X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fbasic.cpp;h=483844c0ee0a81bd66b2e5bb03a2d29b23620179;hp=875bf758135c9bd73e60bf6cc58ec108c608028a;hb=aa171175a88728d1e4c3305122fa4e45e45014ec;hpb=6b3768e8c544739ae53321539cb4d1e3112ded1b

diff --git a/ginac/basic.cpp b/ginac/basic.cpp
index 875bf758..483844c0 100644
--- a/ginac/basic.cpp
+++ b/ginac/basic.cpp
@@ -2,78 +2,115 @@
  *
  *  Implementation of GiNaC's ABC. */
 
+/*
+ *  GiNaC Copyright (C) 1999-2003 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
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  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
+ */
+
 #include <iostream>
-#include <typeinfo>
 #include <stdexcept>
+#ifdef DO_GINAC_ASSERT
+#  include <typeinfo>
+#endif
 
-#include "ginac.h"
+#include "basic.h"
+#include "ex.h"
+#include "numeric.h"
+#include "power.h"
+#include "symbol.h"
+#include "lst.h"
+#include "ncmul.h"
+#include "relational.h"
+#include "operators.h"
+#include "wildcard.h"
+#include "archive.h"
 #include "utils.h"
 
+namespace GiNaC {
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(basic, void,
+  print_func<print_context>(&basic::do_print).
+  print_func<print_tree>(&basic::do_print_tree).
+  print_func<print_python_repr>(&basic::do_print_python_repr))
+
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor, destructor, copy constructor and assignment operator
 //////////
 
 // public
 
-#ifndef INLINE_BASIC_CONSTRUCTORS
-basic::basic() : flags(0), refcount(0), tinfo_key(TINFO_BASIC)
+/** basic copy constructor: implicitly assumes that the other class is of
+ *  the exact same type (as it's used by duplicate()), so it can copy the
+ *  tinfo_key and the hash value. */
+basic::basic(const basic & other) : tinfo_key(other.tinfo_key), flags(other.flags & ~status_flags::dynallocated), hashvalue(other.hashvalue), refcount(0)
 {
-    debugmsg("basic default constructor",LOGLEVEL_CONSTRUCT);
-    // nothing to do
+	GINAC_ASSERT(typeid(*this) == typeid(other));
 }
 
-basic::~basic() 
+/** basic assignment operator: the other object might be of a derived class. */
+const basic & basic::operator=(const basic & other)
 {
-    debugmsg("basic destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
-    ASSERT((!(flags & status_flags::dynallocated))||(refcount==0));
-}
-
-basic::basic(basic const & other) : flags(0), refcount(0), tinfo_key(TINFO_BASIC)
-{
-    debugmsg("basic copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
-}
-#endif
-
-basic const & basic::operator=(basic const & other)
-{
-    debugmsg("basic operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
+	unsigned fl = other.flags & ~status_flags::dynallocated;
+	if (tinfo_key != other.tinfo_key) {
+		// The other object is of a derived class, so clear the flags as they
+		// might no longer apply (especially hash_calculated). Oh, and don't
+		// copy the tinfo_key: it is already set correctly for this object.
+		flags = 0;
+	} else {
+		// The objects are of the exact same class, so copy the hash value.
+		hashvalue = other.hashvalue;
+	}
+	flags = fl;
+	refcount = 0;
+	return *this;
 }
 
 // protected
 
-#if 0
-void basic::copy(basic const & other)
-{
-    flags=other.flags & ~ status_flags::dynallocated;
-    hashvalue=other.hashvalue;
-    tinfo_key=other.tinfo_key;
-}
-#endif
+// none (all inlined)
 
 //////////
 // other constructors
 //////////
 
-#ifndef INLINE_BASIC_CONSTRUCTORS
-basic::basic(unsigned ti) : flags(0), refcount(0), tinfo_key(ti)
-{
-    debugmsg("basic constructor with tinfo_key",LOGLEVEL_CONSTRUCT);
-    // nothing to do
-}
-#endif
+// none (all inlined)
 
 //////////
-// functions overriding virtual functions from bases classes
+// archiving
 //////////
 
-// none
+/** Construct object from archive_node. */
+basic::basic(const archive_node &n, lst &sym_lst) : flags(0), refcount(0)
+{
+	// Reconstruct tinfo_key from class name
+	std::string class_name;
+	if (n.find_string("class", class_name))
+		tinfo_key = find_tinfo_key(class_name);
+	else
+		throw (std::runtime_error("archive node contains no class name"));
+}
+
+/** Unarchive the object. */
+DEFAULT_UNARCHIVE(basic)
+
+/** Archive the object. */
+void basic::archive(archive_node &n) const
+{
+	n.add_string("class", class_name());
+}
 
 //////////
 // new virtual functions which can be overridden by derived classes
@@ -81,311 +118,762 @@ basic::basic(unsigned ti) : flags(0), refcount(0), tinfo_key(ti)
 
 // public
 
-basic * basic::duplicate() const
+/** Output to stream. This performs double dispatch on the dynamic type of
+ *  *this and the dynamic type of the supplied print context.
+ *  @param c print context object that describes the output formatting
+ *  @param level value that is used to identify the precedence or indentation
+ *               level for placing parentheses and formatting */
+void basic::print(const print_context & c, unsigned level) const
 {
-    debugmsg("basic duplicate",LOGLEVEL_DUPLICATE);
-    return new basic(*this);
+	print_dispatch(get_class_info(), c, level);
 }
 
-bool basic::info(unsigned inf) const
+/** Like print(), but dispatch to the specified class. Can be used by
+ *  implementations of print methods to dispatch to the method of the
+ *  superclass.
+ *
+ *  @see basic::print */
+void basic::print_dispatch(const registered_class_info & ri, const print_context & c, unsigned level) const
 {
-    return false; // all possible properties are false for basic objects
+	// Double dispatch on object type and print_context type
+	const registered_class_info * reg_info = &ri;
+	const print_context_class_info * pc_info = &c.get_class_info();
+
+next_class:
+	const std::vector<print_functor> & pdt = reg_info->options.get_print_dispatch_table();
+
+next_context:
+	unsigned id = pc_info->options.get_id();
+	if (id >= pdt.size() || !(pdt[id].is_valid())) {
+
+		// Method not found, try parent print_context class
+		const print_context_class_info * parent_pc_info = pc_info->get_parent();
+		if (parent_pc_info) {
+			pc_info = parent_pc_info;
+			goto next_context;
+		}
+
+		// Method still not found, try parent class
+		const registered_class_info * parent_reg_info = reg_info->get_parent();
+		if (parent_reg_info) {
+			reg_info = parent_reg_info;
+			pc_info = &c.get_class_info();
+			goto next_class;
+		}
+
+		// Method still not found. This shouldn't happen because basic (the
+		// base class of the algebraic hierarchy) registers a method for
+		// print_context (the base class of the print context hierarchy),
+		// so if we end up here, there's something wrong with the class
+		// registry.
+		throw (std::runtime_error(std::string("basic::print(): method for ") + class_name() + "/" + c.class_name() + " not found"));
+
+	} else {
+
+		// Call method
+		pdt[id](*this, c, level);
+	}
 }
 
-int basic::nops() const
+/** Default output to stream. */
+void basic::do_print(const print_context & c, unsigned level) const
 {
-    return 0;
+	c.s << "[" << class_name() << " object]";
 }
 
-ex basic::op(int const i) const
+/** Tree output to stream. */
+void basic::do_print_tree(const print_tree & c, unsigned level) const
 {
-    return (const_cast<basic *>(this))->let_op(i);
+	c.s << std::string(level, ' ') << class_name()
+	    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+	    << ", nops=" << nops()
+	    << std::endl;
+	for (size_t i=0; i<nops(); ++i)
+		op(i).print(c, level + c.delta_indent);
 }
 
-ex & basic::let_op(int const i)
+/** Python parsable output to stream. */
+void basic::do_print_python_repr(const print_python_repr & c, unsigned level) const
 {
-    throw(std::out_of_range("op() out of range"));
+	c.s << class_name() << "()";
 }
 
-ex basic::operator[](ex const & index) const
+/** Little wrapper around print to be called within a debugger.
+ *  This is needed because you cannot call foo.print(cout) from within the
+ *  debugger because it might not know what cout is.  This method can be
+ *  invoked with no argument and it will simply print to stdout.
+ *
+ *  @see basic::print
+ *  @see basic::dbgprinttree */
+void basic::dbgprint() const
 {
-    if (is_exactly_of_type(*index.bp,numeric)) {
-        return op(static_cast<numeric const &>(*index.bp).to_int());
-    }
-    throw(std::invalid_argument("non-numeric indices not supported by this type"));
+	this->print(std::cerr);
+	std::cerr << std::endl;
 }
 
-ex basic::operator[](int const i) const
+/** Little wrapper around printtree to be called within a debugger.
+ *
+ *  @see basic::dbgprint */
+void basic::dbgprinttree() const
 {
-    return op(i);
+	this->print(print_tree(std::cerr));
 }
 
-bool basic::has(ex const & other) const
+/** Return relative operator precedence (for parenthezing output). */
+unsigned basic::precedence() const
 {
-    ASSERT(other.bp!=0);
-    if (is_equal(*other.bp)) return true;
-    if (nops()>0) {
-        for (int i=0; i<nops(); i++) {
-            if (op(i).has(other)) return true;
-        }
-    }
-    return false;
+	return 70;
 }
 
-int basic::degree(symbol const & s) const
+/** Information about the object.
+ *
+ *  @see class info_flags */
+bool basic::info(unsigned inf) const
 {
-    return 0;
+	// all possible properties are false for basic objects
+	return false;
 }
 
-int basic::ldegree(symbol const & s) const
+/** Number of operands/members. */
+size_t basic::nops() const
 {
-    return 0;
+	// iterating from 0 to nops() on atomic objects should be an empty loop,
+	// and accessing their elements is a range error.  Container objects should
+	// override this.
+	return 0;
 }
 
-ex basic::coeff(symbol const & s, int const n) const
+/** Return operand/member at position i. */
+ex basic::op(size_t i) const
 {
-    return n==0 ? *this : exZERO();
+	throw(std::range_error(std::string("basic::op(): ") + class_name() + std::string(" has no operands")));
 }
 
-ex basic::collect(symbol const & s) const
+/** Return modifyable operand/member at position i. */
+ex & basic::let_op(size_t i)
 {
-    ex x;
-    int ldeg=ldegree(s);
-    int deg=degree(s);
-    for (int n=ldeg; n<=deg; n++) {
-        x += coeff(s,n)*power(s,n);
-    }
-    return x;
+	ensure_if_modifiable();
+	throw(std::range_error(std::string("basic::let_op(): ") + class_name() + std::string(" has no operands")));
 }
 
-ex basic::eval(int level) const
+ex basic::operator[](const ex & index) const
 {
-    return this->hold();
+	if (is_exactly_a<numeric>(index))
+		return op(static_cast<size_t>(ex_to<numeric>(index).to_int()));
+
+	throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
 }
 
-ex basic::evalf(int level) const
+ex basic::operator[](size_t i) const
 {
-    return *this;
+	return op(i);
 }
 
-ex basic::subs(lst const & ls, lst const & lr) const
+ex & basic::operator[](const ex & index)
 {
-    return *this;
+	if (is_exactly_a<numeric>(index))
+		return let_op(ex_to<numeric>(index).to_int());
+
+	throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
 }
 
-exvector basic::get_indices(void) const
+ex & basic::operator[](size_t i)
 {
-    return exvector(); // return an empty exvector
+	return let_op(i);
 }
 
-ex basic::simplify_ncmul(exvector const & v) const
+/** Test for occurrence of a pattern.  An object 'has' a pattern if it matches
+ *  the pattern itself or one of the children 'has' it.  As a consequence
+ *  (according to the definition of children) given e=x+y+z, e.has(x) is true
+ *  but e.has(x+y) is false. */
+bool basic::has(const ex & pattern) const
 {
-    return simplified_ncmul(v);
+	lst repl_lst;
+	if (match(pattern, repl_lst))
+		return true;
+	for (size_t i=0; i<nops(); i++)
+		if (op(i).has(pattern))
+			return true;
+	
+	return false;
 }
 
-// protected
+/** Construct new expression by applying the specified function to all
+ *  sub-expressions (one level only, not recursively). */
+ex basic::map(map_function & f) const
+{
+	size_t num = nops();
+	if (num == 0)
+		return *this;
+
+	basic *copy = duplicate();
+	copy->setflag(status_flags::dynallocated);
+	copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
+	for (size_t i=0; i<num; i++)
+		copy->let_op(i) = f(copy->op(i));
+	return *copy;
+}
 
-int basic::compare_same_type(basic const & other) const
+/** Return degree of highest power in object s. */
+int basic::degree(const ex & s) const
 {
-    return compare_pointers(this, &other);
+	return is_equal(ex_to<basic>(s)) ? 1 : 0;
 }
 
-bool basic::is_equal_same_type(basic const & other) const
+/** Return degree of lowest power in object s. */
+int basic::ldegree(const ex & s) const
 {
-    return compare_same_type(other)==0;
+	return is_equal(ex_to<basic>(s)) ? 1 : 0;
 }
 
