From: Christian Bauer Date: Thu, 10 Feb 2000 21:25:38 +0000 (+0000) Subject: - normal() now internally keeps numerator and denominator separated and X-Git-Tag: relase_0-5-1~9 X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=083b0f50275a536be807fa2a34c1e278098e12f5;ds=sidebyside - normal() now internally keeps numerator and denominator separated and doesn't combine them to a fraction until the very end. All implementations of basic::normal() now return a 2-component lst {num, den} instead of a simple expression. - dropped status_flags::normal_form - ex::numer() and ex::denom() didn't work correctly on numerics - lcm(a, b) with a and b being a numeric returned the GCD of a and b (*argh*) --- diff --git a/check/normalization.cpp b/check/normalization.cpp index 4a212988..814c45be 100644 --- a/check/normalization.cpp +++ b/check/normalization.cpp @@ -26,7 +26,7 @@ using namespace GiNaC; #endif // ndef NO_NAMESPACE_GINAC -static symbol x("x"), y("y"), z("z"); +static symbol w("w"), x("x"), y("y"), z("z"); static unsigned check_normal(const ex &e, const ex &d) { @@ -55,21 +55,31 @@ static unsigned normal1(void) result += check_normal(e, d); // Fraction addition - e = numeric(2)/x + y/3; - d = (x*y/3 + 2) / x; + e = 2/x + y/3; + d = (x*y + 6) / (x*3); result += check_normal(e, d); - // Fraction addition e = pow(x, -1) + x/(x+1); d = (pow(x, 2)+x+1)/(x*(x+1)); result += check_normal(e, d); // Fraction cancellation + e = numeric(1)/2 * z * (2*x + 2*y); + d = z * (x + y); + result += check_normal(e, d); + + e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w); + d = z * (x + y) * (x + w); + result += check_normal(e, d); + + e = (3*x + 3*y) * (w/3 + z/3); + d = (x + y) * (w + z); + result += check_normal(e, d); + e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3); d = (x + y) / (pow(x, 2) + pow(y, 2) - x * y * 2); result += check_normal(e, d); - // Fraction cancellation e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2); d = pow(x * 2, -1); result += check_normal(e, d); diff --git a/ginac/basic.h b/ginac/basic.h index 4e9b5171..c54cc381 100644 --- a/ginac/basic.h +++ b/ginac/basic.h @@ -163,9 +163,9 @@ public: const basic & hold(void) const; unsigned gethash(void) const {if (flags & status_flags::hash_calculated) return hashvalue; else return calchash();} unsigned tinfo(void) const {return tinfo_key;} -protected: const basic & setflag(unsigned f) const {flags |= f; return *this;} const basic & clearflag(unsigned f) const {flags &= ~f; return *this;} +protected: void ensure_if_modifiable(void) const; // member variables diff --git a/ginac/container.pl b/ginac/container.pl index 3a7f9bd8..0ef3b896 100755 --- a/ginac/container.pl +++ b/ginac/container.pl @@ -231,6 +231,11 @@ inline const ${CONTAINER} &ex_to_${CONTAINER}(const ex &e) return static_cast(*e.bp); } +inline ${CONTAINER} &ex_to_nonconst_${CONTAINER}(const ex &e) +{ + return static_cast<${CONTAINER} &>(*e.bp); +} + #ifndef NO_NAMESPACE_GINAC } // namespace GiNaC #endif // ndef NO_NAMESPACE_GINAC diff --git a/ginac/ex.cpp b/ginac/ex.cpp index 412f8c95..ec6e9649 100644 --- a/ginac/ex.cpp +++ b/ginac/ex.cpp @@ -238,33 +238,7 @@ void ex::dbgprinttree(void) const bool ex::info(unsigned inf) const { - if (inf == info_flags::normal_form) { - - // Polynomials are in normal form - if (info(info_flags::polynomial)) - return true; - - // polynomial^(-int) is in normal form - if (is_ex_exactly_of_type(*this, power)) - return op(1).info(info_flags::negint); - - // polynomial^(int) * polynomial^(int) * ... is in normal form - if (!is_ex_exactly_of_type(*this, mul)) - return false; - for (unsigned i=0; iinfo(inf); - } + return bp->info(inf); } unsigned ex::nops() const @@ -306,13 +280,17 @@ ex ex::coeff(const symbol & s, int n) const ex ex::numer(bool normalize) const { ex n; - if (normalize && !info(info_flags::normal_form)) + if (normalize) n = normal(); else n = *this; + // number + if (is_ex_exactly_of_type(n, numeric)) + return ex_to_numeric(n).numer(); + // polynomial - if (n.info(info_flags::polynomial)) + if (n.info(info_flags::cinteger_polynomial)) return n; // something^(-int) @@ -324,8 +302,13 @@ ex ex::numer(bool normalize) const return n; ex res = _ex1(); for (unsigned i=0; isetflag(status_flags::dynallocated); } -/** Implementation of ex::normal() for symbols. This returns the unmodifies symbol. +/** 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 { - return *this; + return (new lst(*this, _ex1()))->setflag(status_flags::dynallocated); } @@ -1378,40 +1387,42 @@ ex symbol::normal(lst &sym_lst, lst &repl_lst, int level) const * @see ex::normal */ ex numeric::normal(lst &sym_lst, lst &repl_lst, int level) const { - if (is_real()) - if (is_rational()) - return *this; - else - return replace_with_symbol(*this, sym_lst, repl_lst); - else { // complex - numeric re = real(), im = imag(); + numeric num = numer(); + ex numex = num; + + if (num.is_real()) { + if (!num.is_integer()) + numex = replace_with_symbol(numex, sym_lst, repl_lst); + } 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); - return re_ex + im_ex * replace_with_symbol(I, sym_lst, repl_lst); + numex = re_ex + im_ex * replace_with_symbol(I, sym_lst, repl_lst); } + + // Denominator is always a real integer (see numeric::denom()) + return (new lst(numex, denom()))->setflag(status_flags::dynallocated); } /** Fraction cancellation. * @param n numerator * @param d denominator - * @return cancelled fraction n/d */ + * @return cancelled fraction {n, d} as a list */ static ex frac_cancel(const ex &n, const ex &d) { ex num = n; ex den = d; numeric pre_factor = _num1(); +//clog << "frac_cancel num = " << num << ", den = " << den << endl; + // Handle special cases where numerator or denominator is 0 if (num.is_zero()) - return _ex0(); + return (new lst(_ex0(), _ex1()))->setflag(status_flags::dynallocated); if (den.expand().is_zero()) throw(std::overflow_error("frac_cancel: division by zero in frac_cancel")); - // More special cases - if (is_ex_exactly_of_type(den, numeric)) - return num / den; - // Bring numerator and denominator to Z[X] by multiplying with // LCM of all coefficients' denominators numeric num_lcm = lcm_of_coefficients_denominators(num); @@ -1436,7 +1447,9 @@ static ex frac_cancel(const ex &n, const ex &d) den *= _ex_1(); } } - return pre_factor * num / den; + + // Return result as list + return (new lst(num * pre_factor.numer(), den * pre_factor.denom()))->setflag(status_flags::dynallocated); } @@ -1445,47 +1458,67 @@ static ex frac_cancel(const ex &n, const ex &d) * @see ex::normal */ ex add::normal(lst &sym_lst, lst &repl_lst, int level) const { - // Normalize and expand children + // Normalize and expand children, chop into summands exvector o; o.reserve(seq.size()+1); epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { + + // Normalize and expand child ex n = recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1).expand(); - if (is_ex_exactly_of_type(n, add)) { - epvector::const_iterator bit = (static_cast(n.bp))->seq.begin(), bitend = (static_cast(n.bp))->seq.end(); + + // If numerator is a sum, chop into summands + if (is_ex_exactly_of_type(n.op(0), add)) { + epvector::const_iterator bit = ex_to_add(n.op(0)).seq.begin(), bitend = ex_to_add(n.op(0)).seq.end(); while (bit != bitend) { - o.push_back(recombine_pair_to_ex(*bit)); + o.push_back((new lst(recombine_pair_to_ex(*bit), n.op(1)))->setflag(status_flags::dynallocated)); bit++; } - o.push_back((static_cast(n.bp))->overall_coeff); + + // The overall_coeff is already normalized (== rational), we just + // split it into numerator and denominator + GINAC_ASSERT(ex_to_numeric(ex_to_add(n.op(0)).overall_coeff).is_rational()); + numeric overall = ex_to_numeric(ex_to_add(n.op(0)).overall_coeff); + o.push_back((new lst(overall.numer(), overall.denom()))->setflag(status_flags::dynallocated)); } else o.push_back(n); it++; } o.push_back(overall_coeff.bp->normal(sym_lst, repl_lst, level-1)); + // o is now a vector of {numerator, denominator} lists + // Determine common denominator ex den = _ex1(); exvector::const_iterator ait = o.begin(), aitend = o.end(); while (ait != aitend) { - den = lcm((*ait).denom(false), den, false); + den = lcm(ait->op(1), den, false); ait++; } // Add fractions - if (den.is_equal(_ex1())) - return (new add(o))->setflag(status_flags::dynallocated); - else { + if (den.is_equal(_ex1())) { + + // Common denominator is 1, simply add all numerators + exvector num_seq; + for (ait=o.begin(); ait!=aitend; ait++) { + num_seq.push_back(ait->op(0)); + } + return (new lst((new add(num_seq))->setflag(status_flags::dynallocated), den))->setflag(status_flags::dynallocated); + + } else { + + // Perform fractional addition exvector num_seq; for (ait=o.begin(); ait!=aitend; ait++) { ex q; - if (!divide(den, (*ait).denom(false), q, false)) { + if (!divide(den, ait->op(1), q, false)) { // should not happen throw(std::runtime_error("invalid expression in add::normal, division failed")); } - num_seq.push_back((*ait).numer(false) * q); + num_seq.push_back(ait->op(0) * q); } - ex num = add(num_seq); + ex num = (new add(num_seq))->setflag(status_flags::dynallocated); // Cancel common factors from num/den return frac_cancel(num, den); @@ -1498,17 +1531,23 @@ ex add::normal(lst &sym_lst, lst &repl_lst, int level) const * @see ex::normal() */ ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const { - // Normalize children - exvector o; - o.reserve(seq.size()+1); + // Normalize children, separate into numerator and denominator + ex num = _ex1(); + ex den = _ex1(); + ex n; epvector::const_iterator it = seq.begin(), itend = seq.end(); while (it != itend) { - o.push_back(recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1)); + n = recombine_pair_to_ex(*it).bp->normal(sym_lst, repl_lst, level-1); + num *= n.op(0); + den *= n.op(1); it++; } - o.push_back(overall_coeff.bp->normal(sym_lst, repl_lst, level-1)); - ex n = (new mul(o))->setflag(status_flags::dynallocated); - return frac_cancel(n.numer(false), n.denom(false)); + n = overall_coeff.bp->normal(sym_lst, repl_lst, level-1); + num *= n.op(0); + den *= n.op(1); + + // Perform fraction cancellation + return frac_cancel(num, den); } @@ -1518,16 +1557,18 @@ ex mul::normal(lst &sym_lst, lst &repl_lst, int level) const * @see ex::normal */ ex power::normal(lst &sym_lst, lst &repl_lst, int level) const { - if (exponent.info(info_flags::integer)) { + if (exponent.info(info_flags::posint)) { + // Integer powers are distributed + ex n = basis.bp->normal(sym_lst, repl_lst, level-1); + return (new lst(power(n.op(0), exponent), power(n.op(1), exponent)))->setflag(status_flags::dynallocated); + } else if (exponent.info(info_flags::negint)) { // Integer powers are distributed ex n = basis.bp->normal(sym_lst, repl_lst, level-1); - ex num = n.numer(false); - ex den = n.denom(false); - return power(num, exponent) / power(den, exponent); + return (new lst(power(n.op(1), -exponent), power(n.op(0), -exponent)))->setflag(status_flags::dynallocated); } else { // Non-integer powers are replaced by temporary symbol (after normalizing basis) - ex n = power(basis.bp->normal(sym_lst, repl_lst, level-1), exponent); - return replace_with_symbol(n, sym_lst, repl_lst); + ex n = basis.bp->normal(sym_lst, repl_lst, level-1); + return (new lst(replace_with_symbol(power(n.op(0) / n.op(1), exponent), sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); } } @@ -1545,9 +1586,8 @@ ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const new_seq.push_back(expair(it->rest.normal(), it->coeff)); it++; } - ex n = pseries(var, point, new_seq); - return replace_with_symbol(n, sym_lst, repl_lst); + return (new lst(replace_with_symbol(n, sym_lst, repl_lst), _ex1()))->setflag(status_flags::dynallocated); } @@ -1566,11 +1606,16 @@ ex pseries::normal(lst &sym_lst, lst &repl_lst, int level) const 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)); + + // Re-insert replaced symbols if (sym_lst.nops() > 0) - return e.subs(sym_lst, repl_lst); - else - return e; + e = e.subs(sym_lst, repl_lst); + + // Convert {numerator, denominator} form back to fraction + return e.op(0) / e.op(1); } #ifndef NO_NAMESPACE_GINAC