]> www.ginac.de Git - ginac.git/blobdiff - ginac/ex.cpp
inlined ex::swap() and provided versions of iter_swap() for ex and expair
[ginac.git] / ginac / ex.cpp
index a8b7b2f2808b2bcef7f7f4668f537e783c5a610d..c41abee74b5131ea157c9b0b27d842016caddd5c 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's light-weight expression handles. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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
@@ -21,6 +21,7 @@
  */
 
 #include <iostream>
+#include <stdexcept>
 
 #include "ex.h"
 #include "add.h"
 #include "ncmul.h"
 #include "numeric.h"
 #include "power.h"
-#include "debugmsg.h"
+#include "lst.h"
+#include "relational.h"
+#include "input_lexer.h"
+#include "utils.h"
 
-#ifndef NO_GINAC_NAMESPACE
 namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// other ctors
 //////////
 
-// public
-
-#ifndef INLINE_EX_CONSTRUCTORS
-
-ex::ex() : bp(exZERO().bp)
-{
-    debugmsg("ex default constructor",LOGLEVEL_CONSTRUCT);
-    GINAC_ASSERT(exZERO().bp!=0);
-    GINAC_ASSERT(exZERO().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(ex const & other) : bp(other.bp)
-{
-    debugmsg("ex copy constructor",LOGLEVEL_CONSTRUCT);
-    GINAC_ASSERT(bp!=0);
-    GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-    ++bp->refcount;
-}
-
-ex const & ex::operator=(ex const & 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;
-}
-
-#endif // ndef INLINE_EX_CONSTRUCTORS
-
-//////////
-// other constructors
-//////////
-
-// public
-
-#ifndef INLINE_EX_CONSTRUCTORS
-ex::ex(basic const & other)
-{
-    debugmsg("ex constructor from basic",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(other);
-}
-#endif
-
-ex::ex(int const i)
-{
-    debugmsg("ex constructor from int",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(numeric(i));
-}
-
-ex::ex(unsigned int const i)
-{
-    debugmsg("ex constructor from unsigned int",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(numeric(i));
-}
-
-ex::ex(long const i)
-{
-    debugmsg("ex constructor from long",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(numeric(i));
-}
-
-ex::ex(unsigned long const i)
-{
-    debugmsg("ex constructor from unsigned long",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(numeric(i));
-}
-
-ex::ex(double const d)
-{
-    debugmsg("ex constructor from double",LOGLEVEL_CONSTRUCT);
-    construct_from_basic(numeric(d));
-}
-    
-//////////
-// 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
-
-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;
-}
-
-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 (int 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);
-    }
-}
-
-int ex::nops() const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->nops();
-}
-
-ex ex::expand(unsigned options) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->expand(options);
-}
-
-bool ex::has(ex const & other) 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
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->has(other);
+       GINAC_ASSERT(bp!=0);
+       bp->print(c, level);
 }
 
-int ex::degree(symbol const & s) const
+/** Print expression to stream in a tree-like format suitable for debugging. */
+void ex::printtree(std::ostream & os) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->degree(s);
+       GINAC_ASSERT(bp!=0);
+       bp->print(print_tree(os));
 }
 
-int ex::ldegree(symbol const & s) const
+/** Little wrapper arount print to be called within a debugger. */
+void ex::dbgprint(void) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->ldegree(s);
+       GINAC_ASSERT(bp!=0);
+       bp->dbgprint();
 }
 
-ex ex::coeff(symbol const & s, int const n) const
+/** Little wrapper arount printtree to be called within a debugger. */
+void ex::dbgprinttree(void) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->coeff(s,n);
+       GINAC_ASSERT(bp!=0);
+       bp->dbgprinttree();
 }
 
-ex ex::numer(bool normalize) const
-{
-    ex n;
-    if (normalize && !info(info_flags::normal_form))
-        n = normal();
-    else
-        n = *this;
-
-    // polynomial
-    if (n.info(info_flags::polynomial))
-        return n;
-
-    // something^(-int)
-    if (is_ex_exactly_of_type(n, power) && n.op(1).info(info_flags::negint))
-        return exONE();
-
-    // something^(int) * something^(int) * ...
-    if (!is_ex_exactly_of_type(n, mul))
-        return n;
-    ex res = exONE();
-    for (int 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))
-            res *= n.op(i);
-    }
-    return res;
-}
-
-ex ex::denom(bool normalize) const
-{
-    ex n;
-    if (normalize && !info(info_flags::normal_form))
-        n = normal();
-    else
-        n = *this;
-
-    // polynomial
-    if (n.info(info_flags::polynomial))
-        return exONE();
-
-    // something^(-int)
-    if (is_ex_exactly_of_type(n, power) && n.op(1).info(info_flags::negint))
-        return power(n.op(0), -(n.op(1)));
-
-    // something^(int) * something^(int) * ...
-    if (!is_ex_exactly_of_type(n, mul))
-        return exONE();
-    ex res = exONE();
-    for (int 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))
-            res *= power(n.op(i), -1);
-    }
-    return res;
-}
-
-ex ex::collect(symbol const & s) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->collect(s);
-}
-
-ex ex::eval(int level) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->eval(level);
-}
-
-ex ex::evalf(int level) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->evalf(level);
-}
-
-ex ex::subs(lst const & ls, lst const & lr) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->subs(ls,lr);
-}
-
-ex ex::subs(ex const & e) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->subs(e);
-}
-
-exvector ex::get_indices(void) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->get_indices();
-}
-
-ex ex::simplify_ncmul(exvector const & v) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->simplify_ncmul(v);
-}
-
-ex ex::operator[](ex const & index) const
-{
-    debugmsg("ex operator[ex]",LOGLEVEL_OPERATOR);
-    GINAC_ASSERT(bp!=0);
-    return (*bp)[index];
-}
-
-ex ex::operator[](int const i) const
-{
-    debugmsg("ex operator[int]",LOGLEVEL_OPERATOR);
-    GINAC_ASSERT(bp!=0);
-    return (*bp)[i];
-}
-
-ex ex::op(int const i) const
+ex ex::expand(unsigned options) const
 {
-    debugmsg("ex op()",LOGLEVEL_MEMBER_FUNCTION);
-    GINAC_ASSERT(bp!=0);
-    return bp->op(i);
+       GINAC_ASSERT(bp!=0);
+       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 *bp;
+       else
+               return bp->expand(options);
 }
 
-ex & ex::let_op(int const i)
+/** 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
 {
-    debugmsg("ex let_op()",LOGLEVEL_MEMBER_FUNCTION);
-    makewriteable();
-    GINAC_ASSERT(bp!=0);
-    return bp->let_op(i);
-}
+       GINAC_ASSERT(bp!=0);
 
-#ifndef INLINE_EX_CONSTRUCTORS
-int ex::compare(ex const & 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);
+       if (!nth)
+               return *this;
+       else
+               return bp->diff(s, nth);
 }
-#endif // ndef INLINE_EX_CONSTRUCTORS
 
-#ifndef INLINE_EX_CONSTRUCTORS
-bool ex::is_equal(ex const & other) const
+/** Check whether expression matches a specified pattern. */
+bool ex::match(const ex & pattern) 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 true; 
-    }
-    return bp->is_equal(*other.bp);
+       lst repl_lst;
+       return bp->match(pattern, repl_lst);
 }
-#endif // ndef INLINE_EX_CONSTRUCTORS
 
-unsigned ex::return_type(void) 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, lst & found) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->return_type();
+       if (match(pattern)) {
+               found.append(*this);
+               found.sort();
+               found.unique();
+               return true;
+       }
+       bool any_found = false;
+       for (unsigned i=0; i<nops(); i++)
+               if (op(i).find(pattern, found))
+                       any_found = true;
+       return any_found;
 }
 
-unsigned ex::return_type_tinfo(void) const
+ex ex::operator[](const ex & index) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->return_type_tinfo();
+       GINAC_ASSERT(bp!=0);
+       return (*bp)[index];
 }
 
-unsigned ex::gethash(void) const
+ex ex::operator[](int i) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->gethash();
+       GINAC_ASSERT(bp!=0);
+       return (*bp)[i];
 }
 
-ex ex::exadd(ex const & rh) const
+/** Return modifyable operand/member at position i. */
+ex & ex::let_op(int i)
 {
-    return (new add(*this,rh))->setflag(status_flags::dynallocated);
+       makewriteable();
+       GINAC_ASSERT(bp!=0);
+       return bp->let_op(i);
 }
 
-ex ex::exmul(ex const & rh) const
+/** Left hand side of relational expression. */
+ex ex::lhs(void) const
 {
-    return (new mul(*this,rh))->setflag(status_flags::dynallocated);
+       if (!is_ex_of_type(*this,relational))
+               throw std::runtime_error("ex::lhs(): not a relation");
+       return (*static_cast<relational *>(bp)).lhs();
 }
 
-ex ex::exncmul(ex const & rh) const
+/** Right hand side of relational expression. */
+ex ex::rhs(void) const
 {
-    return (new ncmul(*this,rh))->setflag(status_flags::dynallocated);
+       if (!is_ex_of_type(*this,relational))
+               throw std::runtime_error("ex::rhs(): not a relation");
+       return (*static_cast<relational *>(bp)).rhs();
 }
 
 // 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);
-}    
-
-void ex::construct_from_basic(basic const & other)
-{
-    if ( (other.flags & status_flags::evaluated)==0 ) {
-        // cf. copy constructor
-        ex const & 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);
-}
-
+       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);
+}
+
+/** Ctor from basic implementation.
+ *  @see ex::ex(const basic &) */
+void ex::construct_from_basic(const basic & other)
+{
+       if (!(other.flags & status_flags::evaluated)) {
+               const ex & tmpex = other.eval(1); // evaluate only one (top) level
+               bp = tmpex.bp;
+               GINAC_ASSERT(bp->flags & status_flags::dynallocated);
+               ++bp->refcount;
+               if ((other.refcount==0) && (other.flags & status_flags::dynallocated))
+                       delete &const_cast<basic &>(other);
+       } else {
+               if (other.flags & status_flags::dynallocated) {
+                       // ok, it is already on the heap, so just copy bp:
+                       bp = &const_cast<basic &>(other);
+               } else {
+                       // create a duplicate on the heap:
+                       bp = other.duplicate();
+                       bp->setflag(status_flags::dynallocated);
+               }
+               GINAC_ASSERT(bp!=0);
+               ++bp->refcount;
+       }
+       GINAC_ASSERT(bp!=0);
+       GINAC_ASSERT(bp->flags & status_flags::dynallocated);
+}
+
+void ex::construct_from_int(int i)
+{
+       switch (i) {  // prefer flyweights over new objects
+       case -12:
+               bp = (basic*)_num_12_p;
+               ++bp->refcount;
+               break;
+       case -11:
+               bp = (basic*)_num_11_p;
+               ++bp->refcount;
+               break;
+       case -10:
+               bp = (basic*)_num_10_p;
+               ++bp->refcount;
+               break;
+       case -9:
+               bp = (basic*)_num_9_p;
+               ++bp->refcount;
+               break;
+       case -8:
+               bp = (basic*)_num_8_p;
+               ++bp->refcount;
+               break;
+       case -7:
+               bp = (basic*)_num_7_p;
+               ++bp->refcount;
+               break;
+       case -6:
+               bp = (basic*)_num_6_p;
+               ++bp->refcount;
+               break;
+       case -5:
+               bp = (basic*)_num_5_p;
+               ++bp->refcount;
+               break;
+       case -4:
+               bp = (basic*)_num_4_p;
+               ++bp->refcount;
+               break;
+       case -3:
+               bp = (basic*)_num_3_p;
+               ++bp->refcount;
+               break;
+       case -2:
+               bp = (basic*)_num_2_p;
+               ++bp->refcount;
+               break;
+       case -1:
+               bp = (basic*)_num_1_p;
+               ++bp->refcount;
+               break;
+       case 0:
+               bp = (basic*)_num0_p;
+               ++bp->refcount;
+               break;
+       case 1:
+               bp = (basic*)_num1_p;
+               ++bp->refcount;
+               break;
+       case 2:
+               bp = (basic*)_num2_p;
+               ++bp->refcount;
+               break;
+       case 3:
+               bp = (basic*)_num3_p;
+               ++bp->refcount;
+               break;
+       case 4:
+               bp = (basic*)_num4_p;
+               ++bp->refcount;
+               break;
+       case 5:
+               bp = (basic*)_num5_p;
+               ++bp->refcount;
+               break;
+       case 6:
+               bp = (basic*)_num6_p;
+               ++bp->refcount;
+               break;
+       case 7:
+               bp = (basic*)_num7_p;
+               ++bp->refcount;
+               break;
+       case 8:
+               bp = (basic*)_num8_p;
+               ++bp->refcount;
+               break;
+       case 9:
+               bp = (basic*)_num9_p;
+               ++bp->refcount;
+               break;
+       case 10:
+               bp = (basic*)_num10_p;
+               ++bp->refcount;
+               break;
+       case 11:
+               bp = (basic*)_num11_p;
+               ++bp->refcount;
+               break;
+       case 12:
+               bp = (basic*)_num12_p;
+               ++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) {  // prefer flyweights over new objects
+       case 0:
+               bp = (basic*)_num0_p;
+               ++bp->refcount;
+               break;
+       case 1:
+               bp = (basic*)_num1_p;
+               ++bp->refcount;
+               break;
+       case 2:
+               bp = (basic*)_num2_p;
+               ++bp->refcount;
+               break;
+       case 3:
+               bp = (basic*)_num3_p;
+               ++bp->refcount;
+               break;
+       case 4:
+               bp = (basic*)_num4_p;
+               ++bp->refcount;
+               break;
+       case 5:
+               bp = (basic*)_num5_p;
+               ++bp->refcount;
+               break;
+       case 6:
+               bp = (basic*)_num6_p;
+               ++bp->refcount;
+               break;
+       case 7:
+               bp = (basic*)_num7_p;
+               ++bp->refcount;
+               break;
+       case 8:
+               bp = (basic*)_num8_p;
+               ++bp->refcount;
+               break;
+       case 9:
+               bp = (basic*)_num9_p;
+               ++bp->refcount;
+               break;
+       case 10:
+               bp = (basic*)_num10_p;
+               ++bp->refcount;
+               break;
+       case 11:
+               bp = (basic*)_num11_p;
+               ++bp->refcount;
+               break;
+       case 12:
+               bp = (basic*)_num12_p;
+               ++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) {  // prefer flyweights over new objects
+       case -12:
+               bp = (basic*)_num_12_p;
+               ++bp->refcount;
+               break;
+       case -11:
+               bp = (basic*)_num_11_p;
+               ++bp->refcount;
+               break;
+       case -10:
+               bp = (basic*)_num_10_p;
+               ++bp->refcount;
+               break;
+       case -9:
+               bp = (basic*)_num_9_p;
+               ++bp->refcount;
+               break;
+       case -8:
+               bp = (basic*)_num_8_p;
+               ++bp->refcount;
+               break;
+       case -7:
+               bp = (basic*)_num_7_p;
+               ++bp->refcount;
+               break;
+       case -6:
+               bp = (basic*)_num_6_p;
+               ++bp->refcount;
+               break;
+       case -5:
+               bp = (basic*)_num_5_p;
+               ++bp->refcount;
+               break;
+       case -4:
+               bp = (basic*)_num_4_p;
+               ++bp->refcount;
+               break;
+       case -3:
+               bp = (basic*)_num_3_p;
+               ++bp->refcount;
+               break;
+       case -2:
+               bp = (basic*)_num_2_p;
+               ++bp->refcount;
+               break;
+       case -1:
+               bp = (basic*)_num_1_p;
+               ++bp->refcount;
+               break;
+       case 0:
+               bp = (basic*)_num0_p;
+               ++bp->refcount;
+               break;
+       case 1:
+               bp = (basic*)_num1_p;
+               ++bp->refcount;
+               break;
+       case 2:
+               bp = (basic*)_num2_p;
+               ++bp->refcount;
+               break;
+       case 3:
+               bp = (basic*)_num3_p;
+               ++bp->refcount;
+               break;
+       case 4:
+               bp = (basic*)_num4_p;
+               ++bp->refcount;
+               break;
+       case 5:
+               bp = (basic*)_num5_p;
+               ++bp->refcount;
+               break;
+       case 6:
+               bp = (basic*)_num6_p;
+               ++bp->refcount;
+               break;
+       case 7:
+               bp = (basic*)_num7_p;
+               ++bp->refcount;
+               break;
+       case 8:
+               bp = (basic*)_num8_p;
+               ++bp->refcount;
+               break;
+       case 9:
+               bp = (basic*)_num9_p;
+               ++bp->refcount;
+               break;
+       case 10:
+               bp = (basic*)_num10_p;
+               ++bp->refcount;
+               break;
+       case 11:
+               bp = (basic*)_num11_p;
+               ++bp->refcount;
+               break;
+       case 12:
+               bp = (basic*)_num12_p;
+               ++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) {  // prefer flyweights over new objects
+       case 0:
+               bp = (basic*)_num0_p;
+               ++bp->refcount;
+               break;
+       case 1:
+               bp = (basic*)_num1_p;
+               ++bp->refcount;
+               break;
+       case 2:
+               bp = (basic*)_num2_p;
+               ++bp->refcount;
+               break;
+       case 3:
+               bp = (basic*)_num3_p;
+               ++bp->refcount;
+               break;
+       case 4:
+               bp = (basic*)_num4_p;
+               ++bp->refcount;
+               break;
+       case 5:
+               bp = (basic*)_num5_p;
+               ++bp->refcount;
+               break;
+       case 6:
+               bp = (basic*)_num6_p;
+               ++bp->refcount;
+               break;
+       case 7:
+               bp = (basic*)_num7_p;
+               ++bp->refcount;
+               break;
+       case 8:
+               bp = (basic*)_num8_p;
+               ++bp->refcount;
+               break;
+       case 9:
+               bp = (basic*)_num9_p;
+               ++bp->refcount;
+               break;
+       case 10:
+               bp = (basic*)_num10_p;
+               ++bp->refcount;
+               break;
+       case 11:
+               bp = (basic*)_num11_p;
+               ++bp->refcount;
+               break;
+       case 12:
+               bp = (basic*)_num12_p;
+               ++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 std::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
 //////////
@@ -474,48 +603,7 @@ void ex::construct_from_basic(basic const & other)
 // global functions
 //////////
 
-ex const & exZERO(void)
-{
-    static ex * eZERO=new ex(numZERO());
-    return *eZERO;
-}
-
-ex const & exONE(void)
-{
-    static ex * eONE=new ex(numONE());
-    return *eONE;
-}
-
-ex const & exTWO(void)
-{
-    static ex * eTWO=new ex(numTWO());
-    return *eTWO;
-}
-
-ex const & exTHREE(void)
-{
-    static ex * eTHREE=new ex(numTHREE());
-    return *eTHREE;
-}
-
-ex const & exMINUSONE(void)
-{
-    static ex * eMINUSONE=new ex(numMINUSONE());
-    return *eMINUSONE;
-}
-
-ex const & exHALF(void)
-{
-    static ex * eHALF=new ex(ex(1)/ex(2));
-    return *eHALF;
-}
+// none
 
-ex const & exMINUSHALF(void)
-{
-    static ex * eMINUSHALF=new ex(numeric(-1,2));
-    return *eMINUSHALF;
-}
 
-#ifndef NO_GINAC_NAMESPACE
 } // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE