]> www.ginac.de Git - ginac.git/blobdiff - ginac/ex.cpp
Add support for Texinfo-5.0.
[ginac.git] / ginac / ex.cpp
index d53cb9585b94b22a3d82257a13fdee58e5d33b41..21cb140aa8e0291c531612b571f291a0cde17002 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's light-weight expression handles. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2011 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
  *
  *  You should have received a copy of the GNU General Public License
  *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include <iostream>
-#include <stdexcept>
-
 #include "ex.h"
 #include "add.h"
 #include "mul.h"
 #include "ncmul.h"
 #include "numeric.h"
+#include "matrix.h"
 #include "power.h"
+#include "lst.h"
 #include "relational.h"
-#include "input_lexer.h"
-#include "debugmsg.h"
 #include "utils.h"
 
-#ifndef NO_NAMESPACE_GINAC
-namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
-
-//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
-//////////
-
-// public
-
-#ifndef INLINE_EX_CONSTRUCTORS
-
-ex::ex() : bp(ex0().bp)
-{
-    debugmsg("ex default constructor",LOGLEVEL_CONSTRUCT);
-    GINAC_ASSERT(ex0().bp!=0);
-    GINAC_ASSERT(ex0().bp->flags & status_flags::dynallocated);
-    GINAC_ASSERT(bp!=0);
-    ++bp->refcount;
-}
-
-ex::~ex()
-{
-    debugmsg("ex destructor",LOGLEVEL_DESTRUCT);
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-    if (--bp->refcount == 0) {
-        delete bp;
-    }
-}
-
-ex::ex(const ex & other) : bp(other.bp)
-{
-    debugmsg("ex copy constructor",LOGLEVEL_CONSTRUCT);
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-    ++bp->refcount;
-}
-
-const ex & ex::operator=(const ex & other)
-{
-    debugmsg("ex operator=",LOGLEVEL_ASSIGNMENT);
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-    GINAC_ASSERT(other.bp!=0);
-    GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
-    ++other.bp->refcount;
-    basic * tmpbp=other.bp;
-    if (--bp->refcount==0) {
-            delete bp;
-    }
-    bp=tmpbp;
-    return *this;
-}
+#include <iostream>
+#include <stdexcept>
 
-#endif // ndef INLINE_EX_CONSTRUCTORS
+namespace GiNaC {
 
 //////////
 // other constructors
 //////////
 
-// public
-
-#ifndef INLINE_EX_CONSTRUCTORS
-
-ex::ex(const basic & other)
-{
-    debugmsg("ex constructor from basic",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(other);
-}
-
-ex::ex(int i)
-{
-    debugmsg("ex constructor from int",LOGLEVEL_CONSTRUCT);
-    construct_from_int(i);
-}
-
-ex::ex(unsigned int i)
-{
-    debugmsg("ex constructor from unsigned int",LOGLEVEL_CONSTRUCT);
-    construct_from_uint(i);
-}
-
-ex::ex(long i)
-{
-    debugmsg("ex constructor from long",LOGLEVEL_CONSTRUCT);
-    construct_from_long(i);
-}
-
-ex::ex(unsigned long i)
-{
-    debugmsg("ex constructor from unsigned long",LOGLEVEL_CONSTRUCT);
-    construct_from_ulong(i);
-}
-
-ex::ex(double const d)
-{
-    debugmsg("ex constructor from double",LOGLEVEL_CONSTRUCT);
-    construct_from_double(d);
-}
-
-ex::ex(const string &s, const ex &l)
-{
-    debugmsg("ex constructor from string,lst",LOGLEVEL_CONSTRUCT);
-    construct_from_string_and_lst(s, l);
-}
-
-#endif // ndef INLINE_EX_CONSTRUCTORS
-
-//////////
-// functions overriding virtual functions from bases classes
-//////////
-
-// none
-
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
-
-// none
+// none (all inlined)
 
