- 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 4a212988e3d8def83dd21097236207fe97c9060d..814c45be9cdfc80fa00d50be60a7932701d0288c 100644 (file)
--- 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 4e9b5171e3bf397e57e2b871483d8f28ac409d6b..c54cc3816f49b67ab184b07ac9202d7948ea619d 100644 (file)
--- 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 3a7f9bd81e5d784bd1db33a9d9daf65c1f7606b4..0ef3b896d47908f8c4355b1a86637b75c9120d59 100755 (executable)
--- a/ginac/container.pl
+++ b/ginac/container.pl
@@ -231,6 +231,11 @@ inline const ${CONTAINER} &ex_to_${CONTAINER}(const ex &e)
     return static_cast<const ${CONTAINER} &>(*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 412f8c95509fb3af03367b5a4a9de4d90474e44d..ec6e96494fb40b6ca6828ed21cf1d0c8f252f202 100644 (file)
--- 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; i<nops(); i++) {
-        if (is_ex_exactly_of_type(op(i), power)) {
-            if (!op(i).op(1).info(info_flags::integer))
-                return false;
-            if (!op(i).op(0).info(info_flags::polynomial))
-                return false;
-        } else
-            if (!op(i).info(info_flags::polynomial))
-                return false;
-    }
-    return true;
-    } else {
-        return bp->info(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; i<n.nops(); i++) {
-        if (!is_ex_exactly_of_type(n.op(i), power) || !n.op(i).op(1).info(info_flags::negint))
+               if (is_ex_exactly_of_type(n.op(i), power) && n.op(i).op(1).info(info_flags::negint)) {
+                       // something^(-int) belongs to the denominator
+               } else if (is_ex_exactly_of_type(n.op(i), numeric)) {
+                       res *= ex_to_numeric(n.op(i)).numer();
+               } else {
             res *= n.op(i);
+               }
     }
     return res;
 }
@@ -333,13 +316,17 @@ ex ex::numer(bool normalize) const
 ex ex::denom(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).denom();
+
     // polynomial
-    if (n.info(info_flags::polynomial))
+    if (n.info(info_flags::cinteger_polynomial))
         return _ex1();
 
     // something^(-int)
@@ -351,8 +338,13 @@ ex ex::denom(bool normalize) const
         return _ex1();
     ex res = _ex1();
     for (unsigned i=0; i<n.nops(); i++) {
-        if (is_ex_exactly_of_type(n.op(i), power) && n.op(i).op(1).info(info_flags::negint))
+        if (is_ex_exactly_of_type(n.op(i), power) && n.op(i).op(1).info(info_flags::negint)) {
             res *= power(n.op(i), -1);
+               } else if (is_ex_exactly_of_type(n.op(i), numeric)) {
+                       res *= ex_to_numeric(n.op(i)).denom();
+               } else {
+                       // everything else belongs to the numerator
+               }
     }
     return res;
 }

diff --git a/ginac/flags.h b/ginac/flags.h
index d7e63825b353b0ff40f8b92d564aee3fbb5065aa..0152c01e1931c3ba87fbe31dfc8d1c6762b5822d 100644 (file)
--- a/ginac/flags.h
+++ b/ginac/flags.h
@@ -89,9 +89,6 @@ public:
            crational_polynomial,
            rational_function,
 
-           // answered by class ex
-           normal_form,
-           
            // answered by class indexed
            indexed,      // class can carry indices
            has_indices,  // object has at least one index

diff --git a/ginac/normal.cpp b/ginac/normal.cpp
index 28ea9e6c1ff0d18f573094f58d38e6da00fe80d1..1c2dc823f7911b76fbd60a5d7fd1ebaa0bd87900 100644 (file)
--- a/ginac/normal.cpp
+++ b/ginac/normal.cpp
@@ -1248,7 +1248,7 @@ factored_b:
 ex lcm(const ex &a, const ex &b, bool check_args)
 {
     if (is_ex_exactly_of_type(a, numeric) && is_ex_exactly_of_type(b, numeric))
-        return gcd(ex_to_numeric(a), ex_to_numeric(b));
+        return lcm(ex_to_numeric(a), ex_to_numeric(b));
     if (check_args && !a.info(info_flags::rational_polynomial) || !b.info(info_flags::rational_polynomial))
         throw(std::invalid_argument("lcm: arguments must be polynomials over the rationals"));
     
@@ -1333,9 +1333,18 @@ ex sqrfree(const ex &a, const symbol &x)
  *  Normal form of rational functions
  */
 
-// Create a symbol for replacing the expression "e" (or return a previously
-// assigned symbol). The symbol is appended to sym_list and returned, the
-// expression is appended to repl_list.
+/*
+ *  Note: The internal normal() functions (= basic::normal() and overloaded
+ *  functions) all return lists of the form {numerator, denominator}. This
+ *  is to get around mul::eval()'s automatic expansion of numeric coefficients.
+ *  E.g. (a+b)/3 is automatically converted to a/3+b/3 but we want to keep
+ *  the information that (a+b) is the numerator and 3 is the denominator.
+ */
+
+/** Create a symbol for replacing the expression "e" (or return a previously
+ *  assigned symbol). The symbol is appended to sym_list and returned, the
+ *  expression is appended to repl_list.
+ *  @see ex::normal */
 static ex replace_with_symbol(const ex &e, lst &sym_lst, lst &repl_lst)
 {
     // Expression already in repl_lst? Then return the assigned symbol
@@ -1360,15 +1369,15 @@ static ex replace_with_symbol(const ex &e, lst &sym_lst, lst &repl_lst)
  *  @see ex::normal */
 ex basic::normal(lst &sym_lst, lst &repl_lst, int level) const
 {
-    return replace_with_symbol(*this, sym_lst, repl_lst);
+    return (new lst(replace_with_symbol(*this, sym_lst, repl_lst), _ex1()))->setflag(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<add *>(n.bp))->seq.begin(), bitend = (static_cast<add *>(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<add *>(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