X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnormal.cpp;h=4b490ed0e9824d301cb979fc830433b98aa22019;hp=c948680f6cb5231d4c3b3858a5a1b0500c030e02;hb=274c1632d78ec31575c4b3b328d75ad95a7855aa;hpb=2862087ce55d944c1ac5d37283944b2b37507fd2 diff --git a/ginac/normal.cpp b/ginac/normal.cpp index c948680f..4b490ed0 100644 --- a/ginac/normal.cpp +++ b/ginac/normal.cpp @@ -74,10 +74,10 @@ static int heur_gcd_failed = 0; static struct _stat_print { _stat_print() {} ~_stat_print() { - cout << "gcd() called " << gcd_called << " times\n"; - cout << "sr_gcd() called " << sr_gcd_called << " times\n"; - cout << "heur_gcd() called " << heur_gcd_called << " times\n"; - cout << "heur_gcd() failed " << heur_gcd_failed << " times\n"; + std::cout << "gcd() called " << gcd_called << " times\n"; + std::cout << "sr_gcd() called " << sr_gcd_called << " times\n"; + std::cout << "heur_gcd() called " << heur_gcd_called << " times\n"; + std::cout << "heur_gcd() failed " << heur_gcd_failed << " times\n"; } } stat_print; #endif @@ -231,14 +231,14 @@ static numeric lcmcoeff(const ex &e, const numeric &l) if (e.info(info_flags::rational)) return lcm(ex_to(e).denom(), l); else if (is_ex_exactly_of_type(e, add)) { - numeric c = _num1(); + numeric c = _num1; for (unsigned i=0; irest,numeric)); - GINAC_ASSERT(is_ex_exactly_of_type(it->coeff,numeric)); + GINAC_ASSERT(!is_exactly_a(it->rest)); + GINAC_ASSERT(is_exactly_a(it->coeff)); c = gcd(ex_to(it->coeff), c); it++; } - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); c = gcd(ex_to(overall_coeff),c); return c; } @@ -338,11 +338,11 @@ numeric mul::integer_content(void) const epvector::const_iterator it = seq.begin(); epvector::const_iterator itend = seq.end(); while (it != itend) { - GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric)); + GINAC_ASSERT(!is_exactly_a(recombine_pair_to_ex(*it))); ++it; } #endif // def DO_GINAC_ASSERT - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); return abs(ex_to(overall_coeff)); } @@ -368,7 +368,7 @@ ex quo(const ex &a, const ex &b, const symbol &x, bool check_args) return a / b; #if FAST_COMPARE if (a.is_equal(b)) - return _ex1(); + return _ex1; #endif if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))) throw(std::invalid_argument("quo: arguments must be polynomials over the rationals")); @@ -381,7 +381,7 @@ ex quo(const ex &a, const ex &b, const symbol &x, bool check_args) int rdeg = r.degree(x); ex blcoeff = b.expand().coeff(x, bdeg); bool blcoeff_is_numeric = is_ex_exactly_of_type(blcoeff, numeric); - exvector v; v.reserve(rdeg - bdeg + 1); + exvector v; v.reserve(std::max(rdeg - bdeg + 1, 0)); while (rdeg >= bdeg) { ex term, rcoeff = r.coeff(x, rdeg); if (blcoeff_is_numeric) @@ -416,13 +416,13 @@ ex rem(const ex &a, const ex &b, const symbol &x, bool check_args) throw(std::overflow_error("rem: division by zero")); if (is_ex_exactly_of_type(a, numeric)) { if (is_ex_exactly_of_type(b, numeric)) - return _ex0(); + return _ex0; else return a; } #if FAST_COMPARE if (a.is_equal(b)) - return _ex0(); + return _ex0; #endif if (check_args && (!a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))) throw(std::invalid_argument("rem: arguments must be polynomials over the rationals")); @@ -485,7 +485,7 @@ ex prem(const ex &a, const ex &b, const symbol &x, bool check_args) throw(std::overflow_error("prem: division by zero")); if (is_ex_exactly_of_type(a, numeric)) { if (is_ex_exactly_of_type(b, numeric)) - return _ex0(); + return _ex0; else return b; } @@ -501,18 +501,18 @@ ex prem(const ex &a, const ex &b, const symbol &x, bool check_args) if (bdeg <= rdeg) { blcoeff = eb.coeff(x, bdeg); if (bdeg == 0) - eb = _ex0(); + eb = _ex0; else eb -= blcoeff * power(x, bdeg); } else - blcoeff = _ex1(); + blcoeff = _ex1; int delta = rdeg - bdeg + 1, i = 0; while (rdeg >= bdeg && !r.is_zero()) { ex rlcoeff = r.coeff(x, rdeg); ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand(); if (rdeg == 0) - r = _ex0(); + r = _ex0; else r -= rlcoeff * power(x, rdeg); r = (blcoeff * r).expand() - term; @@ -537,7 +537,7 @@ ex sprem(const ex &a, const ex &b, const symbol &x, bool check_args) throw(std::overflow_error("prem: division by zero")); if (is_ex_exactly_of_type(a, numeric)) { if (is_ex_exactly_of_type(b, numeric)) - return _ex0(); + return _ex0; else return b; } @@ -553,17 +553,17 @@ ex sprem(const ex &a, const ex &b, const symbol &x, bool check_args) if (bdeg <= rdeg) { blcoeff = eb.coeff(x, bdeg); if (bdeg == 0) - eb = _ex0(); + eb = _ex0; else eb -= blcoeff * power(x, bdeg); } else - blcoeff = _ex1(); + blcoeff = _ex1; while (rdeg >= bdeg && !r.is_zero()) { ex rlcoeff = r.coeff(x, rdeg); ex term = (power(x, rdeg - bdeg) * eb * rlcoeff).expand(); if (rdeg == 0) - r = _ex0(); + r = _ex0; else r -= rlcoeff * power(x, rdeg); r = (blcoeff * r).expand() - term; @@ -581,14 +581,15 @@ ex sprem(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 "true" when exact division succeeds (quotient returned in q), - * "false" otherwise */ + * "false" otherwise (q left untouched) */ bool divide(const ex &a, const ex &b, ex &q, bool check_args) { - q = _ex0(); if (b.is_zero()) throw(std::overflow_error("divide: division by zero")); - if (a.is_zero()) + if (a.is_zero()) { + q = _ex0; return true; + } if (is_ex_exactly_of_type(b, numeric)) { q = a / b; return true; @@ -596,7 +597,7 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args) return false; #if FAST_COMPARE if (a.is_equal(b)) { - q = _ex1(); + q = _ex1; return true; } #endif @@ -611,13 +612,15 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args) // Polynomial long division (recursive) ex r = a.expand(); - if (r.is_zero()) + if (r.is_zero()) { + q = _ex0; return true; + } int bdeg = b.degree(*x); int rdeg = r.degree(*x); ex blcoeff = b.expand().coeff(*x, bdeg); bool blcoeff_is_numeric = is_ex_exactly_of_type(blcoeff, numeric); - exvector v; v.reserve(rdeg - bdeg + 1); + exvector v; v.reserve(std::max(rdeg - bdeg + 1, 0)); while (rdeg >= bdeg) { ex term, rcoeff = r.coeff(*x, rdeg); if (blcoeff_is_numeric) @@ -676,10 +679,10 @@ typedef std::map ex2_exbool_remember; * @see get_symbol_stats, heur_gcd */ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_iterator var) { - q = _ex0(); + q = _ex0; if (b.is_zero()) throw(std::overflow_error("divide_in_z: division by zero")); - if (b.is_equal(_ex1())) { + if (b.is_equal(_ex1)) { q = a; return true; } @@ -692,7 +695,7 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite } #if FAST_COMPARE if (a.is_equal(b)) { - q = _ex1(); + q = _ex1; return true; } #endif @@ -723,24 +726,24 @@ static bool divide_in_z(const ex &a, const ex &b, ex &q, sym_desc_vec::const_ite // Compute values at evaluation points 0..adeg vector alpha; alpha.reserve(adeg + 1); exvector u; u.reserve(adeg + 1); - numeric point = _num0(); + numeric point = _num0; ex c; for (i=0; i<=adeg; i++) { ex bs = b.subs(*x == point); while (bs.is_zero()) { - point += _num1(); + point += _num1; bs = b.subs(*x == point); } if (!divide_in_z(a.subs(*x == point), bs, c, var+1)) return false; alpha.push_back(point); u.push_back(c); - point += _num1(); + point += _num1; } // Compute inverses vector rcp; rcp.reserve(adeg + 1); - rcp.push_back(_num0()); + rcp.push_back(_num0); for (k=1; k<=adeg; k++) { numeric product = alpha[k] - alpha[0]; for (i=1; i= bdeg) { ex term, rcoeff = r.coeff(*x, rdeg); if (!divide_in_z(rcoeff, blcoeff, term, var+1)) @@ -819,7 +822,7 @@ ex ex::unit(const symbol &x) const { ex c = expand().lcoeff(x); if (is_ex_exactly_of_type(c, numeric)) - return c < _ex0() ? _ex_1() : _ex1(); + return c < _ex0 ? _ex_1 : _ex1; else { const symbol *y; if (get_first_symbol(c, y)) @@ -840,12 +843,12 @@ ex ex::unit(const symbol &x) const ex ex::content(const symbol &x) const { if (is_zero()) - return _ex0(); + return _ex0; if (is_ex_exactly_of_type(*this, numeric)) return info(info_flags::negative) ? -*this : *this; ex e = expand(); if (e.is_zero()) - return _ex0(); + return _ex0; // First, try the integer content ex c = e.integer_content(); @@ -859,7 +862,7 @@ ex ex::content(const symbol &x) const int ldeg = e.ldegree(x); if (deg == ldeg) return e.lcoeff(x) / e.unit(x); - c = _ex0(); + c = _ex0; for (int i=ldeg; i<=deg; i++) c = gcd(e.coeff(x, i), c, NULL, NULL, false); return c; @@ -876,13 +879,13 @@ ex ex::content(const symbol &x) const ex ex::primpart(const symbol &x) const { if (is_zero()) - return _ex0(); + return _ex0; if (is_ex_exactly_of_type(*this, numeric)) - return _ex1(); + return _ex1; ex c = content(x); if (c.is_zero()) - return _ex0(); + return _ex0; ex u = unit(x); if (is_ex_exactly_of_type(c, numeric)) return *this / (c * u); @@ -901,11 +904,11 @@ ex ex::primpart(const symbol &x) const ex ex::primpart(const symbol &x, const ex &c) const { if (is_zero()) - return _ex0(); + return _ex0; if (c.is_zero()) - return _ex0(); + return _ex0; if (is_ex_exactly_of_type(*this, numeric)) - return _ex1(); + return _ex1; ex u = unit(x); if (is_ex_exactly_of_type(c, numeric)) @@ -1091,7 +1094,7 @@ static ex red_gcd(const ex &a, const ex &b, const symbol *x) d = d.primpart(*x, cont_d); // First element of divisor sequence - ex r, ri = _ex1(); + ex r, ri = _ex1; int delta = cdeg - ddeg; for (;;) { @@ -1165,7 +1168,7 @@ static ex sr_gcd(const ex &a, const ex &b, sym_desc_vec::const_iterator var) //std::clog << " content " << gamma << " removed, continuing with sr_gcd(" << c << "," << d << ")\n"; // First element of subresultant sequence - ex r = _ex0(), ri = _ex1(), psi = _ex1(); + ex r = _ex0, ri = _ex1, psi = _ex1; int delta = cdeg - ddeg; for (;;) { @@ -1216,7 +1219,7 @@ numeric ex::max_coefficient(void) const * @see heur_gcd */ numeric basic::max_coefficient(void) const { - return _num1(); + return _num1; } numeric numeric::max_coefficient(void) const @@ -1228,11 +1231,11 @@ numeric add::max_coefficient(void) const { epvector::const_iterator it = seq.begin(); epvector::const_iterator itend = seq.end(); - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); numeric cur_max = abs(ex_to(overall_coeff)); while (it != itend) { numeric a; - GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric)); + GINAC_ASSERT(!is_exactly_a(it->rest)); a = abs(ex_to(it->coeff)); if (a > cur_max) cur_max = a; @@ -1247,11 +1250,11 @@ numeric mul::max_coefficient(void) const epvector::const_iterator it = seq.begin(); epvector::const_iterator itend = seq.end(); while (it != itend) { - GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric)); + GINAC_ASSERT(!is_exactly_a(recombine_pair_to_ex(*it))); it++; } #endif // def DO_GINAC_ASSERT - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); return abs(ex_to(overall_coeff)); } @@ -1279,13 +1282,13 @@ ex add::smod(const numeric &xi) const epvector::const_iterator it = seq.begin(); epvector::const_iterator itend = seq.end(); while (it != itend) { - GINAC_ASSERT(!is_ex_exactly_of_type(it->rest,numeric)); + GINAC_ASSERT(!is_exactly_a(it->rest)); numeric