X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fex.cpp;h=77c7983300ed10edc670ea076be17a481be8e313;hp=a8b7b2f2808b2bcef7f7f4668f537e783c5a610d;hb=d508ca04e9c2f4ee103c9f21f33a98c87116df13;hpb=afdd7fa8c6c0a587f7c80789198551383e8beb7b

diff --git a/ginac/ex.cpp b/ginac/ex.cpp
index a8b7b2f2..77c79833 100644
--- a/ginac/ex.cpp
+++ b/ginac/ex.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's light-weight expression handles. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2001 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"
@@ -28,109 +29,20 @@
 #include "ncmul.h"
 #include "numeric.h"
 #include "power.h"
+#include "relational.h"
+#include "indexed.h"
+#include "input_lexer.h"
 #include "debugmsg.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
+// none (all inlined)
 
-//////////
-// 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
 //////////
@@ -149,315 +61,347 @@ ex::ex(double const d)
 
 // public
 
+/** Efficiently 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;
-}
-
-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
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->has(other);
-}
-
-int ex::degree(symbol const & s) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->degree(s);
-}
-
-int ex::ldegree(symbol const & s) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->ldegree(s);
-}
-
-ex ex::coeff(symbol const & s, int const n) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->coeff(s,n);
-}
-
-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;
-}
+	debugmsg("ex swap",LOGLEVEL_MEMBER_FUNCTION);
 
-ex ex::collect(symbol const & s) const
-{
-    GINAC_ASSERT(bp!=0);
-    return bp->collect(s);
+	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;
 }
 
-ex ex::eval(int level) 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->eval(level);
+	debugmsg("ex print", LOGLEVEL_PRINT);
+	GINAC_ASSERT(bp!=0);
+	bp->print(c, level);
 }
 
-ex ex::evalf(int level) 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->evalf(level);
+	debugmsg("ex printtree", LOGLEVEL_PRINT);
+	GINAC_ASSERT(bp!=0);
+	bp->print(print_tree(os));
 }
 
-ex ex::subs(lst const & ls, lst const & lr) const
+/** Little wrapper arount print to be called within a debugger. */
+void ex::dbgprint(void) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->subs(ls,lr);
+	debugmsg("ex dbgprint", LOGLEVEL_PRINT);
+	GINAC_ASSERT(bp!=0);
+	bp->dbgprint();
 }
 
-ex ex::subs(ex const & e) const
+/** Little wrapper arount printtree to be called within a debugger. */
+void ex::dbgprinttree(void) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->subs(e);
+	debugmsg("ex dbgprinttree", LOGLEVEL_PRINT);
+	GINAC_ASSERT(bp!=0);
+	bp->dbgprinttree();
 }
 
-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
+ex ex::expand(unsigned options) const
 {
-    debugmsg("ex operator[ex]",LOGLEVEL_OPERATOR);
-    GINAC_ASSERT(bp!=0);
-    return (*bp)[index];
+	GINAC_ASSERT(bp!=0);
+	if (bp->flags & status_flags::expanded)
+		return *bp;
+	else
+		return bp->expand(options);
 }
 
-ex ex::operator[](int const i) 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
 {
-    debugmsg("ex operator[int]",LOGLEVEL_OPERATOR);
-    GINAC_ASSERT(bp!=0);
-    return (*bp)[i];
-}
+	GINAC_ASSERT(bp!=0);
 
-ex ex::op(int const i) const
-{
-    debugmsg("ex op()",LOGLEVEL_MEMBER_FUNCTION);
-    GINAC_ASSERT(bp!=0);
-    return bp->op(i);
+	if (!nth)
+		return *this;
+	else
+		return bp->diff(s, nth);
 }
 
-ex & ex::let_op(int const i)
+/** Simplify/canonicalize expression containing indexed objects. This
+ *  performs contraction of dummy indices where possible and checks whether
+ *  the free indices in sums are consistent.
+ *
+ *  @return simplified expression */
+ex ex::simplify_indexed(void) const
 {
-    debugmsg("ex let_op()",LOGLEVEL_MEMBER_FUNCTION);
-    makewriteable();
-    GINAC_ASSERT(bp!=0);
-    return bp->let_op(i);
+	return GiNaC::simplify_indexed(*this);
 }
 
