Fixing map_sympy

Author: kpeeters

core/algorithms/evaluate.cc

@@ -159,6 +159,7 @@ Ex::iterator evaluate::handle_sum(iterator it)
 	auto sib2=sib1;
 	++sib2;
 	while(sib2!=tr.end(it)) {
+		std::cerr << "merging components " << Ex(sib1) << " and " << Ex(sib2) << std::endl;
 		merge_components(sib1, sib2);
 		sib2=tr.erase(sib2);
 		}

core/algorithms/map_sympy.cc

@@ -13,22 +13,80 @@ map_sympy::map_sympy(const Kernel& k, Ex& tr, const std::string& head)
 
 bool map_sympy::can_apply(iterator st)
 	{
+	left.clear();
+	index_factors.clear();
 	index_map_t ind_free, ind_dummy;
 	classify_indices(st, ind_free, ind_dummy);
+
+	bool still_ok=true;
+
+	// Determine if any of the free indices are harmless (Coordinates or Symbols).
 	for(auto& ind: ind_free) {
 		const Coordinate *cdn=kernel.properties.get_composite<Coordinate>(ind.second, true);
 		const Symbol     *smb=kernel.properties.get_composite<Symbol>(ind.second, true);
-		if(cdn==0 && smb==0)
-			return false;
+		if(cdn==0 && smb==0) {
+			still_ok=false;
+			break;
+			}
+		}
+
+	if(still_ok && ind_dummy.size()==0) return true;
+	
+   // In a product, it is still possible that there is a sub-product which
+	// contains no indices.
+	if(*st->name=="\\prod") {
+		for(auto& ind: ind_free) {
+			const Coordinate *cdn=kernel.properties.get_composite<Coordinate>(ind.second, true);
+			const Symbol     *smb=kernel.properties.get_composite<Symbol>(ind.second, true);
+			if(cdn==0 && smb==0) {
+				auto fac=tr.parent(ind.second);
+				while(tr.parent(fac)!=iterator(st))
+					fac=tr.parent(fac);
+				index_factors.insert(fac);
+				}
+			}
+		for(auto& ind: ind_dummy) {
+			const Coordinate *cdn=kernel.properties.get_composite<Coordinate>(ind.second, true);
+			const Symbol     *smb=kernel.properties.get_composite<Symbol>(ind.second, true);
+			if(cdn==0 && smb==0) {
+				auto fac=tr.parent(ind.second);
+				while(tr.parent(fac)!=iterator(st))
+					fac=tr.parent(fac);
+				index_factors.insert(fac);
+				}
+			}
+		sibling_iterator sib=tr.begin(st);
+		while(sib!=tr.end(st)) {
+			if(index_factors.find(iterator(sib))==index_factors.end())
+				left.push_back(sib);
+			++sib;
+			}
+		return left.size()>0;
 		}
-	return (ind_dummy.size()==0);
+
+	return false;
 	}
 
 Algorithm::result_t map_sympy::apply(iterator& it)
 	{
 	std::vector<std::string> wrap;
 	wrap.push_back(head_);
-	sympy::apply(kernel, tr, it, wrap, "", "");
-	it.skip_children();
-	return result_t::l_applied;
+
+	if(left.size()>0) {
+		std::cerr << "Sub-product with " << left.size() << " non-index carrying factors" << std::endl;
+		Ex prod("\\prod");
+		for(auto& fac: left)
+			prod.append_child(fac);
+		auto top=prod.begin();
+		sympy::apply(kernel, prod, top, wrap, "", "");
+		for(auto& kl: index_factors)
+			tr.erase(kl);
+		
+		return result_t::l_no_action;
+		}
+	else {
+		sympy::apply(kernel, tr, it, wrap, "", "");
+		it.skip_children();
+		return result_t::l_applied;
+		}
 	}

core/algorithms/map_sympy.hh

@@ -19,7 +19,9 @@ class map_sympy : public Algorithm {
 		virtual result_t apply(iterator&);
 
 	private:
-		std::string head_;
+		std::string               head_;
+		std::vector<Ex::iterator> left;
+		std::set<Ex::iterator>    index_factors;
 };
 
 }

doc/cadabra2_hep.tex

@@ -333,7 +333,7 @@ \subsection{Tensors, indices and symmetries}
 \botrule
 The first line indicates that the tensor has the symmetries of the
 \raisebox{2ex}{$\ftableau{ac,bd}$} tableau (the numbers in the \verb|indices| argument
-refer to the index positions). The \verb|canonicalise| command writes
+refer to the index positions). The \verb|canonicalise| algorithm writes
 the input in canonical form with respect to mono-term symmetries
 (anti-symmetry in the two index pairs and symmetry under pair
 exchange). The Ricci symmetry is also encoded in the Young tableau and
@@ -421,10 +421,10 @@ \subsection{Bianchi, Ricci and Schouten identities}
 have seen earlier.} Here it effectively associates the $\nabla$
 operator to the Riemann tensor. We can see this in action, for
 instance, by verifying that the Bianchi identity indeed holds,
-\footnote{The ``2'' following the exclamation mark on
-  {\tt @young\_project\_tensor!2(\%)} indicates that this command should
-  only be applied at ``level 2'' of the expression, i.e.~at the level
-  of the terms of the sum.}
+\footnote{The {\tt depth=1} parameter of the
+  {\tt young\_project\_tensor} algorithm indicates that this command
+  should only be applied at ``level 1'' of the expression, i.e.~at the
+  level of the terms of the sum.}
 \end{cdbcom}
 \begin{cdbcont}
 ex:= \nabla_{m}{R_{p q r s}} + \nabla_{p}{R_{q m r s}} + \nabla_{q}{R_{m p r s}}:

tests/components.cdb

@@ -452,3 +452,19 @@ test23()
 # ex:= \partial_{a}{ A_{b} };
 # rl:= \partial_{r}{ A_{t} } = 1;
 # evaluate(ex, rl);
+
+{\theta, \varphi}::Coordinate;
+{\alpha, \beta, \gamma, \delta, \rho, \sigma, \mu, \nu, \lambda}::Indices(values={\varphi, \theta}, position=fixed);
+\partial{#}::PartialDerivative;
+g_{\alpha\beta}::Metric.
+g^{\alpha\beta}::InverseMetric.
+
+sphe:={ g_{\theta\theta} = r**2,
+         g_{\varphi\varphi} = r**2 \sin(\theta)**2 }.
+complete(sphe, $g^{\alpha\beta}$);
+
+ch:= \Gamma^{\alpha}_{\mu\nu} = 1/2 g^{\alpha\beta} ( \partial_{\nu}{g_{\beta\mu}}
+                                                      +\partial_{\mu}{g_{\beta\nu}}
+                                                      -\partial_{\beta}{g_{\mu\nu}} );
+
+evaluate(ch, sphe, rhsonly=True);

tests/display.cnb

@@ -9,20 +9,20 @@
 				{
 					"cell_origin" : "server",
 					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}\\text{Attached property PartialDerivative to~}\\partial{\\#}.\\end{dmath*}"
+					"source" : "\\begin{dmath*}{}\\text{Attached property Coordinate to~}r.\\end{dmath*}"
 				},
 				{
 					"cell_origin" : "server",
 					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}\\text{Attached property Depends to~}A.\\end{dmath*}"
+					"source" : "\\begin{dmath*}{}\\text{Attached property PartialDerivative to~}\\partial{\\#}.\\end{dmath*}"
 				},
 				{
 					"cell_origin" : "server",
 					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}\\text{Attached property Coordinate to~}r.\\end{dmath*}"
+					"source" : "\\begin{dmath*}{}\\text{Attached property Depends to~}A.\\end{dmath*}"
 				}
 			],
-			"source" : "\\partial{#}::PartialDerivative;\nA::Depends(r);\nr::Coordinate;"
+			"source" : "r::Coordinate;\n\\partial{#}::PartialDerivative;\nA::Depends(r);"
 		},
 		{
 			"cell_origin" : "client",
@@ -48,20 +48,7 @@
 					"source" : "\\begin{dmath*}{}4{r}^{2}+\\frac{1}{2}\\left(-\\cos{4A}+1\\right) {\\left(\\partial_{r}{A}\\right)}^{2}+4{A}^{2} {\\left(\\partial_{r}{A}\\right)}^{2}\\end{dmath*}"
 				}
 			],
-			"source" : "scas(ex,\"simplify\");"
-		},
-		{
-			"cell_origin" : "client",
-			"cell_type" : "input",
-			"cells" : 
-			[
-				{
-					"cell_origin" : "server",
-					"cell_type" : "output",
-					"source" : "\\begin{verbatim}{\\sum}  (0x7f26d4029738)\n  1:{\\pow}  (0x7f26d401f8d8)\n  2:  {\\partial}  (0x7f26d4021e78)\n  3:    _{r}  (0x7f26d4033008)\n  4:    {\\pow}  (0x7f26d4033058)\n  5:      {\\sin}  (0x7f26d40341c8)\n  6:        {A}  (0x7f26d400b148)\n  7:      {1}  2  (0x7f26d4034218)\n  8:  {1}  2  (0x7f26d4044828)\n  9:{\\pow}  (0x7f26d4044878)\n 10:  {\\partial}  (0x7f26d4027ca8)\n 11:    _{r}  (0x7f26d4027cf8)\n 12:    {\\pow}  (0x7f26d4031228)\n 13:      {A}  (0x7f26d4031278)\n 14:      {1}  2  (0x7f26d40344b8)\n 15:  {1}  2  (0x7f26d4034508)\n 16:{\\pow}  (0x7f26d4027e88)\n 17:  {\\partial}  (0x7f26d4027ed8)\n 18:    _{r}  (0x7f26d4046c18)\n 19:    {\\pow}  (0x7f26d4046c68)\n 20:      {r}  (0x7f26d4036bf8)\n 21:      {1}  2  (0x7f26d4036c48)\n 22:  {1}  2  (0x7f26d4036c98)\n\n\\end{verbatim}"
-				}
-			],
-			"source" : "print(tree(ex))"
+			"source" : "map_sympy(ex,\"simplify\");"
 		},
 		{
 			"cell_origin" : "client",
@@ -87,25 +74,7 @@
 					"source" : "\\begin{dmath*}{}2r\\end{dmath*}"
 				}
 			],
-			"source" : "ex3=scas(ex2, \"simplify\");"
-		},
-		{
-			"cell_origin" : "client",
-			"cell_type" : "input",
-			"cells" : 
-			[
-				{
-					"cell_origin" : "server",
-					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}\\partial_{r}{{r}^{2}}\\end{dmath*}"
-				},
-				{
-					"cell_origin" : "server",
-					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}2r\\end{dmath*}"
-				}
-			],
-			"source" : "ex2;\nex3;"
+			"source" : "ex3=map_sympy(ex2, \"simplify\");"
 		},
 		{
 			"cell_origin" : "client",
@@ -115,7 +84,7 @@
 				{
 					"cell_origin" : "server",
 					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}4 r^{2} + 4 A^{2}{\\left (r \\right )} \\frac{d}{d r} A{\\left (r \\right )}^{2} + 4 \\sin^{2}{\\left (A{\\left (r \\right )} \\right )} \\cos^{2}{\\left (A{\\left (r \\right )} \\right )} \\frac{d}{d r} A{\\left (r \\right )}^{2}\\end{dmath*}"
+					"source" : "\\begin{dmath*}{}4 r^{2} + \\left(- \\frac{1}{2} \\cos{\\left (4 A{\\left (r \\right )} \\right )} + \\frac{1}{2}\\right) \\frac{d}{d r} A{\\left (r \\right )}^{2} + 4 A^{2}{\\left (r \\right )} \\frac{d}{d r} A{\\left (r \\right )}^{2}\\end{dmath*}"
 				},
 				{
 					"cell_origin" : "server",
@@ -133,7 +102,7 @@
 				{
 					"cell_origin" : "server",
 					"cell_type" : "latex_view",
-					"source" : "\\begin{dmath*}{}{\\left(\\partial_{r}{{\\left(\\sin{A}\\right)}^{2}}\\right)}^{2}+{\\left(\\partial_{r}{{A}^{2}}\\right)}^{2}+{\\left(\\partial_{r}{{r}^{2}}\\right)}^{2}\\end{dmath*}"
+					"source" : "\\begin{dmath*}{}4{r}^{2}+\\frac{1}{2}\\left(-\\cos{4A}+1\\right) {\\left(\\partial_{r}{A}\\right)}^{2}+4{A}^{2} {\\left(\\partial_{r}{A}\\right)}^{2}\\end{dmath*}"
 				}
 			],
 			"source" : "ex;"

tests/paper.cdb

@@ -129,6 +129,16 @@ print(timeit.timeit(test08,number=1))
 
 #-------
 
+def test0b():
+    __cdbkernel__=create_scope() 
+    \ftableau{#}::FilledTableau(dimension=10);
+    ex:=\ftableau{0,0}{1,1} \ftableau{a,a}{b,b};
+    lr_tensor(_);    
+
+print(timeit.timeit(test08b, number=1))
+        
+#-------
+
 def test09():
     __cdbkernel__=create_scope()