X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnormal.cpp;h=98efe98539e264fea938294fcd3aa0e54cfeb053;hp=cd2ad8eca5a0b29024bc142e81c19866f031bea7;hb=2053dbc953da03b57dfd7da01fcdc196e8b8e912;hpb=68fdf425abf14d016d5f95ee7b9d06a19a3c5926 diff --git a/ginac/normal.cpp b/ginac/normal.cpp index cd2ad8ec..98efe985 100644 --- a/ginac/normal.cpp +++ b/ginac/normal.cpp @@ -6,7 +6,7 @@ * computation, square-free factorization and rational function normalization. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2004 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 @@ -89,12 +89,12 @@ static struct _stat_print { * function returns for a given expression. * * @param e expression to search - * @param x pointer to first symbol found (returned) + * @param x first symbol found (returned) * @return "false" if no symbol was found, "true" otherwise */ -static bool get_first_symbol(const ex &e, const symbol *&x) +static bool get_first_symbol(const ex &e, ex &x) { if (is_a(e)) { - x = &ex_to(e); + x = e; return true; } else if (is_exactly_a(e) || is_exactly_a(e)) { for (size_t i=0; i sym_desc_vec; // Add symbol the sym_desc_vec (used internally by get_symbol_stats()) -static void add_symbol(const symbol *s, sym_desc_vec &v) +static void add_symbol(const ex &s, sym_desc_vec &v) { sym_desc_vec::const_iterator it = v.begin(), itend = v.end(); while (it != itend) { - if (it->sym->compare(*s) == 0) // If it's already in there, don't add it a second time + if (it->sym.is_equal(s)) // If it's already in there, don't add it a second time return; ++it; } @@ -171,7 +171,7 @@ static void add_symbol(const symbol *s, sym_desc_vec &v) static void collect_symbols(const ex &e, sym_desc_vec &v) { if (is_a(e)) { - add_symbol(&ex_to(e), v); + add_symbol(e, v); } else if (is_exactly_a(e) || is_exactly_a(e)) { for (size_t i=0; isym)); - int deg_b = b.degree(*(it->sym)); + int deg_a = a.degree(it->sym); + int deg_b = b.degree(it->sym); it->deg_a = deg_a; it->deg_b = deg_b; it->max_deg = std::max(deg_a, deg_b); - it->max_lcnops = std::max(a.lcoeff(*(it->sym)).nops(), b.lcoeff(*(it->sym)).nops()); - it->ldeg_a = a.ldegree(*(it->sym)); - it->ldeg_b = b.ldegree(*(it->sym)); + it->max_lcnops = std::max(a.lcoeff(it->sym).nops(), b.lcoeff(it->sym).nops()); + it->ldeg_a = a.ldegree(it->sym); + it->ldeg_b = b.ldegree(it->sym); ++it; } std::sort(v.begin(), v.end()); @@ -214,8 +214,8 @@ static void get_symbol_stats(const ex &a, const ex &b, sym_desc_vec &v) std::clog << "Symbols:\n"; it = v.begin(); itend = v.end(); while (it != itend) { - std::clog << " " << *it->sym << ": deg_a=" << it->deg_a << ", deg_b=" << it->deg_b << ", ldeg_a=" << it->ldeg_a << ", ldeg_b=" << it->ldeg_b << ", max_deg=" << it->max_deg << ", max_lcnops=" << it->max_lcnops << endl; - std::clog << " lcoeff_a=" << a.lcoeff(*(it->sym)) << ", lcoeff_b=" << b.lcoeff(*(it->sym)) << endl; + std::clog << " " << it->sym << ": deg_a=" << it->deg_a << ", deg_b=" << it->deg_b << ", ldeg_a=" << it->ldeg_a << ", ldeg_b=" << it->ldeg_b << ", max_deg=" << it->max_deg << ", max_lcnops=" << it->max_lcnops << endl; + std::clog << " lcoeff_a=" << a.lcoeff(it->sym) << ", lcoeff_b=" << b.lcoeff(it->sym) << endl; ++it; } #endif @@ -300,7 +300,6 @@ static ex multiply_lcm(const ex &e, const numeric &lcm) /** Compute the integer content (= GCD of all numeric coefficients) of an * expanded polynomial. * - * @param e expanded polynomial * @return integer content */ numeric ex::integer_content() const { @@ -361,7 +360,7 @@ numeric mul::integer_content() const * @param check_args check whether a and b are polynomials with rational * coefficients (defaults to "true") * @return quotient of a and b in Q[x] */ -ex quo(const ex &a, const ex &b, const symbol &x, bool check_args) +ex quo(const ex &a, const ex &b, const ex &x, bool check_args) { if (b.is_zero()) throw(std::overflow_error("quo: division by zero")); @@ -411,7 +410,7 @@ ex quo(const ex &a, const ex &b, const symbol &x, bool check_args) * @param check_args check whether a and b are polynomials with rational * coefficients (defaults to "true") * @return remainder of a(x) and b(x) in Q[x] */ -ex rem(const ex &a, const ex &b, const symbol &x, bool check_args) +ex rem(const ex &a, const ex &b, const ex &x, bool check_args) { if (b.is_zero()) throw(std::overflow_error("rem: division by zero")); @@ -460,7 +459,7 @@ ex rem(const ex &a, const ex &b, const symbol &x, bool check_args) * @param a rational function in x * @param x a is a function of x * @return decomposed function. */ -ex decomp_rational(const ex &a, const symbol &x) +ex decomp_rational(const ex &a, const ex &x) { ex nd = numer_denom(a); ex numer = nd.op(0), denom = nd.op(1); @@ -480,7 +479,7 @@ ex decomp_rational(const ex &a, const symbol &x) * @param check_args check whether a and b are polynomials with rational * coefficients (defaults to "true") * @return pseudo-remainder of a(x) and b(x) in Q[x] */ -ex prem(const ex &a, const ex &b, const symbol &x, bool check_args) +ex prem(const ex &a, const ex &b, const ex &x, bool check_args) { if (b.is_zero()) throw(std::overflow_error("prem: division by zero")); @@ -532,7 +531,7 @@ ex prem(const ex &a, const ex &b, const symbol &x, bool check_args) * @param check_args check whether a and b are polynomials with rational * coefficients (defaults to "true") * @return sparse pseudo-remainder of a(x) and b(x) in Q[x] */ -ex sprem(const ex &a, const ex &b, const symbol &x, bool check_args) +ex sprem(const ex &a, const ex &b, const ex &x, bool check_args) { if (b.is_zero()) throw(std::overflow_error("prem: division by zero")); @@ -607,7 +606,7 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args) throw(std::invalid_argument("divide: arguments must be polynomials over the rationals")); // Find first symbol - const symbol *x; + ex x; if (!get_first_symbol(a, x) && !get_first_symbol(b, x)) throw(std::invalid_argument("invalid expression in divide()")); @@ -617,26 +616,26 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args) q = _ex0; return true; } - int bdeg = b.degree(*x); - int rdeg = r.degree(*x); - ex blcoeff = b.expand().coeff(*x, bdeg); + int bdeg = b.degree(x); + int rdeg = r.degree(x); + ex blcoeff = b.expand().coeff(x, bdeg); bool blcoeff_is_numeric = is_exactly_a(blcoeff); exvector v; v.reserve(std::max(rdeg - bdeg + 1, 0)); while (rdeg >= bdeg) { - ex term, rcoeff = r.coeff(*x, rdeg); + ex term, rcoeff = r.coeff(x, rdeg); if (blcoeff_is_numeric) term = rcoeff / blcoeff; else if (!divide(rcoeff, blcoeff, term, false)) return false; - term *= power(*x, rdeg - bdeg); + term *= power(x, rdeg - bdeg); v.push_back(term); r -= (term * b).expand(); if (r.is_zero()) { q = (new add(v))->setflag(status_flags::dynallocated); return true; } - rdeg = r.degree(*x); + rdeg = r.degree(x); } return false; } @@ -665,7 +664,7 @@ typedef std::map ex2_exbool_remember; /** Exact polynomial division of a(X) by b(X) in Z[X]. * This functions works like divide() but the input and output polynomials are * in Z[X] instead of Q[X] (i.e. they have integer coefficients). Unlike - * divide(), it doesn´t check whether the input polynomials really are integer + * divide(), it doesn't check whether the input polynomials really are integer * polynomials, so be careful of what you pass in. Also, you have to run * get_symbol_stats() over the input polynomials before calling this function * and pass an iterator to the first element of the sym_desc vector. This @@ -712,10 +711,10 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite #endif // Main symbol - const symbol *x = var->sym; + const ex &x = var->sym; // Compare degrees - int adeg = a.degree(*x), bdeg = b.degree(*x); + int adeg = a.degree(x), bdeg = b.degree(x); if (bdeg > adeg) return false; @@ -730,12 +729,12 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite numeric point = _num0; ex c; for (i=0; i<=adeg; i++) { - ex bs = b.subs(*x == point); + ex bs = b.subs(x == point, subs_options::no_pattern); while (bs.is_zero()) { point += _num1; - bs = b.subs(*x == point); + bs = b.subs(x == point, subs_options::no_pattern); } - if (!divide_in_z(a.subs(*x == point), bs, c, var+1)) + if (!divide_in_z(a.subs(x == point, subs_options::no_pattern), bs, c, var+1)) return false; alpha.push_back(point); u.push_back(c); @@ -765,9 +764,9 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite // Convert from Newton form to standard form c = v[adeg]; for (k=adeg-1; k>=0; k--) - c = c * (*x - alpha[k]) + v[k]; + c = c * (x - alpha[k]) + v[k]; - if (c.degree(*x) == (adeg - bdeg)) { + if (c.degree(x) == (adeg - bdeg)) { q = c.expand(); return true; } else @@ -781,13 +780,13 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite return true; int rdeg = adeg; ex eb = b.expand(); - ex blcoeff = eb.coeff(*x, bdeg); + ex blcoeff = eb.coeff(x, bdeg); exvector v; v.reserve(std::max(rdeg - bdeg + 1, 0)); while (rdeg >= bdeg) { - ex term, rcoeff = r.coeff(*x, rdeg); + ex term, rcoeff = r.coeff(x, rdeg); if (!divide_in_z(rcoeff, blcoeff, term, var+1)) break; - term = (term * power(*x, rdeg - bdeg)).expand(); + term = (term * power(x, rdeg - bdeg)).expand(); v.push_back(term); r -= (term * eb).expand(); if (r.is_zero()) { @@ -797,7 +796,7 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite #endif return true; } - rdeg = r.degree(*x); + rdeg = r.degree(x); } #if USE_REMEMBER dr_remember[ex2(a, b)] = exbool(q, false); @@ -819,15 +818,15 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite * @param x variable in which to compute the unit part * @return unit part * @see ex::content, ex::primpart */ -ex ex::unit(const symbol &x) const +ex ex::unit(const ex &x) const { ex c = expand().lcoeff(x); if (is_exactly_a(c)) return c < _ex0 ? _ex_1 : _ex1; else { - const symbol *y; + ex y; if (get_first_symbol(c, y)) - return c.unit(*y); + return c.unit(y); else throw(std::invalid_argument("invalid expression in unit()")); } @@ -841,7 +840,7 @@ ex ex::unit(const symbol &x) const * @param x variable in which to compute the content part * @return content part * @see ex::unit, ex::primpart */ -ex ex::content(const symbol &x) const +ex ex::content(const ex &x) const { if (is_zero()) return _ex0; @@ -877,7 +876,7 @@ ex ex::content(const symbol &x) const * @param x variable in which to compute the primitive part * @return primitive part * @see ex::unit, ex::content */ -ex ex::primpart(const symbol &x) const +ex ex::primpart(const ex &x) const { if (is_zero()) return _ex0; @@ -902,7 +901,7 @@ ex ex::primpart(const symbol &x) const * @param x variable in which to compute the primitive part * @param c previously computed content part * @return primitive part */ -ex ex::primpart(const symbol &x, const ex &c) const +ex ex::primpart(const ex &x, const ex &c) const { if (is_zero()) return _ex0; @@ -939,7 +938,7 @@ static ex sr_gcd(const ex &a, const ex &b, sym_desc_vec::const_iterator var) #endif // The first symbol is our main variable - const symbol &x = *(var->sym); + const ex &x = var->sym; // Sort c and d so that c has higher degree ex c, d; @@ -1003,7 +1002,6 @@ static ex sr_gcd(const ex &a, const ex &b, sym_desc_vec::const_iterator var) /** Return maximum (absolute value) coefficient of a polynomial. * This function is used internally by heur_gcd(). * - * @param e expanded multivariate polynomial * @return maximum coefficient * @see heur_gcd */ numeric ex::max_coefficient() const @@ -1109,7 +1107,7 @@ ex mul::smod(const numeric &xi) const /** xi-adic polynomial interpolation */ -static ex interpolate(const ex &gamma, const numeric &xi, const symbol &x, int degree_hint = 1) +static ex interpolate(const ex &gamma, const numeric &xi, const ex &x, int degree_hint = 1) { exvector g; g.reserve(degree_hint); ex e = gamma; @@ -1161,7 +1159,7 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const } // The first symbol is our main variable - const symbol &x = *(var->sym); + const ex &x = var->sym; // Remove integer content numeric gc = gcd(a.integer_content(), b.integer_content()); @@ -1187,7 +1185,7 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const // Apply evaluation homomorphism and calculate GCD ex cp, cq; - ex gamma = heur_gcd(p.subs(x == xi), q.subs(x == xi), &cp, &cq, var+1).expand(); + ex gamma = heur_gcd(p.subs(x == xi, subs_options::no_pattern), q.subs(x == xi, subs_options::no_pattern), &cp, &cq, var+1).expand(); if (!is_exactly_a(gamma)) { // Reconstruct polynomial from GCD of mapped polynomials @@ -1220,6 +1218,8 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const * * @param a first multivariate polynomial * @param b second multivariate polynomial + * @param ca pointer to expression that will receive the cofactor of a, or NULL + * @param cb pointer to expression that will receive the cofactor of b, or NULL * @param check_args check whether a and b are polynomials with rational * coefficients (defaults to "true") * @return the GCD as a new expression */ @@ -1378,7 +1378,7 @@ factored_b: // The symbol with least degree is our main variable sym_desc_vec::const_iterator var = sym_stats.begin(); - const symbol &x = *(var->sym); + const ex &x = var->sym; // Cancel trivial common factor int ldeg_a = var->ldeg_a; @@ -1498,7 +1498,7 @@ static exvector sqrfree_yun(const ex &a, const symbol &x) /** Compute a square-free factorization of a multivariate polynomial in Q[X]. * * @param a multivariate polynomial over Q[X] - * @param x lst of variables to factor in, may be left empty for autodetection + * @param l lst of variables to factor in, may be left empty for autodetection * @return a square-free factorization of \p a. * * \note @@ -1545,7 +1545,7 @@ ex sqrfree(const ex &a, const lst &l) get_symbol_stats(a, _ex0, sdv); sym_desc_vec::const_iterator it = sdv.begin(), itend = sdv.end(); while (it != itend) { - args.append(*it->sym); + args.append(it->sym); ++it; } } else { @@ -1562,7 +1562,7 @@ ex sqrfree(const ex &a, const lst &l) const ex tmp = multiply_lcm(a,lcm); // find the factors - exvector factors = sqrfree_yun(tmp,x); + exvector factors = sqrfree_yun(tmp, x); // construct the next list of symbols with the first element popped lst newargs = args; @@ -1681,47 +1681,44 @@ ex sqrfree_parfrac(const ex & a, const symbol & x) /** Create a symbol for replacing the expression "e" (or return a previously - * assigned symbol). The symbol is appended to sym_lst and returned, the - * expression is appended to repl_lst. + * assigned symbol). The symbol and expression are appended to repl, for + * a later application of subs(). * @see ex::normal */ -static ex replace_with_symbol(const ex &e, lst &sym_lst, lst &repl_lst) +static ex replace_with_symbol(const ex & e, exmap & repl, exmap & rev_lookup) { - // Expression already in repl_lst? Then return the assigned symbol - lst::const_iterator its, itr; - for (its = sym_lst.begin(), itr = repl_lst.begin(); itr != repl_lst.end(); ++its, ++itr) - if (itr->is_equal(e)) - return *its; + // Expression already replaced? Then return the assigned symbol + exmap::const_iterator it = rev_lookup.find(e); + if (it != rev_lookup.end()) + return it->second; // Otherwise create new symbol and add to list, taking care that the - // replacement expression doesn't contain symbols from the sym_lst + // replacement expression doesn't itself contain symbols from repl, // because subs() is not recursive - symbol s; - ex es(s); - ex e_replaced = e.subs(sym_lst, repl_lst); - sym_lst.append(es); - repl_lst.append(e_replaced); + ex es = (new symbol)->setflag(status_flags::dynallocated); + ex e_replaced = e.subs(repl, subs_options::no_pattern); + repl.insert(std::make_pair(es, e_replaced)); + rev_lookup.insert(std::make_pair(e_replaced, es)); return es; } /** Create a symbol for replacing the expression "e" (or return a previously - * assigned symbol). An expression of the form "symbol == expression" is added - * to repl_lst and the symbol is returned. + * assigned symbol). The symbol and expression are appended to repl, and the + * symbol is returned. * @see basic::to_rational * @see basic::to_polynomial */ -static ex replace_with_symbol(const ex &e, lst &repl_lst) +static ex replace_with_symbol(const ex & e, exmap & repl) { - // Expression already in repl_lst? Then return the assigned symbol - for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) - if (it->op(1).is_equal(e)) - return it->op(0); + // Expression already replaced? Then return the assigned symbol + for (exmap::const_iterator it = repl.begin(); it != repl.end(); ++it) + if (it->second.is_equal(e)) + return it->first; // Otherwise create new symbol and add to list, taking care that the - // replacement expression doesn't contain symbols from the sym_lst + // replacement expression doesn't itself contain symbols from repl, // because subs() is not recursive - symbol s; - ex es(s); - ex e_replaced = e.subs(repl_lst); - repl_lst.append(es == e_replaced); + ex es = (new symbol)->setflag(status_flags::dynallocated); + ex e_replaced = e.subs(repl, subs_options::no_pattern); + repl.insert(std::make_pair(es, e_replaced)); return es; } @@ -1736,18 +1733,18 @@ struct normal_map_function : public map_function { /** Default implementation of ex::normal(). It normalizes the children and * replaces the object with a temporary symbol. * @see ex::normal */ -ex basic::normal(lst &sym_lst, lst &repl_lst, int level) const +ex basic::normal(exmap & repl, exmap & rev_lookup, int level) const { if (nops() == 0) - return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); else { if (level == 1) - return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); else { normal_map_function map_normal(level - 1); - return (new lst(replace_with_symbol(map(map_normal), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(map(map_normal), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); } } } @@ -1755,7 +1752,7 @@ ex basic::normal(lst &sym_lst, lst &repl_lst, int level) const /** Implementation of ex::normal() for symbols. This returns the unmodified symbol. * @see ex::normal */ -ex symbol::normal(lst &sym_lst, lst &repl_lst, int level) const +ex symbol::normal(exmap & repl, exmap & rev_lookup, int level) const { return (new lst(*this, _ex1))->setflag(status_flags::dynallocated); } @@ -1765,19 +1762,19 @@ ex symbol::normal(lst &sym_lst, lst &repl_lst, int level) const * into re+I*im and replaces I and non-rational real numbers with a temporary * symbol. * @see ex::normal */ -ex numeric::normal(lst &sym_lst, lst &repl_lst, int level) const +ex numeric::normal(exmap & repl, exmap & rev_lookup, int level) const { numeric num = numer(); ex numex = num; if (num.is_real()) { if (!num.is_integer()) - numex = replace_with_symbol(numex, sym_lst, repl_lst); + numex = replace_with_symbol(numex, repl, rev_lookup); } else { // complex numeric re = num.real(), im = num.imag(); - ex re_ex = re.is_rational() ? re : replace_with_symbol(re, sym_lst, repl_lst); - ex im_ex = im.is_rational() ? im : replace_with_symbol(im, sym_lst, repl_lst); - numex = re_ex + im_ex * replace_with_symbol(I, sym_lst, repl_lst); + ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl, rev_lookup); + ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl, rev_lookup); + numex = re_ex + im_ex * replace_with_symbol(I, repl, rev_lookup); } // Denominator is always a real integer (see numeric::denom()) @@ -1830,10 +1827,10 @@ static ex frac_cancel(const ex &n, const ex &d) den *= _ex_1; } } else { - const symbol *x; + ex x; if (get_first_symbol(den, x)) { - GINAC_ASSERT(is_exactly_a(den.unit(*x))); - if (ex_to(den.unit(*x)).is_negative()) { + GINAC_ASSERT(is_exactly_a(den.unit(x))); + if (ex_to(den.unit(x)).is_negative()) { num *= _ex_1; den *= _ex_1; } @@ -1849,10 +1846,10 @@ static ex frac_cancel(const ex &n, const ex &d) /** Implementation of ex::normal() for a sum. It expands terms and performs * fractional addition. * @see ex::normal */ -ex add::normal(lst &sym_lst, lst &repl_lst, int level) const +ex add::normal(exmap & repl, exmap & rev_lookup, int level) const { if (level == 1) - return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); @@ -1862,12 +1859,12 @@ ex add::normal(lst &sym_lst, lst &repl_lst, int level) const dens.reserve(seq.size()+1); epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - ex n = ex_to(recombine_pair_to_ex(*it)).normal(sym_lst, repl_lst, level-1); + ex n = ex_to(recombine_pair_to_ex(*it)).normal(repl, rev_lookup, level-1); nums.push_back(n.op(0)); dens.push_back(n.op(1)); it++; } - ex n = ex_to(overall_coeff).normal(sym_lst, repl_lst, level-1); + ex n = ex_to(overall_coeff).normal(repl, rev_lookup, level-1); nums.push_back(n.op(0)); dens.push_back(n.op(1)); GINAC_ASSERT(nums.size() == dens.size()); @@ -1908,10 +1905,10 @@ ex add::normal(lst &sym_lst, lst &repl_lst, int level) const /** Implementation of ex::normal() for a product. It cancels common factors * from fractions. * @see ex::normal() */ -ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const +ex mul::normal(exmap & repl, exmap & rev_lookup, int level) const { if (level == 1) - return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); @@ -1921,12 +1918,12 @@ ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const ex n; epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - n = ex_to(recombine_pair_to_ex(*it)).normal(sym_lst, repl_lst, level-1); + n = ex_to(recombine_pair_to_ex(*it)).normal(repl, rev_lookup, level-1); num.push_back(n.op(0)); den.push_back(n.op(1)); it++; } - n = ex_to(overall_coeff).normal(sym_lst, repl_lst, level-1); + n = ex_to(overall_coeff).normal(repl, rev_lookup, level-1); num.push_back(n.op(0)); den.push_back(n.op(1)); @@ -1936,20 +1933,20 @@ ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const } -/** Implementation of ex::normal() for powers. It normalizes the basis, +/** Implementation of ex::normal([B) for powers. It normalizes the basis, * distributes integer exponents to numerator and denominator, and replaces * non-integer powers by temporary symbols. * @see ex::normal */ -ex power::normal(lst &sym_lst, lst &repl_lst, int level) const +ex power::normal(exmap & repl, exmap & rev_lookup, int level) const { if (level == 1) - return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(*this, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); // Normalize basis and exponent (exponent gets reassembled) - ex n_basis = ex_to(basis).normal(sym_lst, repl_lst, level-1); - ex n_exponent = ex_to(exponent).normal(sym_lst, repl_lst, level-1); + ex n_basis = ex_to(basis).normal(repl, rev_lookup, level-1); + ex n_exponent = ex_to(exponent).normal(repl, rev_lookup, level-1); n_exponent = n_exponent.op(0) / n_exponent.op(1); if (n_exponent.info(info_flags::integer)) { @@ -1970,32 +1967,32 @@ ex power::normal(lst &sym_lst, lst &repl_lst, int level) const if (n_exponent.info(info_flags::positive)) { // (a/b)^x -> {sym((a/b)^x), 1} - return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); } else if (n_exponent.info(info_flags::negative)) { if (n_basis.op(1).is_equal(_ex1)) { // a^-x -> {1, sym(a^x)} - return (new lst(_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), sym_lst, repl_lst)))->setflag(status_flags::dynallocated); + return (new lst(_ex1, replace_with_symbol(power(n_basis.op(0), -n_exponent), repl, rev_lookup)))->setflag(status_flags::dynallocated); } else { // (a/b)^-x -> {sym((b/a)^x), 1} - return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(power(n_basis.op(1) / n_basis.op(0), -n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); } } } // (a/b)^x -> {sym((a/b)^x, 1} - return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(power(n_basis.op(0) / n_basis.op(1), n_exponent), repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); } /** Implementation of ex::normal() for pseries. It normalizes each coefficient * and replaces the series by a temporary symbol. * @see ex::normal */ -ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const +ex pseries::normal(exmap & repl, exmap & rev_lookup, int level) const { epvector newseq; epvector::const_iterator i = seq.begin(), end = seq.end(); @@ -2006,7 +2003,7 @@ ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const ++i; } ex n = pseries(relational(var,point), newseq); - return (new lst(replace_with_symbol(n, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(n, repl, rev_lookup), _ex1))->setflag(status_flags::dynallocated); } @@ -2024,14 +2021,14 @@ ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const * @return normalized expression */ ex ex::normal(int level) const { - lst sym_lst, repl_lst; + exmap repl, rev_lookup; - ex e = bp->normal(sym_lst, repl_lst, level); + ex e = bp->normal(repl, rev_lookup, level); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols - if (sym_lst.nops() > 0) - e = e.subs(sym_lst, repl_lst); + if (!repl.empty()) + e = e.subs(repl, subs_options::no_pattern); // Convert {numerator, denominator} form back to fraction return e.op(0) / e.op(1); @@ -2045,16 +2042,16 @@ ex ex::normal(int level) const * @return numerator */ ex ex::numer() const { - lst sym_lst, repl_lst; + exmap repl, rev_lookup; - ex e = bp->normal(sym_lst, repl_lst, 0); + ex e = bp->normal(repl, rev_lookup, 0); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols - if (sym_lst.nops() > 0) - return e.op(0).subs(sym_lst, repl_lst); - else + if (repl.empty()) return e.op(0); + else + return e.op(0).subs(repl, subs_options::no_pattern); } /** Get denominator of an expression. If the expression is not of the normal @@ -2065,16 +2062,16 @@ ex ex::numer() const * @return denominator */ ex ex::denom() const { - lst sym_lst, repl_lst; + exmap repl, rev_lookup; - ex e = bp->normal(sym_lst, repl_lst, 0); + ex e = bp->normal(repl, rev_lookup, 0); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols - if (sym_lst.nops() > 0) - return e.op(1).subs(sym_lst, repl_lst); - else + if (repl.empty()) return e.op(1); + else + return e.op(1).subs(repl, subs_options::no_pattern); } /** Get numerator and denominator of an expression. If the expresison is not @@ -2085,16 +2082,16 @@ ex ex::denom() const * @return a list [numerator, denominator] */ ex ex::numer_denom() const { - lst sym_lst, repl_lst; + exmap repl, rev_lookup; - ex e = bp->normal(sym_lst, repl_lst, 0); + ex e = bp->normal(repl, rev_lookup, 0); GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols - if (sym_lst.nops() > 0) - return e.subs(sym_lst, repl_lst); - else + if (repl.empty()) return e; + else + return e.subs(repl, subs_options::no_pattern); } @@ -2106,46 +2103,80 @@ ex ex::numer_denom() const * on non-rational functions by applying to_rational() on the arguments, * calling the desired function and re-substituting the temporary symbols * in the result. To make the last step possible, all temporary symbols and - * their associated expressions are collected in the list specified by the - * repl_lst parameter in the form {symbol == expression}, ready to be passed - * as an argument to ex::subs(). + * their associated expressions are collected in the map specified by the + * repl parameter, ready to be passed as an argument to ex::subs(). * - * @param repl_lst collects a list of all temporary symbols and their replacements + * @param repl collects all temporary symbols and their replacements * @return rationalized expression */ -ex ex::to_rational(lst &repl_lst) const +ex ex::to_rational(exmap & repl) const +{ + return bp->to_rational(repl); +} + +// GiNaC 1.1 compatibility function +ex ex::to_rational(lst & repl_lst) const { - return bp->to_rational(repl_lst); + // Convert lst to exmap + exmap m; + for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) + m.insert(std::make_pair(it->op(0), it->op(1))); + + ex ret = bp->to_rational(m); + + // Convert exmap back to lst + repl_lst.remove_all(); + for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) + repl_lst.append(it->first == it->second); + + return ret; } -ex ex::to_polynomial(lst &repl_lst) const +ex ex::to_polynomial(exmap & repl) const { - return bp->to_polynomial(repl_lst); + return bp->to_polynomial(repl); } +// GiNaC 1.1 compatibility function +ex ex::to_polynomial(lst & repl_lst) const +{ + // Convert lst to exmap + exmap m; + for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) + m.insert(std::make_pair(it->op(0), it->op(1))); + + ex ret = bp->to_polynomial(m); + + // Convert exmap back to lst + repl_lst.remove_all(); + for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) + repl_lst.append(it->first == it->second); + + return ret; +} /** Default implementation of ex::to_rational(). This replaces the object with * a temporary symbol. */ -ex basic::to_rational(lst &repl_lst) const +ex basic::to_rational(exmap & repl) const { - return replace_with_symbol(*this, repl_lst); + return replace_with_symbol(*this, repl); } -ex basic::to_polynomial(lst &repl_lst) const +ex basic::to_polynomial(exmap & repl) const { - return replace_with_symbol(*this, repl_lst); + return replace_with_symbol(*this, repl); } /** Implementation of ex::to_rational() for symbols. This returns the * unmodified symbol. */ -ex symbol::to_rational(lst &repl_lst) const +ex symbol::to_rational(exmap & repl) const { return *this; } /** Implementation of ex::to_polynomial() for symbols. This returns the * unmodified symbol. */ -ex symbol::to_polynomial(lst &repl_lst) const +ex symbol::to_polynomial(exmap & repl) const { return *this; } @@ -2154,17 +2185,17 @@ ex symbol::to_polynomial(lst &repl_lst) const /** Implementation of ex::to_rational() for a numeric. It splits complex * numbers into re+I*im and replaces I and non-rational real numbers with a * temporary symbol. */ -ex numeric::to_rational(lst &repl_lst) const +ex numeric::to_rational(exmap & repl) const { if (is_real()) { if (!is_rational()) - return replace_with_symbol(*this, repl_lst); + return replace_with_symbol(*this, repl); } else { // complex numeric re = real(); numeric im = imag(); - ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl_lst); - ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl_lst); - return re_ex + im_ex * replace_with_symbol(I, repl_lst); + ex re_ex = re.is_rational() ? re : replace_with_symbol(re, repl); + ex im_ex = im.is_rational() ? im : replace_with_symbol(im, repl); + return re_ex + im_ex * replace_with_symbol(I, repl); } return *this; } @@ -2172,17 +2203,17 @@ ex numeric::to_rational(lst &repl_lst) const /** Implementation of ex::to_polynomial() for a numeric. It splits complex * numbers into re+I*im and replaces I and non-integer real numbers with a * temporary symbol. */ -ex numeric::to_polynomial(lst &repl_lst) const +ex numeric::to_polynomial(exmap & repl) const { if (is_real()) { if (!is_integer()) - return replace_with_symbol(*this, repl_lst); + return replace_with_symbol(*this, repl); } else { // complex numeric re = real(); numeric im = imag(); - ex re_ex = re.is_integer() ? re : replace_with_symbol(re, repl_lst); - ex im_ex = im.is_integer() ? im : replace_with_symbol(im, repl_lst); - return re_ex + im_ex * replace_with_symbol(I, repl_lst); + ex re_ex = re.is_integer() ? re : replace_with_symbol(re, repl); + ex im_ex = im.is_integer() ? im : replace_with_symbol(im, repl); + return re_ex + im_ex * replace_with_symbol(I, repl); } return *this; } @@ -2190,36 +2221,36 @@ ex numeric::to_polynomial(lst &repl_lst) const /** Implementation of ex::to_rational() for powers. It replaces non-integer * powers by temporary symbols. */ -ex power::to_rational(lst &repl_lst) const +ex power::to_rational(exmap & repl) const { if (exponent.info(info_flags::integer)) - return power(basis.to_rational(repl_lst), exponent); + return power(basis.to_rational(repl), exponent); else - return replace_with_symbol(*this, repl_lst); + return replace_with_symbol(*this, repl); } /** Implementation of ex::to_polynomial() for powers. It replaces non-posint * powers by temporary symbols. */ -ex power::to_polynomial(lst &repl_lst) const +ex power::to_polynomial(exmap & repl) const { if (exponent.info(info_flags::posint)) - return power(basis.to_rational(repl_lst), exponent); + return power(basis.to_rational(repl), exponent); else - return replace_with_symbol(*this, repl_lst); + return replace_with_symbol(*this, repl); } /** Implementation of ex::to_rational() for expairseqs. */ -ex expairseq::to_rational(lst &repl_lst) const +ex expairseq::to_rational(exmap & repl) const { epvector s; s.reserve(seq.size()); epvector::const_iterator i = seq.begin(), end = seq.end(); while (i != end) { - s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_rational(repl_lst))); + s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_rational(repl))); ++i; } - ex oc = overall_coeff.to_rational(repl_lst); + ex oc = overall_coeff.to_rational(repl); if (oc.info(info_flags::numeric)) return thisexpairseq(s, overall_coeff); else @@ -2228,16 +2259,16 @@ ex expairseq::to_rational(lst &repl_lst) const } /** Implementation of ex::to_polynomial() for expairseqs. */ -ex expairseq::to_polynomial(lst &repl_lst) const +ex expairseq::to_polynomial(exmap & repl) const { epvector s; s.reserve(seq.size()); epvector::const_iterator i = seq.begin(), end = seq.end(); while (i != end) { - s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_polynomial(repl_lst))); + s.push_back(split_ex_to_pair(recombine_pair_to_ex(*i).to_polynomial(repl))); ++i; } - ex oc = overall_coeff.to_polynomial(repl_lst); + ex oc = overall_coeff.to_polynomial(repl); if (oc.info(info_flags::numeric)) return thisexpairseq(s, overall_coeff); else @@ -2249,7 +2280,7 @@ ex expairseq::to_polynomial(lst &repl_lst) const /** Remove the common factor in the terms of a sum 'e' by calculating the GCD, * and multiply it into the expression 'factor' (which needs to be initialized * to 1, unless you're accumulating factors). */ -static ex find_common_factor(const ex & e, ex & factor, lst & repl) +static ex find_common_factor(const ex & e, ex & factor, exmap & repl) { if (is_exactly_a(e)) { @@ -2334,10 +2365,10 @@ ex collect_common_factors(const ex & e) { if (is_exactly_a(e) || is_exactly_a(e)) { - lst repl; + exmap repl; ex factor = 1; ex r = find_common_factor(e, factor, repl); - return factor.subs(repl) * r.subs(repl); + return factor.subs(repl, subs_options::no_pattern) * r.subs(repl, subs_options::no_pattern); } else return e;