-#ifndef INLINE_EX_CONSTRUCTORS
-int ex::compare(ex const & other) const
+/** Simplify/canonicalize expression containing indexed objects. This
+ *  performs contraction of dummy indices where possible, checks whether
+ *  the free indices in sums are consistent, and automatically replaces
+ *  scalar products by known values if desired.
+ *
+ *  @param sp Scalar products to be replaced automatically
+ *  @return simplified expression */
+ex ex::simplify_indexed(const scalar_products & sp) 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);
+	return GiNaC::simplify_indexed(*this, sp);
 }
-#endif // ndef INLINE_EX_CONSTRUCTORS
 
-#ifndef INLINE_EX_CONSTRUCTORS
-bool ex::is_equal(ex const & other) const
+ex ex::operator[](const ex & index) 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);
+	debugmsg("ex operator[ex]",LOGLEVEL_OPERATOR);
+	GINAC_ASSERT(bp!=0);
+	return (*bp)[index];
 }
-#endif // ndef INLINE_EX_CONSTRUCTORS
 
-unsigned ex::return_type(void) const
+ex ex::operator[](int i) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->return_type();
+	debugmsg("ex operator[int]",LOGLEVEL_OPERATOR);
+	GINAC_ASSERT(bp!=0);
+	return (*bp)[i];
 }
 
-unsigned ex::return_type_tinfo(void) const
+/** Return modifyable operand/member at position i. */
+ex & ex::let_op(int i)
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->return_type_tinfo();
+	debugmsg("ex let_op()",LOGLEVEL_MEMBER_FUNCTION);
+	makewriteable();
+	GINAC_ASSERT(bp!=0);
+	return bp->let_op(i);
 }
 
-unsigned ex::gethash(void) const
+/** Left hand side of relational expression. */
+ex ex::lhs(void) const
 {
-    GINAC_ASSERT(bp!=0);
-    return bp->gethash();
+	debugmsg("ex lhs()",LOGLEVEL_MEMBER_FUNCTION);
+	if (!is_ex_of_type(*this,relational))
+		throw std::runtime_error("ex::lhs(): not a relation");
+	return (*static_cast<relational *>(bp)).lhs();
 }
 
-ex ex::exadd(ex const & rh) const
+/** Right hand side of relational expression. */
+ex ex::rhs(void) const
 {
-    return (new add(*this,rh))->setflag(status_flags::dynallocated);
+	debugmsg("ex rhs()",LOGLEVEL_MEMBER_FUNCTION);
+	if (!is_ex_of_type(*this,relational))
+		throw std::runtime_error("ex::rhs(): not a relation");
+	return (*static_cast<relational *>(bp)).rhs();
 }
 
-ex ex::exmul(ex const & rh) const
+/** Used internally by operator+() to add two ex objects together. */
+ex ex::exadd(const ex & rh) const
 {
-    return (new mul(*this,rh))->setflag(status_flags::dynallocated);
+	return (new add(*this,rh))->setflag(status_flags::dynallocated);
 }
 
-ex ex::exncmul(ex const & rh) const
+/** Used internally by operator*() to multiply two ex objects together. */
+ex ex::exmul(const ex & rh) const
 {
-    return (new ncmul(*this,rh))->setflag(status_flags::dynallocated);
+	// Check if we are constructing a mul object or a ncmul object.  Due to
+	// ncmul::eval()'s rule to pull out commutative elements we need to check
+	// only one of the elements.
+	if (rh.bp->return_type()==return_types::commutative ||
+	    bp->return_type()==return_types::commutative)
+		return (new mul(*this,rh))->setflag(status_flags::dynallocated);
+	else
+		return (new ncmul(*this,rh))->setflag(status_flags::dynallocated);
 }
 
 // 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);
-}
-
+	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);
+}
+
+/** Ctor from basic implementation.
+ *  @see ex::ex(const basic &) */
+void ex::construct_from_basic(const basic & other)
+{
+	if ((other.flags & status_flags::evaluated)==0) {
+		// cf. copy ctor
+		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) {
+			// 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) {  // 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 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 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 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 +418,7 @@ 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