-unsigned basic::return_type(void) const
+/** Return coefficient of degree n in object s. */
+ex basic::coeff(const ex & s, int n) const
 {
-    return return_types::commutative;
+	if (is_equal(ex_to<basic>(s)))
+		return n==1 ? _ex1 : _ex0;
+	else
+		return n==0 ? *this : _ex0;
 }
 
-unsigned basic::return_type_tinfo(void) const
+/** Sort expanded expression in terms of powers of some object(s).
+ *  @param s object(s) to sort in
+ *  @param distributed recursive or distributed form (only used when s is a list) */
+ex basic::collect(const ex & s, bool distributed) const
 {
-    return tinfo();
+	ex x;
+	if (is_a<lst>(s)) {
+
+		// List of objects specified
+		if (s.nops() == 0)
+			return *this;
+		if (s.nops() == 1)
+			return collect(s.op(0));
+
+		else if (distributed) {
+
+			// Get lower/upper degree of all symbols in list
+			size_t num = s.nops();
+			struct sym_info {
+				ex sym;
+				int ldeg, deg;
+				int cnt;  // current degree, 'counter'
+				ex coeff; // coefficient for degree 'cnt'
+			};
+			sym_info *si = new sym_info[num];
+			ex c = *this;
+			for (size_t i=0; i<num; i++) {
+				si[i].sym = s.op(i);
+				si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
+				si[i].deg = this->degree(si[i].sym);
+				c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
+			}
+
+			while (true) {
+
+				// Calculate coeff*x1^c1*...*xn^cn
+				ex y = _ex1;
+				for (size_t i=0; i<num; i++) {
+					int cnt = si[i].cnt;
+					y *= power(si[i].sym, cnt);
+				}
+				x += y * si[num - 1].coeff;
+
+				// Increment counters
+				size_t n = num - 1;
+				while (true) {
+					++si[n].cnt;
+					if (si[n].cnt <= si[n].deg) {
+						// Update coefficients
+						ex c;
+						if (n == 0)
+							c = *this;
+						else
+							c = si[n - 1].coeff;
+						for (size_t i=n; i<num; i++)
+							c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
+						break;
+					}
+					if (n == 0)
+						goto done;
+					si[n].cnt = si[n].ldeg;
+					n--;
+				}
+			}
+
+done:		delete[] si;
+
+		} else {
+
+			// Recursive form
+			x = *this;
+			size_t n = s.nops() - 1;
+			while (true) {
+				x = x.collect(s[n]);
+				if (n == 0)
+					break;
+				n--;
+			}
+		}
+
+	} else {
+
+		// Only one object specified
+		for (int n=this->ldegree(s); n<=this->degree(s); ++n)
+			x += this->coeff(s,n)*power(s,n);
+	}
+	
+	// correct for lost fractional arguments and return
+	return x + (*this - x).expand();
+}
+
+/** Perform automatic non-interruptive term rewriting rules. */
+ex basic::eval(int level) const
+{
+	// There is nothing to do for basic objects:
+	return hold();
 }
 
-unsigned basic::calchash(void) const
+/** Function object to be applied by basic::evalf(). */
+struct evalf_map_function : public map_function {
+	int level;
+	evalf_map_function(int l) : level(l) {}
+	ex operator()(const ex & e) { return evalf(e, level); }
+};
+
+/** Evaluate object numerically. */
+ex basic::evalf(int level) const
 {
-    unsigned v=golden_ratio_hash(tinfo());
-    for (int i=0; i<nops(); i++) {
-        v=rotate_left_31(v);
-        v ^= (const_cast<basic *>(this))->let_op(i).gethash();
-    }
+	if (nops() == 0)
+		return *this;
+	else {
+		if (level == 1)
+			return *this;
+		else if (level == -max_recursion_level)
+			throw(std::runtime_error("max recursion level reached"));
+		else {
+			evalf_map_function map_evalf(level - 1);
+			return map(map_evalf);
+		}
+	}
+}
 
-    v = v & 0x7FFFFFFFU;
-    
-    // store calculated hash value only if object is already evaluated
-    if (flags & status_flags::evaluated) {
-        setflag(status_flags::hash_calculated);
-        hashvalue=v;
-    }
+/** Function object to be applied by basic::evalm(). */
+struct evalm_map_function : public map_function {
+	ex operator()(const ex & e) { return evalm(e); }
+} map_evalm;
 
-    return v;
+/** Evaluate sums, products and integer powers of matrices. */
+ex basic::evalm() const
+{
+	if (nops() == 0)
+		return *this;
+	else
+		return map(map_evalm);
 }
 
-ex basic::expand(unsigned options) const
+/** Perform automatic symbolic evaluations on indexed expression that
+ *  contains this object as the base expression. */
+ex basic::eval_indexed(const basic & i) const
+ // this function can't take a "const ex & i" because that would result
+ // in an infinite eval() loop
 {
-    return this->setflag(status_flags::expanded);
+	// There is nothing to do for basic objects
+	return i.hold();
 }
 
-//////////
-// non-virtual functions in this class
-//////////
+/** Add two indexed expressions. They are guaranteed to be of class indexed
+ *  (or a subclass) and their indices are compatible. This function is used
+ *  internally by simplify_indexed().
+ *
+ *  @param self First indexed expression; it's base object is *this
+ *  @param other Second indexed expression
+ *  @return sum of self and other 
+ *  @see ex::simplify_indexed() */
+ex basic::add_indexed(const ex & self, const ex & other) const
+{
+	return self + other;
+}
 
-// public
+/** Multiply an indexed expression with a scalar. This function is used
+ *  internally by simplify_indexed().
+ *
+ *  @param self Indexed expression; it's base object is *this
+ *  @param other Numeric value
+ *  @return product of self and other
+ *  @see ex::simplify_indexed() */
+ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
+{
+	return self * other;
+}
 
-ex basic::subs(ex const & e) const
-{
-    // accept 2 types of replacement expressions:
-    //   - symbol==ex
-    //   - lst(symbol1==ex1,symbol2==ex2,...)
-    // convert to subs(lst(symbol1,symbol2,...),lst(ex1,ex2,...))
-    // additionally, idx can be used instead of symbol
-    if (e.info(info_flags::relation_equal)) {
-        return subs(lst(e));
-    }
-    if (!e.info(info_flags::list)) {
-        throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
-    }
-    lst ls;
-    lst lr;
-    for (int i=0; i<e.nops(); i++) {
-        if (!e.op(i).info(info_flags::relation_equal)) {
-            throw(std::invalid_argument("basic::subs(ex): argument must be a list or equations"));
-        }
-        if (!e.op(i).op(0).info(info_flags::symbol)) {
-            if (!e.op(i).op(0).info(info_flags::idx)) {
-                throw(std::invalid_argument("basic::subs(ex): lhs must be a symbol or an idx"));
-            }
-        }
-        ls.append(e.op(i).op(0));
-        lr.append(e.op(i).op(1));
-    }
-    return subs(ls,lr);
-}
-
-// compare functions to sort expressions canonically
-// all compare functions return: -1 for *this less than other, 0 equal, 1 greater
+/** Try to contract two indexed expressions that appear in the same product. 
+ *  If a contraction exists, the function overwrites one or both of the
+ *  expressions and returns true. Otherwise it returns false. It is
+ *  guaranteed that both expressions are of class indexed (or a subclass)
+ *  and that at least one dummy index has been found. This functions is
+ *  used internally by simplify_indexed().
+ *
+ *  @param self Pointer to first indexed expression; it's base object is *this
+ *  @param other Pointer to second indexed expression
+ *  @param v The complete vector of factors
+ *  @return true if the contraction was successful, false otherwise
+ *  @see ex::simplify_indexed() */
+bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+	// Do nothing
+	return false;
+}
 
-/*
-int basic::compare(basic const & other) const
+/** Check whether the expression matches a given pattern. For every wildcard
+ *  object in the pattern, an expression of the form "wildcard == matching_expression"
+ *  is added to repl_lst. */
+bool basic::match(const ex & pattern, lst & repl_lst) const
 {
-    const type_info & typeid_this = typeid(*this);
-    const type_info & typeid_other = typeid(other);
+/*
+	Sweet sweet shapes, sweet sweet shapes,
+	That's the key thing, right right.
+	Feed feed face, feed feed shapes,
+	But who is the king tonight?
+	Who is the king tonight?
+	Pattern is the thing, the key thing-a-ling,
+	But who is the king of Pattern?
+	But who is the king, the king thing-a-ling,
+	Who is the king of Pattern?
+	Bog is the king, the king thing-a-ling,
+	Bog is the king of Pattern.
+	Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
+	Bog is the king of Pattern.
+*/
+
+	if (is_exactly_a<wildcard>(pattern)) {
+
+		// Wildcard matches anything, but check whether we already have found
+		// a match for that wildcard first (if so, it the earlier match must
+		// be the same expression)
+		for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
+			if (it->op(0).is_equal(pattern))
+				return is_equal(ex_to<basic>(it->op(1)));
+		}
+		repl_lst.append(pattern == *this);
+		return true;
 
-    if (typeid_this==typeid_other) {
-        return compare_same_type(other);
-    }
+	} else {
 
-    // special rule: sort numeric() to end
-    if (typeid_this==typeid_numeric) return 1;
-    if (typeid_other==typeid_numeric) return -1;
+		// Expression must be of the same type as the pattern
+		if (tinfo() != ex_to<basic>(pattern).tinfo())
+			return false;
 
-    // otherwise: sort according to type_info order (arbitrary, but well defined)
-    return typeid_this.before(typeid_other) ? -1 : 1;
+		// Number of subexpressions must match
+		if (nops() != pattern.nops())
+			return false;
+
+		// No subexpressions? Then just compare the objects (there can't be
+		// wildcards in the pattern)
+		if (nops() == 0)
+			return is_equal_same_type(ex_to<basic>(pattern));
+
+		// Check whether attributes that are not subexpressions match
+		if (!match_same_type(ex_to<basic>(pattern)))
+			return false;
+
+		// Otherwise the subexpressions must match one-to-one
+		for (size_t i=0; i<nops(); i++)
+			if (!op(i).match(pattern.op(i), repl_lst))
+				return false;
+
+		// Looks similar enough, match found
+		return true;
+	}
 }
-*/
 
-int basic::compare(basic const & other) const
+/** Helper function for subs(). Does not recurse into subexpressions. */
+ex basic::subs_one_level(const exmap & m, unsigned options) const
 {
-    unsigned hash_this = gethash();
-    unsigned hash_other = other.gethash();
+	exmap::const_iterator it;
+
+	if (options & subs_options::no_pattern) {
+		it = m.find(*this);
+		if (it != m.end())
+			return it->second;
+	} else {
+		for (it = m.begin(); it != m.end(); ++it) {
+			lst repl_lst;
+			if (match(ex_to<basic>(it->first), repl_lst))
+				return it->second.subs(repl_lst, options | subs_options::no_pattern); // avoid infinite recursion when re-substituting the wildcards
+		}
+	}
 
-    if (hash_this<hash_other) return -1;
-    if (hash_this>hash_other) return 1;
+	return *this;
+}
 
-    unsigned typeid_this = tinfo();
-    unsigned typeid_other = other.tinfo();
+/** Substitute a set of objects by arbitrary expressions. The ex returned
+ *  will already be evaluated. */
+ex basic::subs(const exmap & m, unsigned options) const
+{
+	size_t num = nops();
+	if (num) {
 
-    if (typeid_this<typeid_other) {
-        /*
-        cout << "hash collision, different types: " 
-             << *this << " and " << other << endl;
-        this->printraw(cout);
-        cout << " and ";
-        other.printraw(cout);
-        cout << endl;
-        */
-        return -1;
-    }
-    if (typeid_this>typeid_other) {
-        /*
-        cout << "hash collision, different types: " 
-             << *this << " and " << other << endl;
-        this->printraw(cout);
-        cout << " and ";
-        other.printraw(cout);
-        cout << endl;
-        */
-        return 1;
-    }
+		// Substitute in subexpressions
+		for (size_t i=0; i<num; i++) {
+			const ex & orig_op = op(i);
+			const ex & subsed_op = orig_op.subs(m, options);
+			if (!are_ex_trivially_equal(orig_op, subsed_op)) {
 
-    ASSERT(typeid(*this)==typeid(other));
+				// Something changed, clone the object
+				basic *copy = duplicate();
+				copy->setflag(status_flags::dynallocated);
+				copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
 
-    int cmpval=compare_same_type(other);
-    if ((cmpval!=0)&&(hash_this<0x80000000U)) {
-        /*
-        cout << "hash collision, same type: " 
-             << *this << " and " << other << endl;
-        this->printraw(cout);
-        cout << " and ";
-        other.printraw(cout);
-        cout << endl;
-        */
-    }
-    return cmpval;
+				// Substitute the changed operand
+				copy->let_op(i++) = subsed_op;
+
+				// Substitute the other operands
+				for (; i<num; i++)
+					copy->let_op(i) = op(i).subs(m, options);
+
+				// Perform substitutions on the new object as a whole
+				return copy->subs_one_level(m, options);
+			}
+		}
+	}
+
+	// Nothing changed or no subexpressions
+	return subs_one_level(m, options);
+}
+
+/** Default interface of nth derivative ex::diff(s, n).  It should be called
+ *  instead of ::derivative(s) for first derivatives and for nth derivatives it
+ *  just recurses down.
+ *
+ *  @param s symbol to differentiate in
+ *  @param nth order of differentiation
+ *  @see ex::diff */
+ex basic::diff(const symbol & s, unsigned nth) const
+{
+	// trivial: zeroth derivative
+	if (nth==0)
+		return ex(*this);
+	
+	// evaluate unevaluated *this before differentiating
+	if (!(flags & status_flags::evaluated))
+		return ex(*this).diff(s, nth);
+	
+	ex ndiff = this->derivative(s);
+	while (!ndiff.is_zero() &&    // stop differentiating zeros
+	       nth>1) {
+		ndiff = ndiff.diff(s);
+		--nth;
+	}
+	return ndiff;
 }
 
-bool basic::is_equal(basic const & other) const
+/** Return a vector containing the free indices of an expression. */
+exvector basic::get_free_indices() const
 {
-    unsigned hash_this = gethash();
-    unsigned hash_other = other.gethash();
+	return exvector(); // return an empty exvector
+}
 
-    if (hash_this!=hash_other) return false;
+ex basic::eval_ncmul(const exvector & v) const
+{
+	return hold_ncmul(v);
+}
 
-    unsigned typeid_this = tinfo();
-    unsigned typeid_other = other.tinfo();
+// protected
 
-    if (typeid_this!=typeid_other) return false;
+/** Function object to be applied by basic::derivative(). */
+struct derivative_map_function : public map_function {
+	const symbol &s;
+	derivative_map_function(const symbol &sym) : s(sym) {}
+	ex operator()(const ex & e) { return diff(e, s); }
+};
 
-    ASSERT(typeid(*this)==typeid(other));
+/** Default implementation of ex::diff(). It maps the operation on the
+ *  operands (or returns 0 when the object has no operands).
+ *
+ *  @see ex::diff */
+ex basic::derivative(const symbol & s) const
+{
+	if (nops() == 0)
+		return _ex0;
+	else {
+		derivative_map_function map_derivative(s);
+		return map(map_derivative);
+	}
+}
 
-    return is_equal_same_type(other);
+/** Returns order relation between two objects of same type.  This needs to be
+ *  implemented by each class. It may never return anything else than 0,
+ *  signalling equality, or +1 and -1 signalling inequality and determining
+ *  the canonical ordering.  (Perl hackers will wonder why C++ doesn't feature
+ *  the spaceship operator <=> for denoting just this.) */
+int basic::compare_same_type(const basic & other) const
+{
+	return compare_pointers(this, &other);
 }
 
-// protected
+/** Returns true if two objects of same type are equal.  Normally needs
+ *  not be reimplemented as long as it wasn't overwritten by some parent
+ *  class, since it just calls compare_same_type().  The reason why this
+ *  function exists is that sometimes it is easier to determine equality
+ *  than an order relation and then it can be overridden. */
+bool basic::is_equal_same_type(const basic & other) const
+{
+	return compare_same_type(other)==0;
+}
 
-basic const & basic::hold(void) const
+/** Returns true if the attributes of two objects are similar enough for
+ *  a match. This function must not match subexpressions (this is already
+ *  done by basic::match()). Only attributes not accessible by op() should
+ *  be compared. This is also the reason why this function doesn't take the
+ *  wildcard replacement list from match() as an argument: only subexpressions
+ *  are subject to wildcard matches. Also, this function only needs to be
+ *  implemented for container classes because is_equal_same_type() is
+ *  automatically used instead of match_same_type() if nops() == 0.
+ *
+ *  @see basic::match */
+bool basic::match_same_type(const basic & other) const
 {
-    return setflag(status_flags::evaluated);
+	// The default is to only consider subexpressions, but not any other
+	// attributes
+	return true;
 }
 
-void basic::ensure_if_modifiable(void) const
+unsigned basic::return_type() const
 {
-    if (refcount>1) {
-        throw(std::runtime_error("cannot modify multiply referenced object"));
-    }
+	return return_types::commutative;
 }
 
-//////////
-// static member variables
-//////////
+unsigned basic::return_type_tinfo() const
+{
+	return tinfo();
+}
 
-// protected
+/** Compute the hash value of an object and if it makes sense to store it in
+ *  the objects status_flags, do so.  The method inherited from class basic
+ *  computes a hash value based on the type and hash values of possible
+ *  members.  For this reason it is well suited for container classes but
+ *  atomic classes should override this implementation because otherwise they
+ *  would all end up with the same hashvalue. */
+unsigned basic::calchash() const
+{
+	unsigned v = golden_ratio_hash(tinfo());
+	for (size_t i=0; i<nops(); i++) {
+		v = rotate_left(v);
+		v ^= this->op(i).gethash();
+	}
+
+	// store calculated hash value only if object is already evaluated
+	if (flags & status_flags::evaluated) {
+		setflag(status_flags::hash_calculated);
+		hashvalue = v;
+	}
+
+	return v;
+}
+
+/** Function object to be applied by basic::expand(). */
+struct expand_map_function : public map_function {
+	unsigned options;
+	expand_map_function(unsigned o) : options(o) {}
+	ex operator()(const ex & e) { return expand(e, options); }
+};
+
+/** Expand expression, i.e. multiply it out and return the result as a new
+ *  expression. */
+ex basic::expand(unsigned options) const
+{
+	if (nops() == 0)
+		return (options == 0) ? setflag(status_flags::expanded) : *this;
+	else {
+		expand_map_function map_expand(options);
+		return ex_to<basic>(map(map_expand)).setflag(options == 0 ? status_flags::expanded : 0);
+	}
+}
 
-unsigned basic::precedence=70;
-unsigned basic::delta_indent=4;
 
 //////////
-// global constants
+// non-virtual functions in this class
 //////////
 
-const basic some_basic;
-type_info const & typeid_basic=typeid(some_basic);
+// public
+
+/** Compare objects syntactically to establish canonical ordering.
+ *  All compare functions return: -1 for *this less than other, 0 equal,
+ *  1 greater. */
+int basic::compare(const basic & other) const
+{
+	const unsigned hash_this = gethash();
+	const unsigned hash_other = other.gethash();
+	if (hash_this<hash_other) return -1;
+	if (hash_this>hash_other) return 1;
+
+	const unsigned typeid_this = tinfo();
+	const unsigned typeid_other = other.tinfo();
+	if (typeid_this==typeid_other) {
+		GINAC_ASSERT(typeid(*this)==typeid(other));
+// 		int cmpval = compare_same_type(other);
+// 		if (cmpval!=0) {
+// 			std::cout << "hash collision, same type: " 
+// 			          << *this << " and " << other << std::endl;
+// 			this->print(print_tree(std::cout));
+// 			std::cout << " and ";
+// 			other.print(print_tree(std::cout));
+// 			std::cout << std::endl;
+// 		}
+// 		return cmpval;
+		return compare_same_type(other);
+	} else {
+// 		std::cout << "hash collision, different types: " 
+// 		          << *this << " and " << other << std::endl;
+// 		this->print(print_tree(std::cout));
+// 		std::cout << " and ";
+// 		other.print(print_tree(std::cout));
+// 		std::cout << std::endl;
+		return (typeid_this<typeid_other ? -1 : 1);
+	}
+}
+
+/** Test for syntactic equality.
+ *  This is only a quick test, meaning objects should be in the same domain.
+ *  You might have to .expand(), .normal() objects first, depending on the
+ *  domain of your computation, to get a more reliable answer.
+ *
+ *  @see is_equal_same_type */
+bool basic::is_equal(const basic & other) const
+{
+	if (this->gethash()!=other.gethash())
+		return false;
+	if (this->tinfo()!=other.tinfo())
+		return false;
+	
+	GINAC_ASSERT(typeid(*this)==typeid(other));
+	
+	return is_equal_same_type(other);
+}
+
+// protected
+
+/** Stop further evaluation.
+ *
+ *  @see basic::eval */
+const basic & basic::hold() const
+{
+	return setflag(status_flags::evaluated);
+}
+
+/** Ensure the object may be modified without hurting others, throws if this
+ *  is not the case. */
+void basic::ensure_if_modifiable() const
+{
+	if (refcount > 1)
+		throw(std::runtime_error("cannot modify multiply referenced object"));
+	clearflag(status_flags::hash_calculated | status_flags::evaluated);
+}
 
 //////////
 // global variables
 //////////
 
-int max_recursion_level=1024;
+int max_recursion_level = 1024;
+
+} // namespace GiNaC