X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpseries.cpp;h=7ae30a9c7266a17e5d9481b1776cb975e8079783;hp=1477449c0bf3233f6f829549c14ad46cf3515f15;hb=11c7f91bf740646e78ffa0711ef405aefca96705;hpb=b9cd4b49ffbfbf3e1c36a2b594ec3148a5baca64 diff --git a/ginac/pseries.cpp b/ginac/pseries.cpp index 1477449c..7ae30a9c 100644 --- a/ginac/pseries.cpp +++ b/ginac/pseries.cpp @@ -25,7 +25,7 @@ #include "pseries.h" #include "add.h" -#include "inifcns.h" +#include "inifcns.h" // for Order function #include "lst.h" #include "mul.h" #include "power.h" @@ -77,10 +77,10 @@ DEFAULT_DESTROY(pseries) pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_) { 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)); + GINAC_ASSERT(is_exactly_a(rel_)); + GINAC_ASSERT(is_exactly_a(rel_.lhs())); point = rel_.rhs(); - var = *static_cast(rel_.lhs().bp); + var = rel_.lhs(); } @@ -119,20 +119,21 @@ void pseries::archive(archive_node &n) const DEFAULT_UNARCHIVE(pseries) ////////// -// functions overriding virtual functions from bases classes +// functions overriding virtual functions from base classes ////////// void pseries::print(const print_context & c, unsigned level) const { debugmsg("pseries print", LOGLEVEL_PRINT); - if (is_of_type(c, print_tree)) { + 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; - 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.size() == 0) + if (seq.empty()) c.s << '0'; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + epvector::const_iterator i = seq.begin(), end = seq.end(); + while (i != end) { // print a sign, if needed if (i != seq.begin()) c.s << '+'; @@ -168,7 +170,7 @@ void pseries::print(const print_context & c, unsigned level) const } // print 'coeff', something like (x-1)^42 if (!i->coeff.is_zero()) { - if (is_of_type(c, print_latex)) + if (is_a(c)) c.s << ' '; else c.s << '*'; @@ -185,7 +187,7 @@ void pseries::print(const print_context & c, unsigned level) const i->coeff.print(c); c.s << par_close; } else { - if (is_of_type(c, print_latex)) { + if (is_a(c)) { c.s << '{'; i->coeff.print(c); c.s << '}'; @@ -196,6 +198,7 @@ void pseries::print(const print_context & c, unsigned level) const } } else Order(power(var-point,i->coeff)).print(c); + ++i; } if (precedence() <= level) @@ -263,7 +266,7 @@ 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 { @@ -291,7 +294,7 @@ 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 { @@ -319,7 +322,7 @@ int pseries::ldegree(const ex &s) const 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 @@ -327,8 +330,8 @@ ex pseries::coeff(const ex &s, int n) const int lo = 0, hi = seq.size() - 1; 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); + GINAC_ASSERT(is_exactly_a(seq[mid].coeff)); + int cmp = ex_to(seq[mid].coeff).compare(looking_for); switch (cmp) { case -1: lo = mid + 1; @@ -353,7 +356,7 @@ ex pseries::collect(const ex &s, bool distributed) const return *this; } -/** Evaluate coefficients. */ +/** Perform coefficient-wise automatic term rewriting rules in this class. */ ex pseries::eval(int level) const { if (level == 1) @@ -418,13 +421,15 @@ ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) const ex pseries::expand(unsigned options) const { epvector newseq; - for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) { + 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 @@ -471,7 +476,7 @@ ex pseries::convert_to_poly(bool no_order) const 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); } @@ -487,28 +492,30 @@ 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 = ex_to(r.lhs()); if (!coeff.is_zero()) seq.push_back(expair(coeff, _ex0())); int n; for (n=1; nis_equal(*s.bp)) { + GINAC_ASSERT(is_exactly_a(r.lhs())); + + if (this->is_equal_same_type(ex_to(r.lhs()))) { if (order > 0 && !point.is_zero()) seq.push_back(expair(point, _ex0())); if (order > 1) @@ -566,7 +572,7 @@ 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) { @@ -576,7 +582,7 @@ 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) { @@ -629,10 +635,10 @@ 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; } @@ -677,7 +683,6 @@ ex pseries::mul_series(const pseries &other) const // Series multiplication epvector new_seq; - int a_max = degree(var); int b_max = other.degree(var); int a_min = ldegree(var); @@ -718,30 +723,21 @@ ex pseries::mul_series(const pseries &other) const * @see ex::series */ ex mul::series(const relational & r, int order, unsigned options) const { - ex acc; // Series accumulator - - // Get first term from overall_coeff - acc = overall_coeff.series(r, order, options); - + pseries acc; // Series accumulator + // Multiply with remaining terms - epvector::const_iterator it = seq.begin(); - epvector::const_iterator itend = seq.end(); - for (; it!=itend; ++it) { - ex op = it->rest; - 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)); - 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); + const epvector::const_iterator itbeg = seq.begin(); + const epvector::const_iterator itend = seq.end(); + for (epvector::const_iterator it=itbeg; it!=itend; ++it) { + ex op = recombine_pair_to_ex(*it).series(r, order, options); // Series multiplication - acc = ex_to_pseries(acc).mul_series(ex_to_pseries(op)); + if (it==itbeg) + acc = ex_to(op); + else + acc = ex_to(acc.mul_series(ex_to(op))); } - return acc; + return acc.mul_const(ex_to(overall_coeff)); } @@ -752,6 +748,7 @@ ex mul::series(const relational & r, int order, unsigned options) const ex pseries::power_const(const numeric &p, int deg) const { // method: + // (due to Leonhard Euler) // 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 + ... @@ -771,18 +768,24 @@ ex pseries::power_const(const numeric &p, int deg) const // 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.size()==0) { - // as a spacial case, handle the empty (zero) series honoring the + if (seq.empty()) { + // as a special 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")); + 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)); + throw pole_error("pseries::power_const(): division by zero",1); else return *this; } - int ldeg = ldegree(var); + const int ldeg = ldegree(var); + if (!(p*ldeg).is_integer()) + throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series"); + + // O(x^n)^(-m) is undefined + if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative()) + throw pole_error("pseries::power_const(): division by zero",1); // Compute coefficients of the powered series exvector co; @@ -801,7 +804,7 @@ ex pseries::power_const(const numeric &p, int deg) const } if (!sum.is_zero()) all_sums_zero = false; - co.push_back(sum / coeff(var, ldeg) / numeric(i)); + co.push_back(sum / coeff(var, ldeg) / i); } // Construct new series (of non-zero coefficients) @@ -809,14 +812,14 @@ ex pseries::power_const(const numeric &p, int deg) const bool higher_order = false; for (int i=0; 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); } @@ -836,33 +842,39 @@ pseries pseries::shift_exponents(int deg) const * @see ex::series */ 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 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); + // If basis is already a series, just power it + if (is_ex_exactly_of_type(basis, pseries)) + return ex_to(basis).power_const(ex_to(exponent), order); + + // 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 0^something? - if (!must_expand_basis && !basis.subs(r).is_zero()) - return basic::series(r, order, options); + // Is the expression of type something^(-int)? + if (!must_expand_basis && !exponent.info(info_flags::negint)) + return basic::series(r, order, options); - // Singularity encountered, expand basis into series - e = basis.series(r, order, options); - } else { - // Basis is a series - e = basis; + // Is the expression of type 0^something? + if (!must_expand_basis && !basis.subs(r).is_zero()) + return basic::series(r, order, options); + + // Singularity encountered, is the basis equal to (var - point)? + if (basis.is_equal(r.lhs() - r.rhs())) { + epvector new_seq; + if (ex_to(exponent).to_int() < order) + new_seq.push_back(expair(_ex1(), exponent)); + else + new_seq.push_back(expair(Order(_ex1()), exponent)); + return pseries(r, new_seq); } - - // Power e - return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order); + + // No, expand basis into series + ex e = basis.series(r, order, options); + return ex_to(e).power_const(ex_to(exponent), order); } @@ -870,8 +882,8 @@ ex power::series(const relational & r, int order, unsigned options) const 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); + GINAC_ASSERT(is_exactly_a(r.lhs())); + const symbol &s = ex_to(r.lhs()); if (var.is_equal(s) && point.is_equal(p)) { if (order > degree(s)) @@ -880,7 +892,7 @@ ex pseries::series(const relational & r, int order, unsigned options) const 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; @@ -911,7 +923,7 @@ 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