 //////////
 // non-virtual functions in this class
 //////////
 
 // public
-
-/** Swap the contents of two expressions. */
-void ex::swap(ex & other)
-{
-    debugmsg("ex swap",LOGLEVEL_MEMBER_FUNCTION);
-
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-    GINAC_ASSERT(other.bp!=0);
-    GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
-    
-    basic * tmpbp=bp;
-    bp=other.bp;
-    other.bp=tmpbp;
-}
-
-/** Output formatted to be useful as ginsh input. */
-void ex::print(ostream & os, unsigned upper_precedence) const
-{
-    debugmsg("ex print",LOGLEVEL_PRINT);
-    GINAC_ASSERT(bp!=0);
-    bp->print(os,upper_precedence);
-}
-
-void ex::printraw(ostream & os) const
-{
-    debugmsg("ex printraw",LOGLEVEL_PRINT);
-    GINAC_ASSERT(bp!=0);
-    os << "ex(";
-    bp->printraw(os);
-    os << ")";
-}
-
-void ex::printtree(ostream & os, unsigned indent) const
+       
+/** Print expression to stream. The formatting of the output is determined
+ *  by the kind of print_context object that is passed. Possible formattings
+ *  include ginsh-parsable output (the default), tree-like output for
+ *  debugging, and C++ source.
+ *  @see print_context */
+void ex::print(const print_context & c, unsigned level) const
 {
-    debugmsg("ex printtree",LOGLEVEL_PRINT);
-    GINAC_ASSERT(bp!=0);
-    // os << "refcount=" << bp->refcount << " ";
-    bp->printtree(os,indent);
-}
-
-/** Print expression as a C++ statement. The output looks like
- *  "<type> <var_name> = <expression>;". The "type" parameter has an effect
- *  on how number literals are printed.
- *
- *  @param os output stream
- *  @param type variable type (one of the csrc_types)
- *  @param var_name variable name to be printed */
-void ex::printcsrc(ostream & os, unsigned type, const char *var_name) const
-{
-    debugmsg("ex print csrc", LOGLEVEL_PRINT);
-    GINAC_ASSERT(bp!=0);
-    switch (type) {
-        case csrc_types::ctype_float:
-            os << "float ";
-            break;
-        case csrc_types::ctype_double:
-            os << "double ";
-            break;
-        case csrc_types::ctype_cl_N:
-            os << "cl_N ";
-            break;
-    }
-    os << var_name << " = ";
-    bp->printcsrc(os, type, 0);
-    os << ";\n";
+       bp->print(c, level);
 }
 
 /** Little wrapper arount print to be called within a debugger. */
-void ex::dbgprint(void) const
+void ex::dbgprint() const
 {
-    debugmsg("ex dbgprint",LOGLEVEL_PRINT);
-    GINAC_ASSERT(bp!=0);
-    bp->dbgprint();
+       bp->dbgprint();
 }
 
 /** Little wrapper arount printtree to be called within a debugger. */
-void ex::dbgprinttree(void) const
+void ex::dbgprinttree() const
 {
-    debugmsg("ex dbgprinttree",LOGLEVEL_PRINT);
-    GINAC_ASSERT(bp!=0);
-    bp->dbgprinttree();
-}
-
-bool ex::info(unsigned inf) const
-{
-    return bp->info(inf);
-}
-
-unsigned ex::nops() const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->nops();
+       bp->dbgprinttree();
 }
 
 ex ex::expand(unsigned options) const
 {
-    GINAC_ASSERT(bp!=0);
-    if (bp->flags & status_flags::expanded)
-        return *bp;
-    else
-        return bp->expand(options);
+       if (options == 0 && (bp->flags & status_flags::expanded)) // The "expanded" flag only covers the standard options; someone might want to re-expand with different options
+               return *this;
+       else
+               return bp->expand(options);
 }
 
-bool ex::has(const ex & other) const
+/** Compute partial derivative of an expression.
+ *
+ *  @param s  symbol by which the expression is derived
+ *  @param nth  order of derivative (default 1)
+ *  @return partial derivative as a new expression */
+ex ex::diff(const symbol & s, unsigned nth) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->has(other);
+       if (!nth)
+               return *this;
+       else
+               return bp->diff(s, nth);
 }
 
-int ex::degree(const symbol & s) const
+/** Check whether expression matches a specified pattern. */
+bool ex::match(const ex & pattern) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->degree(s);
+       exmap repl_lst;
+       return bp->match(pattern, repl_lst);
 }
 
-int ex::ldegree(const symbol & s) const
+/** Find all occurrences of a pattern. The found matches are appended to
+ *  the "found" list. If the expression itself matches the pattern, the
+ *  children are not further examined. This function returns true when any
+ *  matches were found. */
+bool ex::find(const ex & pattern, exset& found) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->ldegree(s);
+       if (match(pattern)) {
+               found.insert(*this);
+               return true;
+       }
+       bool any_found = false;
+       for (size_t i=0; i<nops(); i++)
+               if (op(i).find(pattern, found))
+                       any_found = true;
+       return any_found;
 }
 
-ex ex::coeff(const symbol & s, int n) const
+/** Substitute objects in an expression (syntactic substitution) and return
+ *  the result as a new expression. */
+ex ex::subs(const lst & ls, const lst & lr, unsigned options) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->coeff(s,n);
-}
+       GINAC_ASSERT(ls.nops() == lr.nops());
 
-ex ex::collect(const symbol & s) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->collect(s);
-}
+       // Convert the lists to a map
+       exmap m;
+       for (lst::const_iterator its = ls.begin(), itr = lr.begin(); its != ls.end(); ++its, ++itr) {
+               m.insert(std::make_pair(*its, *itr));
 
-ex ex::eval(int level) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->eval(level);
-}
+               // Search for products and powers in the expressions to be substituted
+               // (for an optimization in expairseq::subs())
+               if (is_exactly_a<mul>(*its) || is_exactly_a<power>(*its))
+                       options |= subs_options::pattern_is_product;
+       }
+       if (!(options & subs_options::pattern_is_product))
+               options |= subs_options::pattern_is_not_product;
 
-ex ex::evalf(int level) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->evalf(level);
+       return bp->subs(m, options);
 }
 
-/** Compute partial derivative of an expression.
- *
- *  @param s  symbol by which the expression is derived
- *  @param nth  order of derivative (default 1)
- *  @return partial derivative as a new expression */
-ex ex::diff(const symbol & s, unsigned nth) const
+/** Substitute objects in an expression (syntactic substitution) and return
+ *  the result as a new expression.  There are two valid types of
+ *  replacement arguments: 1) a relational like object==ex and 2) a list of
+ *  relationals lst(object1==ex1,object2==ex2,...). */
+ex ex::subs(const ex & e, unsigned options) const
 {
-    GINAC_ASSERT(bp!=0);
+       if (e.info(info_flags::relation_equal)) {
 
-    if (!nth)
-        return *this;
-    else
-        return bp->diff(s, nth);
-}
+               // Argument is a relation: convert it to a map
+               exmap m;
+               const ex & s = e.op(0);
+               m.insert(std::make_pair(s, e.op(1)));
 
-ex ex::subs(const lst & ls, const lst & lr) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->subs(ls,lr);
-}
+               if (is_exactly_a<mul>(s) || is_exactly_a<power>(s))
+                       options |= subs_options::pattern_is_product;
+               else
+                       options |= subs_options::pattern_is_not_product;
 
-ex ex::subs(const ex & e) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->subs(e);
-}
+               return bp->subs(m, options);
 
-exvector ex::get_indices(void) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->get_indices();
-}
+       } else if (e.info(info_flags::list)) {
 
-ex ex::simplify_ncmul(const exvector & v) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->simplify_ncmul(v);
-}
+               // Argument is a list: convert it to a map
+               exmap m;
+               GINAC_ASSERT(is_a<lst>(e));
+               for (lst::const_iterator it = ex_to<lst>(e).begin(); it != ex_to<lst>(e).end(); ++it) {
+                       ex r = *it;
+                       if (!r.info(info_flags::relation_equal))
+                               throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
+                       const ex & s = r.op(0);
+                       m.insert(std::make_pair(s, r.op(1)));
 
-ex ex::operator[](const ex & index) const
-{
-    debugmsg("ex operator[ex]",LOGLEVEL_OPERATOR);
-    GINAC_ASSERT(bp!=0);
-    return (*bp)[index];
-}
+                       // Search for products and powers in the expressions to be substituted
+                       // (for an optimization in expairseq::subs())
+                       if (is_exactly_a<mul>(s) || is_exactly_a<power>(s))
+                               options |= subs_options::pattern_is_product;
+               }
+               if (!(options & subs_options::pattern_is_product))
+                       options |= subs_options::pattern_is_not_product;
 
-ex ex::operator[](int i) const
-{
-    debugmsg("ex operator[int]",LOGLEVEL_OPERATOR);
-    GINAC_ASSERT(bp!=0);
-    return (*bp)[i];
-}
+               return bp->subs(m, options);
 
-/** Return operand/member at position i. */
-ex ex::op(int i) const
-{
-    debugmsg("ex op()",LOGLEVEL_MEMBER_FUNCTION);
-    GINAC_ASSERT(bp!=0);
-    return bp->op(i);
+       } else
+               throw(std::invalid_argument("ex::subs(ex): argument must be a relation_equal or a list"));
 }
 
-/** Return modifyable operand/member at position i. */
-ex & ex::let_op(int i)
+/** Traverse expression tree with given visitor, preorder traversal. */
+void ex::traverse_preorder(visitor & v) const
 {
-    debugmsg("ex let_op()",LOGLEVEL_MEMBER_FUNCTION);
-    makewriteable();
-    GINAC_ASSERT(bp!=0);
-    return bp->let_op(i);
-}
+       accept(v);
 
-/** Left hand side of relational expression. */
-ex ex::lhs(void) const
-{
-    debugmsg("ex lhs()",LOGLEVEL_MEMBER_FUNCTION);
-    GINAC_ASSERT(is_ex_of_type(*this,relational));
-    return (*static_cast<relational *>(bp)).lhs();
+       size_t n = nops();
+       for (size_t i = 0; i < n; ++i)
+               op(i).traverse_preorder(v);
 }
 
-/** Right hand side of relational expression. */
-ex ex::rhs(void) const
+/** Traverse expression tree with given visitor, postorder traversal. */
+void ex::traverse_postorder(visitor & v) const
 {
-    debugmsg("ex rhs()",LOGLEVEL_MEMBER_FUNCTION);
-    GINAC_ASSERT(is_ex_of_type(*this,relational));
-    return (*static_cast<relational *>(bp)).rhs();
-}
+       size_t n = nops();
+       for (size_t i = 0; i < n; ++i)
+               op(i).traverse_postorder(v);
 
-#ifndef INLINE_EX_CONSTRUCTORS
-int ex::compare(const ex & other) const
-{
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(other.bp!=0);
-    if (bp==other.bp) {
-        // special case: both expression point to same basic, trivially equal
-        return 0; 
-    }
-    return bp->compare(*other.bp);
+       accept(v);
 }
-#endif // ndef INLINE_EX_CONSTRUCTORS
 
-#ifndef INLINE_EX_CONSTRUCTORS
-bool ex::is_equal(const ex & other) const
+/** Return modifyable operand/member at position i. */
+ex & ex::let_op(size_t i)
 {
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(other.bp!=0);
-    if (bp==other.bp) {
-        // special case: both expression point to same basic, trivially equal
-        return true; 
-    }
-    return bp->is_equal(*other.bp);
+       makewriteable();
+       return bp->let_op(i);
 }
-#endif // ndef INLINE_EX_CONSTRUCTORS
 
-unsigned ex::return_type(void) const
+ex & ex::operator[](const ex & index)
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->return_type();
+       makewriteable();
+       return (*bp)[index];
 }
 
-unsigned ex::return_type_tinfo(void) const
+ex & ex::operator[](size_t i)
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->return_type_tinfo();
+       makewriteable();
+       return (*bp)[i];
 }
 
-unsigned ex::gethash(void) const
+/** Left hand side of relational expression. */
+ex ex::lhs() const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->gethash();
+       if (!is_a<relational>(*this))
+               throw std::runtime_error("ex::lhs(): not a relation");
+       return bp->op(0);
 }
 
-ex ex::exadd(const ex & rh) const
+/** Right hand side of relational expression. */
+ex ex::rhs() const
 {
-    return (new add(*this,rh))->setflag(status_flags::dynallocated);
+       if (!is_a<relational>(*this))
+               throw std::runtime_error("ex::rhs(): not a relation");
+       return bp->op(1);
 }
 
-ex ex::exmul(const ex & rh) const
+/** Check whether expression is a polynomial. */
+bool ex::is_polynomial(const ex & vars) const
 {
-    return (new mul(*this,rh))->setflag(status_flags::dynallocated);
+       if (is_a<lst>(vars)) {
+               const lst & varlst = ex_to<lst>(vars);
+               for (lst::const_iterator i=varlst.begin(); i!=varlst.end(); ++i)
+                       if (!bp->is_polynomial(*i))
+                               return false;
+               return true;
+       }
+       else
+               return bp->is_polynomial(vars);
 }
 
-ex ex::exncmul(const ex & rh) const
+/** Check whether expression is zero or zero matrix. */
+bool ex::is_zero_matrix() const
 {
-    return (new ncmul(*this,rh))->setflag(status_flags::dynallocated);
+       if (is_zero())
+               return  true;
+       else {
+               ex e = evalm();
+               return is_a<matrix>(e) && ex_to<matrix>(e).is_zero_matrix();
+       }
 }
 
 // private
 
+/** Make this ex writable (if more than one ex handle the same basic) by 
+ *  unlinking the object and creating an unshared copy of it. */
 void ex::makewriteable()
 {
-    debugmsg("ex makewriteable",LOGLEVEL_MEMBER_FUNCTION);
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-    if (bp->refcount > 1) {
-        basic * bp2 = bp->duplicate();
-        ++bp2->refcount;
-        bp2->setflag(status_flags::dynallocated);
-        --bp->refcount;
-        bp = bp2;
-    }
-    GINAC_ASSERT(bp->refcount == 1);
+       GINAC_ASSERT(bp->flags & status_flags::dynallocated);
+       bp.makewritable();
+       GINAC_ASSERT(bp->get_refcount() == 1);
+}
+
+/** Share equal objects between expressions.
+ *  @see ex::compare(const ex &) */
+void ex::share(const ex & other) const
+{
+       if ((bp->flags | other.bp->flags) & status_flags::not_shareable)
+               return;
+
+       if (bp->get_refcount() <= other.bp->get_refcount())
+               bp = other.bp;
+       else
+               other.bp = bp;
+}
+
+/** Helper function for the ex-from-basic constructor. This is where GiNaC's
+ *  automatic evaluator and memory management are implemented.
+ *  @see ex::ex(const basic &) */
+ptr<basic> ex::construct_from_basic(const basic & other)
+{
+       if (!(other.flags & status_flags::evaluated)) {
+
+               // The object is not yet evaluated, so call eval() to evaluate
+               // the top level. This will return either
+               //  a) the original object with status_flags::evaluated set (when the
+               //     eval() implementation calls hold())
+               // or
+               //  b) a different expression.
+               //
+               // eval() returns an ex, not a basic&, so this will go through
+               // construct_from_basic() a second time. In case a) we end up in
+               // the "else" branch below. In case b) we end up here again and
+               // apply eval() once more. The recursion stops when eval() calls
+               // hold() or returns an object that already has its "evaluated"
+               // flag set, such as a symbol or a numeric.
+               const ex & tmpex = other.eval(1);
+
+               // Eventually, the eval() recursion goes through the "else" branch
+               // below, which assures that the object pointed to by tmpex.bp is
+               // allocated on the heap (either it was already on the heap or it
+               // is a heap-allocated duplicate of another object).
+               GINAC_ASSERT(tmpex.bp->flags & status_flags::dynallocated); 
+
+               // If the original object is not referenced but heap-allocated,
+               // it means that eval() hit case b) above. The original object is
+               // no longer needed (it evaluated into something different), so we
+               // delete it (because nobody else will).
+               if ((other.get_refcount() == 0) && (other.flags & status_flags::dynallocated))
+                       delete &other; // yes, you can apply delete to a const pointer
+
+               // We can't return a basic& here because the tmpex is destroyed as
+               // soon as we leave the function, which would deallocate the
+               // evaluated object.
+               return tmpex.bp;
+
+       } else {
+
+               // The easy case: making an "ex" out of an evaluated object.
+               if (other.flags & status_flags::dynallocated) {
+
+                       // The object is already heap-allocated, so we can just make
+                       // another reference to it.
+                       return ptr<basic>(const_cast<basic &>(other));
+
+               } else {
+
+                       // The object is not heap-allocated, so we create a duplicate
+                       // on the heap.
+                       basic *bp = other.duplicate();
+                       bp->setflag(status_flags::dynallocated);
+                       GINAC_ASSERT(bp->get_refcount() == 0);
+                       return bp;
+               }
+       }
+}
+
+basic & ex::construct_from_int(int i)
+{
+       switch (i) {  // prefer flyweights over new objects
+       case -12:
+               return *const_cast<numeric *>(_num_12_p);
+       case -11:
+               return *const_cast<numeric *>(_num_11_p);
+       case -10:
+               return *const_cast<numeric *>(_num_10_p);
+       case -9:
+               return *const_cast<numeric *>(_num_9_p);
+       case -8:
+               return *const_cast<numeric *>(_num_8_p);
+       case -7:
+               return *const_cast<numeric *>(_num_7_p);
+       case -6:
+               return *const_cast<numeric *>(_num_6_p);
+       case -5:
+               return *const_cast<numeric *>(_num_5_p);
+       case -4:
+               return *const_cast<numeric *>(_num_4_p);
+       case -3:
+               return *const_cast<numeric *>(_num_3_p);
+       case -2:
+               return *const_cast<numeric *>(_num_2_p);
+       case -1:
+               return *const_cast<numeric *>(_num_1_p);
+       case 0:
+               return *const_cast<numeric *>(_num0_p);
+       case 1:
+               return *const_cast<numeric *>(_num1_p);
+       case 2:
+               return *const_cast<numeric *>(_num2_p);
+       case 3:
+               return *const_cast<numeric *>(_num3_p);
+       case 4:
+               return *const_cast<numeric *>(_num4_p);
+       case 5:
+               return *const_cast<numeric *>(_num5_p);
+       case 6:
+               return *const_cast<numeric *>(_num6_p);
+       case 7:
+               return *const_cast<numeric *>(_num7_p);
+       case 8:
+               return *const_cast<numeric *>(_num8_p);
+       case 9:
+               return *const_cast<numeric *>(_num9_p);
+       case 10:
+               return *const_cast<numeric *>(_num10_p);
+       case 11:
+               return *const_cast<numeric *>(_num11_p);
+       case 12:
+               return *const_cast<numeric *>(_num12_p);
+       default:
+               basic *bp = new numeric(i);
+               bp->setflag(status_flags::dynallocated);
+               GINAC_ASSERT(bp->get_refcount() == 0);
+               return *bp;
+       }
+}
+       
+basic & ex::construct_from_uint(unsigned int i)
+{
+       switch (i) {  // prefer flyweights over new objects
+       case 0:
+               return *const_cast<numeric *>(_num0_p);
+       case 1:
+               return *const_cast<numeric *>(_num1_p);
+       case 2:
+               return *const_cast<numeric *>(_num2_p);
+       case 3:
+               return *const_cast<numeric *>(_num3_p);
+       case 4:
+               return *const_cast<numeric *>(_num4_p);
+       case 5:
+               return *const_cast<numeric *>(_num5_p);
+       case 6:
+               return *const_cast<numeric *>(_num6_p);
+       case 7:
+               return *const_cast<numeric *>(_num7_p);
+       case 8:
+               return *const_cast<numeric *>(_num8_p);
+       case 9:
+               return *const_cast<numeric *>(_num9_p);
+       case 10:
+               return *const_cast<numeric *>(_num10_p);
+       case 11:
+               return *const_cast<numeric *>(_num11_p);
+       case 12:
+               return *const_cast<numeric *>(_num12_p);
+       default:
+               basic *bp = new numeric(i);
+               bp->setflag(status_flags::dynallocated);
+               GINAC_ASSERT(bp->get_refcount() == 0);
+               return *bp;
+       }
+}
+       
+basic & ex::construct_from_long(long i)
+{
+       switch (i) {  // prefer flyweights over new objects
+       case -12:
+               return *const_cast<numeric *>(_num_12_p);
+       case -11:
+               return *const_cast<numeric *>(_num_11_p);
+       case -10:
+               return *const_cast<numeric *>(_num_10_p);
+       case -9:
+               return *const_cast<numeric *>(_num_9_p);
+       case -8:
+               return *const_cast<numeric *>(_num_8_p);
+       case -7:
+               return *const_cast<numeric *>(_num_7_p);
+       case -6:
+               return *const_cast<numeric *>(_num_6_p);
+       case -5:
+               return *const_cast<numeric *>(_num_5_p);
+       case -4:
+               return *const_cast<numeric *>(_num_4_p);
+       case -3:
+               return *const_cast<numeric *>(_num_3_p);
+       case -2:
+               return *const_cast<numeric *>(_num_2_p);
+       case -1:
+               return *const_cast<numeric *>(_num_1_p);
+       case 0:
+               return *const_cast<numeric *>(_num0_p);
+       case 1:
+               return *const_cast<numeric *>(_num1_p);
+       case 2:
+               return *const_cast<numeric *>(_num2_p);
+       case 3:
+               return *const_cast<numeric *>(_num3_p);
+       case 4:
+               return *const_cast<numeric *>(_num4_p);
+       case 5:
+               return *const_cast<numeric *>(_num5_p);
+       case 6:
+               return *const_cast<numeric *>(_num6_p);
+       case 7:
+               return *const_cast<numeric *>(_num7_p);
+       case 8:
+               return *const_cast<numeric *>(_num8_p);
+       case 9:
+               return *const_cast<numeric *>(_num9_p);
+       case 10:
+               return *const_cast<numeric *>(_num10_p);
+       case 11:
+               return *const_cast<numeric *>(_num11_p);
+       case 12:
+               return *const_cast<numeric *>(_num12_p);
+       default:
+               basic *bp = new numeric(i);
+               bp->setflag(status_flags::dynallocated);
+               GINAC_ASSERT(bp->get_refcount() == 0);
+               return *bp;
+       }
+}
+       
+basic & ex::construct_from_ulong(unsigned long i)
+{
+       switch (i) {  // prefer flyweights over new objects
+       case 0:
+               return *const_cast<numeric *>(_num0_p);
+       case 1:
+               return *const_cast<numeric *>(_num1_p);
+       case 2:
+               return *const_cast<numeric *>(_num2_p);
+       case 3:
+               return *const_cast<numeric *>(_num3_p);
+       case 4:
+               return *const_cast<numeric *>(_num4_p);
+       case 5:
+               return *const_cast<numeric *>(_num5_p);
+       case 6:
+               return *const_cast<numeric *>(_num6_p);
+       case 7:
+               return *const_cast<numeric *>(_num7_p);
+       case 8:
+               return *const_cast<numeric *>(_num8_p);
+       case 9:
+               return *const_cast<numeric *>(_num9_p);
+       case 10:
+               return *const_cast<numeric *>(_num10_p);
+       case 11:
+               return *const_cast<numeric *>(_num11_p);
+       case 12:
+               return *const_cast<numeric *>(_num12_p);
+       default:
+               basic *bp = new numeric(i);
+               bp->setflag(status_flags::dynallocated);
+               GINAC_ASSERT(bp->get_refcount() == 0);
+               return *bp;
+       }
+}
+       
+basic & ex::construct_from_double(double d)
+{
+       basic *bp = new numeric(d);
+       bp->setflag(status_flags::dynallocated);
+       GINAC_ASSERT(bp->get_refcount() == 0);
+       return *bp;
 }
 
