs(const lst & ls, const lst & lr) const +ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) const { // If expansion variable is being substituted, convert the series to a // polynomial and do the substitution there because the result might // no longer be a power series if (ls.has(var)) - return convert_to_poly(true).subs(ls, lr); + return convert_to_poly(true).subs(ls, lr, no_pattern); // Otherwise construct a new series with substituted coefficients and // expansion point @@ -397,27 +410,28 @@ ex pseries::subs(const lst & ls, const lst & lr) const newseq.reserve(seq.size()); epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - newseq.push_back(expair(it->rest.subs(ls, lr), it->coeff)); + newseq.push_back(expair(it->rest.subs(ls, lr, no_pattern), it->coeff)); ++it; } - return (new pseries(relational(var,point.subs(ls, lr)), newseq))->setflag(status_flags::dynallocated); + return (new pseries(relational(var,point.subs(ls, lr, no_pattern)), newseq))->setflag(status_flags::dynallocated); } - /** Implementation of ex::expand() for a power series. It expands all the - * terms individually and returns the resulting series as a new pseries. - * @see ex::diff */ + * terms individually and returns the resulting series as a new pseries. */ ex pseries::expand(unsigned options) const { epvector newseq; - newseq.reserve(seq.size()); - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) - newseq.push_back(expair(i->rest.expand(), i->coeff)); + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { + ex restexp = i->rest.expand(); + if (!restexp.is_zero()) + newseq.push_back(expair(restexp, i->coeff)); + ++i; + } return (new pseries(relational(var,point), newseq)) - ->setflag(status_flags::dynallocated | status_flags::expanded); + ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)); } - /** Implementation of ex::diff() for a power series. It treats the series as a * polynomial. * @see ex::diff */ @@ -444,14 +458,6 @@ ex pseries::derivative(const symbol & s) const } } - -/* - * Construct ordinary polynomial out of series - */ - -/** Convert a pseries object to an ordinary polynomial. - * - * @param no_order flag: discard higher order terms */ ex pseries::convert_to_poly(bool no_order) const { ex e; @@ -468,16 +474,14 @@ ex pseries::convert_to_poly(bool no_order) const return e; } -/** Returns true if there is no order term, i.e. the series terminates and - * false otherwise. */ bool pseries::is_terminating(void) const { - return seq.size() == 0 || !is_order_function((seq.end()-1)->rest); + return seq.empty() || !is_order_function((seq.end()-1)->rest); } /* - * Implementation of series expansion + * Implementations of series expansion */ /** Default implementation of ex::series(). This performs Taylor expansion. @@ -488,15 +492,15 @@ ex basic::series(const relational & r, int order, unsigned options) const numeric fac(1); ex deriv = *this; ex coeff = deriv.subs(r); - const symbol *s = static_cast(r.lhs().bp); + const symbol &s = static_cast(*r.lhs().bp); if (!coeff.is_zero()) - seq.push_back(expair(coeff, numeric(0))); + seq.push_back(expair(coeff, _ex0())); int n; for (n=1; n(r.lhs().bp); + ex s = r.lhs(); - if (this->is_equal(*s)) { + if (this->is_equal(*s.bp)) { if (order > 0 && !point.is_zero()) seq.push_back(expair(point, _ex0())); if (order > 1) @@ -567,7 +571,7 @@ ex pseries::add_series(const pseries &other) const } break; } else - pow_a = ex_to_numeric((*a).coeff).to_int(); + pow_a = ex_to((*a).coeff).to_int(); // If b is empty, fill up with elements from a and stop if (b == b_end) { @@ -577,7 +581,7 @@ ex pseries::add_series(const pseries &other) const } break; } else - pow_b = ex_to_numeric((*b).coeff).to_int(); + pow_b = ex_to((*b).coeff).to_int(); // a and b are non-empty, compare powers if (pow_a < pow_b) { @@ -630,10 +634,10 @@ ex add::series(const relational & r, int order, unsigned options) const else op = it->rest.series(r, order, options); if (!it->coeff.is_equal(_ex1())) - op = ex_to_pseries(op).mul_const(ex_to_numeric(it->coeff)); + op = ex_to(op).mul_const(ex_to(it->coeff)); // Series addition - acc = ex_to_pseries(acc).add_series(ex_to_pseries(op)); + acc = ex_to(acc).add_series(ex_to(op)); } return acc; } @@ -679,19 +683,18 @@ ex pseries::mul_series(const pseries &other) const // Series multiplication epvector new_seq; - const symbol *s = static_cast(var.bp); - int a_max = degree(*s); - int b_max = other.degree(*s); - int a_min = ldegree(*s); - int b_min = other.ldegree(*s); + int a_max = degree(var); + int b_max = other.degree(var); + int a_min = ldegree(var); + int b_min = other.ldegree(var); int cdeg_min = a_min + b_min; int cdeg_max = a_max + b_max; int higher_order_a = INT_MAX; int higher_order_b = INT_MAX; - if (is_order_function(coeff(*s, a_max))) + if (is_order_function(coeff(var, a_max))) higher_order_a = a_max + b_min; - if (is_order_function(other.coeff(*s, b_max))) + if (is_order_function(other.coeff(var, b_max))) higher_order_b = b_max + a_min; int higher_order_c = std::min(higher_order_a, higher_order_b); if (cdeg_max >= higher_order_c) @@ -701,8 +704,8 @@ ex pseries::mul_series(const pseries &other) const ex co = _ex0(); // c(i)=a(0)b(i)+...+a(i)b(0) for (int i=a_min; cdeg-i>=b_min; ++i) { - ex a_coeff = coeff(*s, i); - ex b_coeff = other.coeff(*s, cdeg-i); + ex a_coeff = coeff(var, i); + ex b_coeff = other.coeff(var, cdeg-i); if (!is_order_function(a_coeff) && !is_order_function(b_coeff)) co += a_coeff * b_coeff; } @@ -711,7 +714,7 @@ ex pseries::mul_series(const pseries &other) const } if (higher_order_c < INT_MAX) new_seq.push_back(expair(Order(_ex1()), numeric(higher_order_c))); - return pseries(relational(var,point), new_seq); + return pseries(relational(var, point), new_seq); } @@ -733,15 +736,15 @@ ex mul::series(const relational & r, int order, unsigned options) const if (op.info(info_flags::numeric)) { // series * const (special case, faster) ex f = power(op, it->coeff); - acc = ex_to_pseries(acc).mul_const(ex_to_numeric(f)); + acc = ex_to(acc).mul_const(ex_to(f)); continue; } else if (!is_ex_exactly_of_type(op, pseries)) op = op.series(r, order, options); if (!it->coeff.is_equal(_ex1())) - op = ex_to_pseries(op).power_const(ex_to_numeric(it->coeff), order); + op = ex_to(op).power_const(ex_to(it->coeff), order); // Series multiplication - acc = ex_to_pseries(acc).mul_series(ex_to_pseries(op)); + acc = ex_to(acc).mul_series(ex_to(op)); } return acc; } @@ -753,20 +756,48 @@ ex mul::series(const relational & r, int order, unsigned options) const * @param deg truncation order of series calculation */ ex pseries::power_const(const numeric &p, int deg) const { - int i; - const symbol *s = static_cast(var.bp); - int ldeg = ldegree(*s); + // method: + // let A(x) be this series and for the time being let it start with a + // constant (later we'll generalize): + // A(x) = a_0 + a_1*x + a_2*x^2 + ... + // We want to compute + // C(x) = A(x)^p + // C(x) = c_0 + c_1*x + c_2*x^2 + ... + // Taking the derivative on both sides and multiplying with A(x) one + // immediately arrives at + // C'(x)*A(x) = p*C(x)*A'(x) + // Multiplying this out and comparing coefficients we get the recurrence + // formula + // c_i = (i*p*a_i*c_0 + ((i-1)*p-1)*a_{i-1}*c_1 + ... + // ... + (p-(i-1))*a_1*c_{i-1})/(a_0*i) + // which can easily be solved given the starting value c_0 = (a_0)^p. + // For the more general case where the leading coefficient of A(x) is not + // a constant, just consider A2(x) = A(x)*x^m, with some integer m and + // repeat the above derivation. The leading power of C2(x) = A2(x)^2 is + // then of course x^(p*m) but the recurrence formula still holds. + + if (seq.empty()) { + // as a spacial case, handle the empty (zero) series honoring the + // usual power laws such as implemented in power::eval() + if (p.real().is_zero()) + throw (std::domain_error("pseries::power_const(): pow(0,I) is undefined")); + else if (p.real().is_negative()) + throw (pole_error("pseries::power_const(): division by zero",1)); + else + return *this; + } + + int ldeg = ldegree(var); - // Calculate coefficients of powered series + // Compute coefficients of the powered series exvector co; co.reserve(deg); - ex co0; - co.push_back(co0 = power(coeff(*s, ldeg), p)); + co.push_back(power(coeff(var, ldeg), p)); bool all_sums_zero = true; - for (i=1; icoeff = i->coeff + deg; + epvector newseq = seq; + epvector::iterator i = newseq.begin(), end = newseq.end(); + while (i != end) { + i->coeff += deg; + ++i; + } return pseries(relational(var, point), newseq); } @@ -812,12 +846,20 @@ ex power::series(const relational & r, int order, unsigned options) const { ex e; if (!is_ex_exactly_of_type(basis, pseries)) { - // Basis is not a series, may there be a singulary? - if (!exponent.info(info_flags::negint)) + // Basis is not a series, may there be a singularity? + bool must_expand_basis = false; + try { + basis.subs(r); + } catch (pole_error) { + must_expand_basis = true; + } + + // Is the expression of type something^(-int)? + if (!must_expand_basis && !exponent.info(info_flags::negint)) return basic::series(r, order, options); - // Expression is of type something^(-int), check for singularity - if (!basis.subs(r).is_zero()) + // Is the expression of type 0^something? + if (!must_expand_basis && !basis.subs(r).is_zero()) return basic::series(r, order, options); // Singularity encountered, expand basis into series @@ -828,7 +870,7 @@ ex power::series(const relational & r, int order, unsigned options) const } // Power e - return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order); + return ex_to(e).power_const(ex_to(exponent), order); } @@ -837,16 +879,16 @@ ex pseries::series(const relational & r, int order, unsigned options) const { const ex p = r.rhs(); GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol)); - const symbol *s = static_cast(r.lhs().bp); + const symbol &s = static_cast(*r.lhs().bp); - if (var.is_equal(*s) && point.is_equal(p)) { - if (order > degree(*s)) + if (var.is_equal(s) && point.is_equal(p)) { + if (order > degree(s)) return *this; else { epvector new_seq; epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - int o = ex_to_numeric(it->coeff).to_int(); + int o = ex_to(it->coeff).to_int(); if (o >= order) { new_seq.push_back(expair(Order(_ex1()), o)); break; @@ -877,7 +919,7 @@ ex ex::series(const ex & r, int order, unsigned options) const relational rel_; if (is_ex_exactly_of_type(r,relational)) - rel_ = ex_to_relational(r); + rel_ = ex_to(r); else if (is_ex_exactly_of_type(r,symbol)) rel_ = relational(r,_ex0()); else @@ -891,11 +933,4 @@ ex ex::series(const ex & r, int order, unsigned options) const return e; } - -// Global constants -const pseries some_pseries; -const std::type_info & typeid_pseries = typeid(some_pseries); - -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC