DisplayMMA.cc

#include "Storage.hh"
#include "Algorithm.hh"
#include "Functional.hh"
#include "DisplayMMA.hh"
#include "PreClean.hh"
#include "properties/Depends.hh"
#include "properties/Accent.hh"
#include <regex>

using namespace cadabra;

DisplayMMA::DisplayMMA(const Kernel& kernel, const Ex& e, bool uuc)
	: DisplayBase(kernel, e), use_unicode(uuc)
	{
	symmap = {
			{"\\cos",  "Cos"},
			{"\\sin",  "Sin"},
			{"\\tan",  "Tan"},
			{"\\sec",  "Sec"},
			{"\\csc",  "Csc"},
			{"\\cot",  "Cot"},

			{"\\cosh", "Cosh"},
			{"\\sinh", "Sinh"},
			{"\\tanh", "Tanh"},

			{"\\scsh", "Sech"},
			{"\\csch", "Csch"},
			{"\\coth", "Coth"},

			{"\\log", "Log"},
			{"\\int", "Integrate" },
			{"\\matrix", "Matrix" },
			{"\\sum", "Plus" },
			{"\\exp", "Exp" },
			{"\\sqrt", "Sqrt" },
			{"\\prod", "Times" },
			{"\\pow",  "Power" },
			{"\\frac", "Rational" },

			{"\\infty",   "Infinity"},

			{"\\alpha",   "α" },
			{"\\beta",    "β" },  // beta seems to be reserved
			{"\\gamma",   "γ" }, // gamma seems to be reserved
			{"\\delta",   "δ" },
			{"\\epsilon", "ε" },
			{"\\zeta",    "ζ" },
			{"\\eta",     "η" },
			{"\\theta",   "θ" },
			{"\\iota",    "ι" },
			{"\\kappa",   "κ" },
			{"\\lambda",  "λ" }, // lambda is reserved
			{"\\mu",      "μ" },
			{"\\nu",      "ν" },
			{"\\xi",      "ξ" },
			{"\\omicron", "ο" },
			{"\\pi",      "π" },
			{"\\rho",     "ρ" },
			{"\\sigma",   "σ" },
			{"\\tau",     "τ" },
			{"\\upsilon", "υ" },
			{"\\phi",     "ϕ" },
			{"\\chi",     "χ" },
			{"\\psi",     "ψ" },
			{"\\omega",   "ω" },

			{"\\Alpha",   "Α" },
			{"\\Beta",    "Β" },
			{"\\Gamma",   "Γ" },
			{"\\Delta",   "Δ" },
			{"\\Epsilon", "Ε" },
			{"\\Zeta",    "Ζ" },
			{"\\Eta",     "Η" },
			{"\\Theta",   "ϴ" },
			{"\\Iota",    "Ι" },
			{"\\Kappa",   "Κ" },
			{"\\Lambda",  "Λ" },
			{"\\Mu",      "Μ" },
			{"\\Nu",      "Ν" },
			{"\\Xi",      "Ξ" },
			{"\\Omicron", "Ο" },
			{"\\Pi",      "Π" },
			{"\\Rho",     "Ρ" },
			{"\\Sigma",   "Σ" },
			{"\\Tau",     "Τ" },
			{"\\Upsilon", "Υ" },
			{"\\Phi",     "Φ" },
			{"\\Chi",     "Χ" },
			{"\\Psi",     "Ψ" },
			{"\\Omega",   "Ω" },

			{"\\partial", "Derivative"}
		};

	regex_map = {
			{"\\alpha",   R"(\[Alpha])"   },
			{"\\beta",    R"(\[Beta])"    },
			{"\\gamma",   R"(\[Gamma])"   },
			{"\\delta",   R"(\[Delta])"   },
			{"\\epsilon", R"(\[Epsilon])" },
			{"\\zeta",    R"(\[Zeta])"    },
			{"\\eta",     R"(\[Eta])"     },
			{"\\theta",   R"(\[Theta])"   },
			{"\\iota",    R"(\[Iota])"    },
			{"\\kappa",   R"(\[Kappa])"   },
			{"\\lambda",  R"(\[Lamda])"   },
			{"\\mu",      R"(\[Mu])"      },
			{"\\nu",      R"(\[Nu])"      },
			{"\\xi",      R"(\[Xi])"      },
			{"\\omicron", R"(\[Omicron])" },
			{"\\pi",      R"(\[Pi])"      },
			{"\\pi",      R"(Pi)"              },
			{"\\rho",     R"(\[Rho])"     },
			{"\\sigma",   R"(\[Sigma])"   },
			{"\\tau",     R"(\[Tau])"     },
			{"\\upsilon", R"(\[Upsilon])" },
			{"\\phi",     R"(\[Phi])"     },
			{"\\varphi",  R"(\[CurlyPhi])"},
			{"\\chi",     R"(\[Chi])"     },
			{"\\psi",     R"(\[Psi])"     },
			{"\\omega",   R"(\[Omega])"   },

			{"\\Alpha",   R"(\[CapitalAlpha])"   },
			{"\\Beta",    R"(\[CapitalBeta])"    },
			{"\\Gamma",   R"(\[CapitalGamma])"   },
			{"\\Delta",   R"(\[CapitalDelta])"   },
			{"\\Epsilon", R"(\[CapitalEpsilon])" },
			{"\\Zeta",    R"(\[CapitalZeta])"    },
			{"\\Eta",     R"(\[CapitalEta])"     },
			{"\\Theta",   R"(\[CapitalTheta])"   },
			{"\\Iota",    R"(\[CapitalIota])"    },
			{"\\Kappa",   R"(\[CapitalKappa])"   },
			{"\\Lambda",  R"(\[CapitalLamda])"   },
			{"\\Mu",      R"(\[CapitalMu])"      },
			{"\\Nu",      R"(\[CapitalNu])"      },
			{"\\Xi",      R"(\[CapitalXi])"      },
			{"\\Omicron", R"(\[CapitalOmicron])" },
			{"\\Pi",      R"(\[CapitalPi])"      },
			{"\\Rho",     R"(\[CapitalRho])"     },
			{"\\Sigma",   R"(\[CapitalSigma])"   },
			{"\\Tau",     R"(\[CapitalTau])"     },
			{"\\Upsilon", R"(\[CapitalUpsilon])" },
			{"\\Phi",     R"(\[CapitalPhi])"     },
			{"\\Chi",     R"(\[CapitalChi])"     },
			{"\\Psi",     R"(\[CapitalPsi])"     },
			{"\\Omega",   R"(\[CapitalOmega])"   },
		};
	}

//TODO: complete this list

bool DisplayMMA::needs_brackets(Ex::iterator it)
	{
	// FIXME: may need looking at properties
	// FIXME: write as individual parent/current tests
	if(tree.is_head(it)) return false;

	std::string parent=*tree.parent(it)->name;
	std::string child =*it->name;


	if(*tree.parent(it)->name=="\\prod" || *tree.parent(it)->name=="\\frac" || *tree.parent(it)->name=="\\pow") {
		if(*it->name=="\\sum" || *it->name=="\\prod") return true;
		if(parent=="\\pow" && ( (tree.index(it)==0 && !it->is_integer()) || child=="\\sum" || child=="\\prod" || child=="\\pow")  ) return true;
		}
	else if(it->fl.parent_rel==str_node::p_none) {
		if(*it->name=="\\sum") return false;
		}
	else {
		if(*it->name=="\\sum")  return true;
		if(*it->name=="\\prod") return true;
		}
	return false;
	}


void DisplayMMA::print_other(std::ostream& str, Ex::iterator it)
	{
	if(needs_brackets(it))
		str << "(";

	// print multiplier and object name
	if(*it->multiplier!=1)
		print_multiplier(str, it);

	if(*it->name=="1") {
		if(*it->multiplier==1 || (*it->multiplier==-1)) // this would print nothing altogether.
			str << "1";

		if(needs_brackets(it))
			str << ")";
		return;
		}

	//	const Accent *ac=properties.get<Accent>(it);
	//	if(!ac) { // accents should never get additional curly brackets, {\bar}{g} does not print.
	//		Ex::sibling_iterator sib=tree.begin(it);
	//		while(sib!=tree.end(it)) {
	//			if(sib->is_index())
	//				needs_extra_brackets=true;
	//			++sib;
	//			}
	//		}

	auto sbit=*it->name;
	if(!use_unicode) {
		auto rn = regex_map.find(sbit);
		if(rn!=regex_map.end())
			sbit = rn->second;
		}
	auto rn = symmap.find(sbit);
	if(rn!=symmap.end())
		str << rn->second;
	else
		str << sbit;

	print_children(str, it);

	if(needs_brackets(it))
		str << ")";
	}

void DisplayMMA::print_children(std::ostream& str, Ex::iterator it, int )
	{
	// Mathematica has no notion of children with different parent relations; it's all
	// functions of functions kind of stuff. What we will do is print upper and
	// lower indices as 'UP(..)' and 'DN(..)' type arguments, and then convert
	// them back later.

	// We need to know if the symbol has implicit dependence on other symbols,
	// as this needs to be made explicit for sympy. We need to strip this
	// dependence off later again.

	const Depends *dep=kernel.properties.get<Depends>(it);
	if(dep) {
		depsyms[it->name]=dep->dependencies(kernel, it);
		//		std::cerr << *it->name << "depends on " << depsyms[it->name] << std::endl;
		}

	Ex::sibling_iterator ch=tree.begin(it);
	if(ch!=tree.end(it) || dep!=0) {
		str << "[";
		bool first=true;
		while(ch!=tree.end(it)) {
			if(first) first=false;
			else      str << ", ";
			if(ch->fl.parent_rel==str_node::p_super)
				str << "UP";
			if(ch->fl.parent_rel==str_node::p_sub)
				str << "DN";

			dispatch(str, ch);

			//			if(ch->fl.parent_rel==str_node::p_super || ch->fl.parent_rel==str_node::p_sub)
			//				str << "]";
			++ch;
			}
		if(dep) {
			if(!first) str << ", ";
			Ex deplist=dep->dependencies(kernel, it);
			// deplist is always a \comma node
			auto sib=tree.begin(deplist.begin());
			while(sib!=tree.end(deplist.begin())) {
				dispatch(str, sib);
				++sib;
				if(sib!=tree.end(deplist.begin()))
					str << ", ";
				}
			//
			//			DisplayMMA ds(kernel, deplist);
			//			ds.output(str);
			}
		str << "]";
		}
	}

void DisplayMMA::print_multiplier(std::ostream& str, Ex::iterator it)
	{
	bool suppress_star=false;
	mpz_class denom=it->multiplier->get_den();

	if(denom!=1) {
		if(false && it->multiplier->get_num()<0)
			str << "(" << it->multiplier->get_num() << ")";
		else
			str << it->multiplier->get_num();
		str << "/" << it->multiplier->get_den();
		}
	else if(*it->multiplier==-1) {
		str << "-";
		suppress_star=true;
		}
	else {
		str << *it->multiplier;
		}

	if(!suppress_star && !(*it->name=="1"))
		str << "*";
	}

void DisplayMMA::print_opening_bracket(std::ostream& str, str_node::bracket_t br)
	{
	switch(br) {
		case str_node::b_pointy:
		case str_node::b_curly:
			throw NotYetImplemented("curly/pointy bracket type");
		case str_node::b_none:
			str << "[";
			break;
		case str_node::b_round:
			str << "[";
			break;
		case str_node::b_square:
			str << "[";
			break;
		default :
			return;
		}
	}

void DisplayMMA::print_closing_bracket(std::ostream& str, str_node::bracket_t br)
	{
	switch(br) {
		case str_node::b_pointy:
		case str_node::b_curly:
			throw NotYetImplemented("curly/pointy bracket type");
		case str_node::b_none:
			str << "]";
			break;
		case str_node::b_round:
			str << "]";
			break;
		case str_node::b_square:
			str << "]";
			break;
		default :
			return;
		}
	}

void DisplayMMA::print_parent_rel(std::ostream& str, str_node::parent_rel_t pr, bool )
	{
	switch(pr) {
		case str_node::p_super:
		case str_node::p_sub:
			throw NotYetImplemented("MMA print of indices");
		case str_node::p_property:
			throw NotYetImplemented("MMA print of properties");
		case str_node::p_exponent:
			str << "^";
			break;
		case str_node::p_none:
			break;
		case str_node::p_components:
			break;
		case str_node::p_invalid:
			throw std::logic_error("DisplayMMA: p_invalid not handled.");
		}
	}

void DisplayMMA::dispatch(std::ostream& str, Ex::iterator it)
	{
	// The node names below should only be reserved node names; all others
	// should be looked up using properties. FIXME
	if(*it->name=="\\prod")        print_productlike(str, it, "*");
	else if(*it->name=="\\sum")    print_sumlike(str, it);
	else if(*it->name=="\\frac")   print_fraclike(str, it);
	else if(*it->name=="\\comma")  print_commalike(str, it);
	else if(*it->name=="\\arrow")  print_arrowlike(str, it);
	else if(*it->name=="\\pow")    print_powlike(str, it);
	else if(*it->name=="\\int")    print_intlike(str, it);
	else if(*it->name=="\\sum")    print_intlike(str, it);
	else if(*it->name=="\\equals") print_equalitylike(str, it);
	else if(*it->name=="\\components") print_components(str, it);
	else if(*it->name=="\\partial") print_partial(str, it);
	else if(*it->name=="\\matrix") print_matrix(str, it);
	else                           print_other(str, it);
	}

void DisplayMMA::print_commalike(std::ostream& str, Ex::iterator it)
	{
	Ex::sibling_iterator sib=tree.begin(it);
	bool first=true;
	str << "{";
	while(sib!=tree.end(it)) {
		if(first)
			first=false;
		else
			str << ", ";
		dispatch(str, sib);
		++sib;
		}
	str << "}";
	//print_closing_bracket(str, (*it).fl.bracket, str_node::p_none);
	}

void DisplayMMA::print_arrowlike(std::ostream& str, Ex::iterator it)
	{
	Ex::sibling_iterator sib=tree.begin(it);
	dispatch(str, sib);
	str << " -> ";
	++sib;
	dispatch(str, sib);
	}

void DisplayMMA::print_fraclike(std::ostream& str, Ex::iterator it)
	{
	Ex::sibling_iterator num=tree.begin(it), den=num;
	++den;

	if(*it->multiplier!=1) {
		print_multiplier(str, it);
		}
	dispatch(str, num);

	str << "/(";

	dispatch(str, den);

	str << ")";
	}

void DisplayMMA::print_productlike(std::ostream& str, Ex::iterator it, const std::string& inbetween)
	{
	if(needs_brackets(it))
		str << "(";

	if(*it->multiplier!=1) {
		print_multiplier(str, it);
		//		Ex::sibling_iterator st=tree.begin(it);
		}

	// To print \prod{\sum{a}{b}}{\sum{c}{d}} correctly:
	// If there is any sum as child, and if the sum children do not
	// all have the same bracket type (different from b_none or b_no),
	// then print brackets.

	str_node::bracket_t previous_bracket_=str_node::b_invalid;
//	bool beginning_of_group=true;
	Ex::sibling_iterator ch=tree.begin(it);
	while(ch!=tree.end(it)) {
		str_node::bracket_t current_bracket_=(*ch).fl.bracket;
		if(previous_bracket_!=current_bracket_) {
			if(current_bracket_!=str_node::b_none) {
				print_opening_bracket(str, current_bracket_);
//				beginning_of_group=true;
				}
			}
		dispatch(str, ch);
		++ch;
		if(ch==tree.end(it)) {
			if(current_bracket_!=str_node::b_none)
				print_closing_bracket(str, current_bracket_);
			}

		if(ch!=tree.end(it)) {
			str << inbetween;
			}
		previous_bracket_=current_bracket_;
		}

	if(needs_brackets(it))
		str << ")";
	//	if(close_bracket) str << ")";
	}

void DisplayMMA::print_sumlike(std::ostream& str, Ex::iterator it)
	{
	assert(*it->multiplier==1);

	if(needs_brackets(it))
		str << "(";

	unsigned int steps=0;

	Ex::sibling_iterator ch=tree.begin(it);
	while(ch!=tree.end(it)) {
		if(++steps==20) {
			steps=0;
			}
		if(*ch->multiplier>=0 && ch!=tree.begin(it))
			str << "+";

		dispatch(str, ch);
		++ch;
		}

	if(needs_brackets(it))
		str << ")";
	str << std::flush;
	}

void DisplayMMA::print_powlike(std::ostream& str, Ex::iterator it)
	{
	if(needs_brackets(it))
		str << "(";

	Ex::sibling_iterator sib=tree.begin(it);
	if(*it->multiplier!=1)
		print_multiplier(str, it);
	dispatch(str, sib);
	str << "^(";
	++sib;
	dispatch(str, sib);
	str << ")";

	if(needs_brackets(it))
		str << ")";
	}

void DisplayMMA::print_intlike(std::ostream& str, Ex::iterator it)
	{
	if(*it->multiplier!=1)
		print_multiplier(str, it);
	str << symmap[*it->name] << "[";
	Ex::sibling_iterator sib=tree.begin(it);
	dispatch(str, sib);
	++sib;
	if(tree.is_valid(sib)) {
		str << ", ";
		dispatch(str, sib);
		}
	str << "]";
	}

void DisplayMMA::print_equalitylike(std::ostream& str, Ex::iterator it)
	{
	Ex::sibling_iterator sib=tree.begin(it);
	dispatch(str, sib);
	str << " == ";
	++sib;
	if(sib==tree.end(it))
		throw ConsistencyException("Found equals node with only one child node.");
	dispatch(str, sib);
	}

void DisplayMMA::print_components(std::ostream& str, Ex::iterator it)
	{
	str << *it->name;
	auto sib=tree.begin(it);
	auto end=tree.end(it);
	--end;
	while(sib!=end) {
		dispatch(str, sib);
		++sib;
		}
	str << "\n";
	sib=tree.begin(end);
	while(sib!=tree.end(end)) {
		str << "    ";
		dispatch(str, sib);
		str << "\n";
		++sib;
		}
	}

void DisplayMMA::print_partial(std::ostream& str, Ex::iterator it)
	{
	if(*it->multiplier!=1)
		print_multiplier(str, it);

	str << "D[";
	Ex::sibling_iterator sib=tree.begin(it);
	while(sib!=tree.end(it)) {
		if(sib->fl.parent_rel==str_node::p_none) {
			dispatch(str, sib);
			break;
			}
		++sib;
		}
	sib=tree.begin(it);
	while(sib!=tree.end(it)) {
		if(sib->fl.parent_rel!=str_node::p_none) {
			str << ", ";
			dispatch(str, sib);
			}
		++sib;
		}
	str << "]";
	}

void DisplayMMA::print_matrix(std::ostream& str, Ex::iterator it)
	{
	str << "Matrix([";
	auto comma=tree.begin(it);
	Ex::sibling_iterator row_it = tree.begin(comma);
	while(row_it!=tree.end(comma)) {
		if(row_it!=tree.begin(comma)) str << ", ";
		Ex::sibling_iterator col_it = tree.begin(row_it);
		str << "[";
		while(col_it!=tree.end(row_it)) {
			if(col_it!=tree.begin(row_it)) str << ", ";
			dispatch(str, col_it);
			++col_it;
			}
		str << "]";
		++row_it;
		}
	str << "])";
	}

bool DisplayMMA::children_have_brackets(Ex::iterator ch) const
	{
	Ex::sibling_iterator chlds=tree.begin(ch);
	str_node::bracket_t childbr=chlds->fl.bracket;
	if(childbr==str_node::b_none || childbr==str_node::b_no)
		return false;
	else return true;
	}

std::string DisplayMMA::preparse_import(const std::string& in)
	{
	std::string ret = in;
	// MMA sends doubled backslash characters, reduce them first.
	ret = replace_all(ret, "\\\\", "\\");
	for(auto& r: regex_map) {
		ret = replace_all(ret, r.second, r.first);
		}
	return ret;
	}

void DisplayMMA::import(Ex& ex)
	{
	cadabra::do_subtree<Ex>(ex, ex.begin(), [&](Ex::iterator it) -> Ex::iterator {
		// Mathematica wraps everything in square brackets, set these to
		// b_none;
		it->fl.bracket=str_node::b_none;

		// Convert symbols.
		for(auto& m: symmap)
			{
			// If we have converted the name of this symbol, convert back.
			if(m.second==*it->name) {
				it->name=name_set.insert(m.first).first;
				break;
				}
			}

		// Move child nodes of partial to the right place.
		// We have to fix the notation for Derivative. A derivative
		// of the type
		//    \partial_{r t t}{f}
		// gets produced as
		//    Derivative[1][2][f][r][t]
		// which at first instance reads
		//    \partial{1}{2}{f}{r}{t}
		// This is even true for simple 1st order derivatives.
		// For 'm' arguments, we have '(m-1)/2' variables.
		
		if(*it->name=="\\partial")
			{
//			std::cerr << "to convert: " << Ex(it) << std::endl;
			int n=ex.number_of_children(it);
			if(n<3 || n%2!=1)
				throw ConsistencyException("Returned unparseable derivative.");
			
			n=(n-1)/2;
			std::vector<int> nums;
			auto args = ex.begin(it);
			for(int i=0; i<n; ++i) {
				nums.push_back( to_long(*(args->multiplier)) );
				args=ex.erase(args);
				}

			args=ex.begin(it);
			++args;
			int p=0;
			while(args!=ex.end(it)) {
				auto nxt=args;
				++nxt;
				for(int i=0; i<nums[p]; ++i)
					ex.insert_subtree(ex.begin(it), args)->fl.parent_rel=str_node::p_sub;
				args=ex.erase(args);
				++p;
				}
			}

		// See if we have added dependencies to this symbol (lookup in map).
		// If yes, strip them off again.
		auto fnd = depsyms.find(it->name);
		if(fnd!=depsyms.end())
			{
			auto args=ex.begin(it);
			// Strip out only those symbols which have been added.
			while(args!=ex.end(it)) {
				if(args->fl.parent_rel==str_node::p_none) {
					auto findsib=fnd->second.begin(fnd->second.begin());
					bool removed=false;
					while(findsib!=fnd->second.end(fnd->second.begin())) {
						if(subtree_equal(0, findsib, args)) {
							args=ex.erase(args);
							removed=true;
							break;
							}
						++findsib;
						}
					if(!removed)
						++args;
					}
				else
					++args;
				}
			//				std::cerr << "stripping from " << *it->name << std::endl;
			////				if(*ex.begin(it)->name=="\\comma")
			//				ex.erase(ex.begin(it));
			}


		return it;
		});
	}