coeff = GiNaC::smod(ex_to(it->coeff), xi); if (!coeff.is_zero()) newseq.push_back(expair(it->rest, coeff)); it++; } - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); numeric coeff = GiNaC::smod(ex_to(overall_coeff), xi); return (new add(newseq,coeff))->setflag(status_flags::dynallocated); } @@ -1296,12 +1299,12 @@ ex mul::smod(const numeric &xi) const epvector::const_iterator it = seq.begin(); epvector::const_iterator itend = seq.end(); while (it != itend) { - GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*it),numeric)); + GINAC_ASSERT(!is_exactly_a(recombine_pair_to_ex(*it))); it++; } #endif // def DO_GINAC_ASSERT mul * mulcopyp = new mul(*this); - GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric)); + GINAC_ASSERT(is_exactly_a(overall_coeff)); mulcopyp->overall_coeff = GiNaC::smod(ex_to(overall_coeff),xi); mulcopyp->clearflag(status_flags::evaluated); mulcopyp->clearflag(status_flags::hash_calculated); @@ -1377,9 +1380,9 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const numeric mq = q.max_coefficient(); numeric xi; if (mp > mq) - xi = mq * _num2() + _num2(); + xi = mq * _num2 + _num2; else - xi = mp * _num2() + _num2(); + xi = mp * _num2 + _num2; // 6 tries maximum for (int t=0; t<6; t++) { @@ -1467,9 +1470,9 @@ ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args) if (ca || cb) { if (g.is_zero()) { if (ca) - *ca = _ex0(); + *ca = _ex0; if (cb) - *cb = _ex0(); + *cb = _ex0; } else { if (ca) *ca = ex_to(a) / g; @@ -1536,7 +1539,7 @@ factored_b: ex exp_a = a.op(1), exp_b = b.op(1); if (exp_a < exp_b) { if (ca) - *ca = _ex1(); + *ca = _ex1; if (cb) *cb = power(p, exp_b - exp_a); return power(p, exp_a); @@ -1544,7 +1547,7 @@ factored_b: if (ca) *ca = power(p, exp_a - exp_b); if (cb) - *cb = _ex1(); + *cb = _ex1; return power(p, exp_b); } } @@ -1554,7 +1557,7 @@ factored_b: if (ca) *ca = power(p, a.op(1) - 1); if (cb) - *cb = _ex1(); + *cb = _ex1; return p; } } @@ -1563,7 +1566,7 @@ factored_b: if (p.is_equal(a)) { // a = p, b = p^n, gcd = p if (ca) - *ca = _ex1(); + *ca = _ex1; if (cb) *cb = power(p, b.op(1) - 1); return p; @@ -1575,31 +1578,31 @@ factored_b: ex aex = a.expand(), bex = b.expand(); if (aex.is_zero()) { if (ca) - *ca = _ex0(); + *ca = _ex0; if (cb) - *cb = _ex1(); + *cb = _ex1; return b; } if (bex.is_zero()) { if (ca) - *ca = _ex1(); + *ca = _ex1; if (cb) - *cb = _ex0(); + *cb = _ex0; return a; } - if (aex.is_equal(_ex1()) || bex.is_equal(_ex1())) { + if (aex.is_equal(_ex1) || bex.is_equal(_ex1)) { if (ca) *ca = a; if (cb) *cb = b; - return _ex1(); + return _ex1; } #if FAST_COMPARE if (a.is_equal(b)) { if (ca) - *ca = _ex1(); + *ca = _ex1; if (cb) - *cb = _ex1(); + *cb = _ex1; return a; } #endif @@ -1659,7 +1662,7 @@ factored_b: // g = peu_gcd(aex, bex, &x); // g = red_gcd(aex, bex, &x); g = sr_gcd(aex, bex, var); - if (g.is_equal(_ex1())) { + if (g.is_equal(_ex1)) { // Keep cofactors factored if possible if (ca) *ca = a; @@ -1673,7 +1676,7 @@ factored_b: } #if 1 } else { - if (g.is_equal(_ex1())) { + if (g.is_equal(_ex1)) { // Keep cofactors factored if possible if (ca) *ca = a; @@ -1723,7 +1726,7 @@ static exvector sqrfree_yun(const ex &a, const symbol &x) ex w = a; ex z = w.diff(x); ex g = gcd(w, z); - if (g.is_equal(_ex1())) { + if (g.is_equal(_ex1)) { res.push_back(a); return res; } @@ -1742,11 +1745,11 @@ static exvector sqrfree_yun(const ex &a, const symbol &x) * * @param a multivariate polynomial over Q[X] * @param x lst of variables to factor in, may be left empty for autodetection - * @return polynomail a in square-free factored form. */ + * @return polynomial a in square-free factored form. */ ex sqrfree(const ex &a, const lst &l) { - if (is_ex_of_type(a,numeric) || // algorithm does not trap a==0 - is_ex_of_type(a,symbol)) // shortcut + if (is_a(a) || // algorithm does not trap a==0 + is_a(a)) // shortcut return a; // If no lst of variables to factorize in was specified we have to @@ -1755,7 +1758,7 @@ ex sqrfree(const ex &a, const lst &l) lst args; if (l.nops()==0) { sym_desc_vec sdv; - get_symbol_stats(a, _ex0(), sdv); + get_symbol_stats(a, _ex0, sdv); sym_desc_vec::const_iterator it = sdv.begin(), itend = sdv.end(); while (it != itend) { args.append(*it->sym); @@ -1768,11 +1771,11 @@ ex sqrfree(const ex &a, const lst &l) // Find the symbol to factor in at this stage if (!is_ex_of_type(args.op(0), symbol)) throw (std::runtime_error("sqrfree(): invalid factorization variable")); - const symbol x = ex_to(args.op(0)); + const symbol &x = ex_to(args.op(0)); // convert the argument from something in Q[X] to something in Z[X] - numeric lcm = lcm_of_coefficients_denominators(a); - ex tmp = multiply_lcm(a,lcm); + const numeric lcm = lcm_of_coefficients_denominators(a); + const ex tmp = multiply_lcm(a,lcm); // find the factors exvector factors = sqrfree_yun(tmp,x); @@ -1781,25 +1784,31 @@ ex sqrfree(const ex &a, const lst &l) lst newargs = args; newargs.remove_first(); - // recurse down the factors in remaining vars + // recurse down the factors in remaining variables if (newargs.nops()>0) { - exvector::iterator i = factors.begin(), end = factors.end(); - while (i != end) { + exvector::iterator i = factors.begin(); + while (i != factors.end()) { *i = sqrfree(*i, newargs); ++i; } } // Done with recursion, now construct the final result - ex result = _ex1(); + ex result = _ex1; exvector::const_iterator it = factors.begin(), itend = factors.end(); for (int p = 1; it!=itend; ++it, ++p) result *= power(*it, p); - // Yun's algorithm does not account for constant factors. (For - // univariate polynomials it works only in the monic case.) We can - // correct this by inserting what has been lost back into the result: - result = result * quo(tmp, result, x); + // Yun's algorithm does not account for constant factors. (For univariate + // polynomials it works only in the monic case.) We can correct this by + // inserting what has been lost back into the result. For completeness + // we'll also have to recurse down that factor in the remaining variables. + if (newargs.nops()>0) + result *= sqrfree(quo(tmp, result, x), newargs); + else + result *= quo(tmp, result, x); + + // Put in the reational overall factor again and return return result * lcm.inverse(); } @@ -1828,10 +1837,10 @@ ex sqrfree_parfrac(const ex & a, const symbol & x) exvector factor; factor.reserve(num_yun); exvector cofac; cofac.reserve(num_yun); for (unsigned i=0; isetflag(status_flags::dynallocated); + return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _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, sym_lst, repl_lst), _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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); } } } @@ -1961,7 +1970,7 @@ ex basic::normal(lst &sym_lst, lst &repl_lst, int level) const * @see ex::normal */ ex symbol::normal(lst &sym_lst, lst &repl_lst, int level) const { - return (new lst(*this, _ex1()))->setflag(status_flags::dynallocated); + return (new lst(*this, _ex1))->setflag(status_flags::dynallocated); } @@ -1997,17 +2006,17 @@ static ex frac_cancel(const ex &n, const ex &d) { ex num = n; ex den = d; - numeric pre_factor = _num1(); + numeric pre_factor = _num1; //std::clog << "frac_cancel num = " << num << ", den = " << den << std::endl; // Handle trivial case where