-void ex::construct_from_basic(const basic & other)
-{
-    if ((other.flags & status_flags::evaluated)==0) {
-        // cf. copy constructor
-        const ex & tmpex = other.eval(1); // evaluate only one (top) level
-        bp = tmpex.bp;
-        GINAC_ASSERT(bp!=0);
-        GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-        ++bp->refcount;
-        if ((other.flags & status_flags::dynallocated)&&(other.refcount==0)) {
-            delete &const_cast<basic &>(other);
-        }
-    } else {
-        if (other.flags & status_flags::dynallocated) {
-            bp = &const_cast<basic &>(other);
-        } else {
-            bp = other.duplicate();
-            bp->setflag(status_flags::dynallocated);
-        }
-        GINAC_ASSERT(bp!=0);
-        // bp->clearflag(status_flags::evaluated);
-        ++bp->refcount;
-    }
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-}
-
-void ex::construct_from_int(int i)
-{
-    switch (i) {  // some tiny efficiency-hack
-    case -2:
-        bp = _ex_2().bp;
-        ++bp->refcount;
-        break;
-    case -1:
-        bp = _ex_1().bp;
-        ++bp->refcount;
-        break;
-    case 0:
-        bp = _ex0().bp;
-        ++bp->refcount;
-        break;
-    case 1:
-        bp = _ex1().bp;
-        ++bp->refcount;
-        break;
-    case 2:
-        bp = _ex2().bp;
-        ++bp->refcount;
-        break;
-    default:
-        bp = new numeric(i);
-        bp->setflag(status_flags::dynallocated);
-        ++bp->refcount;
-        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-        GINAC_ASSERT(bp->refcount=1);
-    }
-}
-    
-void ex::construct_from_uint(unsigned int i)
-{
-    switch (i) {  // some tiny efficiency-hack
-    case -2:
-        bp = _ex_2().bp;
-        ++bp->refcount;
-        break;
-    case -1:
-        bp = _ex_1().bp;
-        ++bp->refcount;
-        break;
-    case 0:
-        bp = _ex0().bp;
-        ++bp->refcount;
-        break;
-    case 1:
-        bp = _ex1().bp;
-        ++bp->refcount;
-        break;
-    case 2:
-        bp = _ex2().bp;
-        ++bp->refcount;
-        break;
-    default:
-        bp = new numeric(i);
-        bp->setflag(status_flags::dynallocated);
-        ++bp->refcount;
-        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-        GINAC_ASSERT(bp->refcount=1);
-    }
-}
-    
-void ex::construct_from_long(long i)
-{
-    switch (i) {  // some tiny efficiency-hack
-    case -2:
-        bp = _ex_2().bp;
-        ++bp->refcount;
-        break;
-    case -1:
-        bp = _ex_1().bp;
-        ++bp->refcount;
-        break;
-    case 0:
-        bp = _ex0().bp;
-        ++bp->refcount;
-        break;
-    case 1:
-        bp = _ex1().bp;
-        ++bp->refcount;
-        break;
-    case 2:
-        bp = _ex2().bp;
-        ++bp->refcount;
-        break;
-    default:
-        bp = new numeric(i);
-        bp->setflag(status_flags::dynallocated);
-        ++bp->refcount;
-        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-        GINAC_ASSERT(bp->refcount=1);
-    }
-}
-    
-void ex::construct_from_ulong(unsigned long i)
-{
-    switch (i) {  // some tiny efficiency-hack
-    case -2:
-        bp = _ex_2().bp;
-        ++bp->refcount;
-        break;
-    case -1:
-        bp = _ex_1().bp;
-        ++bp->refcount;
-        break;
-    case 0:
-        bp = _ex0().bp;
-        ++bp->refcount;
-        break;
-    case 1:
-        bp = _ex1().bp;
-        ++bp->refcount;
-        break;
-    case 2:
-        bp = _ex2().bp;
-        ++bp->refcount;
-        break;
-    default:
-        bp = new numeric(i);
-        bp->setflag(status_flags::dynallocated);
-        ++bp->refcount;
-        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-        GINAC_ASSERT(bp->refcount=1);
-    }
-}
-    
-void ex::construct_from_double(double d)
-{
-    bp = new numeric(d);
-    bp->setflag(status_flags::dynallocated);
-    ++bp->refcount;
-    GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-    GINAC_ASSERT(bp->refcount=1);
-}
-
-void ex::construct_from_string_and_lst(const string &s, const ex &l)
-{
-    set_lexer_string(s);
-    set_lexer_symbols(l);
-    ginac_yyrestart(NULL);
-    if (ginac_yyparse())
-        throw (std::runtime_error(get_parser_error()));
-    else {
-        bp = parsed_ex.bp;
-        GINAC_ASSERT(bp!=0);
-        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-        ++bp->refcount;
-    }
-}
-    
 //////////
 // static member variables
 //////////
@@ -666,6 +571,4 @@ void ex::construct_from_string_and_lst(const string &s, const ex &l)
 // none
 
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC