X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=ffb2cfb98125d658cbaeb1be9a2b13e60aeab34c;hp=d447aaa64de9d98e135beb67ec7e32a03509cc62;hb=43e0a8f5ca5e1c48cef5daaf014acdbca4e44568;hpb=e5362a33f72613b324b3714524a8c2e5f7b7f46f diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index d447aaa6..ffb2cfb9 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -31,23 +31,23 @@ #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); + debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT); } void pseries::copy(const pseries &other) @@ -58,15 +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. @@ -80,7 +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(); @@ -92,10 +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; @@ -108,13 +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); @@ -128,83 +116,124 @@ 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); - if (precedence<=upper_precedence) os << "("; - 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_of_type(c, print_tree)) { + + 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; + for (unsigned i=0; irest)) { + // 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_of_type(c, print_latex)) + 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_of_type(c, print_latex)) { + 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); } - } - if (precedence<=upper_precedence) os << ")"; -} - -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. */ @@ -213,7 +242,6 @@ 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 { @@ -222,17 +250,15 @@ 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 @@ -260,7 +286,7 @@ 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 @@ -283,7 +309,14 @@ 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) @@ -314,13 +347,12 @@ 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 { @@ -341,7 +373,6 @@ 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 { @@ -362,7 +393,6 @@ 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 { // If expansion variable is being substituted, convert the series to a @@ -383,21 +413,20 @@ ex pseries::subs(const lst & ls, const lst & lr) const return (new pseries(relational(var,point.subs(ls, lr)), 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)); + for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + ex restexp = i->rest.expand(); + if (!restexp.is_zero()) + newseq.push_back(expair(restexp, i->coeff)); + } return (new pseries(relational(var,point), newseq)) ->setflag(status_flags::dynallocated | status_flags::expanded); } - /** Implementation of ex::diff() for a power series. It treats the series as a * polynomial. * @see ex::diff */ @@ -424,14 +453,6 @@ 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; @@ -448,8 +469,6 @@ 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); @@ -457,7 +476,7 @@ bool pseries::is_terminating(void) const /* - * Implementation of series expansion + * Implementations of series expansion */ /** Default implementation of ex::series(). This performs Taylor expansion. @@ -468,15 +487,15 @@ 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) @@ -659,19 +678,18 @@ 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) @@ -681,8 +699,8 @@ 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; } @@ -691,7 +709,7 @@ 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); } @@ -752,18 +770,29 @@ ex pseries::power_const(const numeric &p, int deg) const // 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. - const symbol *s = static_cast(var.bp); - int ldeg = ldegree(*s); + + if (seq.size()==0) { + // 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); // Compute coefficients of the powered series exvector co; co.reserve(deg); - co.push_back(power(coeff(*s, ldeg), p)); + co.push_back(power(coeff(var, ldeg), p)); bool all_sums_zero = true; for (int i=1; i(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; @@ -904,6 +933,4 @@ ex ex::series(const ex & r, int order, unsigned options) const unsigned pseries::precedence = 38; // for clarity just below add::precedence -#ifndef NO_NAMESPACE_GINAC } // namespace GiNaC -#endif // ndef NO_NAMESPACE_GINAC