denominator is 1 - if (den.is_equal(_ex1())) + if (den.is_equal(_ex1)) return (new lst(num, den))->setflag(status_flags::dynallocated); // Handle special cases where numerator or denominator is 0 if (num.is_zero()) - return (new lst(num, _ex1()))->setflag(status_flags::dynallocated); + return (new lst(num, _ex1))->setflag(status_flags::dynallocated); if (den.expand().is_zero()) throw(std::overflow_error("frac_cancel: division by zero in frac_cancel")); @@ -2021,7 +2030,7 @@ static ex frac_cancel(const ex &n, const ex &d) // Cancel GCD from numerator and denominator ex cnum, cden; - if (gcd(num, den, &cnum, &cden, false) != _ex1()) { + if (gcd(num, den, &cnum, &cden, false) != _ex1) { num = cnum; den = cden; } @@ -2030,10 +2039,10 @@ static ex frac_cancel(const ex &n, const ex &d) // as defined by get_first_symbol() is made positive) const symbol *x; if (get_first_symbol(den, x)) { - GINAC_ASSERT(is_ex_exactly_of_type(den.unit(*x),numeric)); + GINAC_ASSERT(is_exactly_a(den.unit(*x))); if (ex_to(den.unit(*x)).is_negative()) { - num *= _ex_1(); - den *= _ex_1(); + num *= _ex_1; + den *= _ex_1; } } @@ -2049,7 +2058,7 @@ static ex frac_cancel(const ex &n, const ex &d) ex add::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); @@ -2108,7 +2117,7 @@ ex add::normal(lst &sym_lst, lst &repl_lst, int level) const ex mul::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); @@ -2140,7 +2149,7 @@ ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const ex power::normal(lst &sym_lst, lst &repl_lst, 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); else if (level == -max_recursion_level) throw(std::runtime_error("max recursion level reached")); @@ -2167,25 +2176,25 @@ 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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); } else if (n_exponent.info(info_flags::negative)) { - if (n_basis.op(1).is_equal(_ex1())) { + 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), sym_lst, repl_lst)))->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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); } } else { // n_exponent not numeric // (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), sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); } } } @@ -2205,7 +2214,7 @@ 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, sym_lst, repl_lst), _ex1))->setflag(status_flags::dynallocated); } @@ -2226,7 +2235,7 @@ ex ex::normal(int level) const lst sym_lst, repl_lst; ex e = bp->normal(sym_lst, repl_lst, level); - GINAC_ASSERT(is_ex_of_type(e, lst)); + GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (sym_lst.nops() > 0) @@ -2247,7 +2256,7 @@ ex ex::numer(void) const lst sym_lst, repl_lst; ex e = bp->normal(sym_lst, repl_lst, 0); - GINAC_ASSERT(is_ex_of_type(e, lst)); + GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (sym_lst.nops() > 0) @@ -2267,7 +2276,7 @@ ex ex::denom(void) const lst sym_lst, repl_lst; ex e = bp->normal(sym_lst, repl_lst, 0); - GINAC_ASSERT(is_ex_of_type(e, lst)); + GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (sym_lst.nops() > 0) @@ -2287,7 +2296,7 @@ ex ex::numer_denom(void) const lst sym_lst, repl_lst; ex e = bp->normal(sym_lst, repl_lst, 0); - GINAC_ASSERT(is_ex_of_type(e, lst)); + GINAC_ASSERT(is_a(e)); // Re-insert replaced symbols if (sym_lst.nops() > 0) @@ -2369,7 +2378,7 @@ ex expairseq::to_rational(lst &repl_lst) const if (oc.info(info_flags::numeric)) return thisexpairseq(s, overall_coeff); else - s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1())); + s.push_back(combine_ex_with_coeff_to_pair(oc, _ex1)); return thisexpairseq(s, default_overall_coeff()); }