Use a notation which is closer to what SymPy uses.

Author: Kasper Peeters

core/packages/cdb/sympy/calculus.cnb

@@ -7,20 +7,20 @@
 			"cell_type": "latex",
 			"cells": [
 				{
-					"cell_id": 7825517350706958358,
+					"cell_id": 9687610247019435570,
 					"cell_origin": "client",
 					"cell_type": "latex_view",
-					"source": "\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to a variable.}"
+					"source": "\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to one or more variables.}\n\nThis function mimics the SymPy \\verb|diff| function, except that all expressions need\nto be Cadabra expressions. The function takes an expression and an arbitrary number\nof variables with respect to which to differentiate it."
 				}
 			],
 			"hidden": true,
-			"source": "\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to a variable.}"
+			"source": "\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to one or more variables.}\n\nThis function mimics the SymPy \\verb|diff| function, except that all expressions need\nto be Cadabra expressions. The function takes an expression and an arbitrary number\nof variables with respect to which to differentiate it."
 		},
 		{
 			"cell_id": 3804610120254550473,
 			"cell_origin": "client",
 			"cell_type": "input",
-			"source": "def diff(ex1, ex2):\n   ret = $@(ex1)$\n   sb = SympyBridge(ret)\n   sb.from_sympy( str(sympy.diff( sb.to_sympy(), ex2 ) ) )\n   return ret"
+			"source": "def diff(ex, *args):\n   ret = $@(ex)$\n   sb = SympyBridge(ret)\n   dvars = []\n   for arg in args:\n       sbtmp = SympyBridge(arg)\n       dvars.append( sbtmp.to_sympy() )\n   sb.from_sympy( str(sympy.diff( sb.to_sympy(), *dvars ) ) )\n   return ret"
 		},
 		{
 			"cell_id": 12308609622224851480,
@@ -43,36 +43,44 @@
 			"cell_type": "input",
 			"cells": [
 				{
-					"cell_id": 12523925591190418952,
+					"cell_id": 1348085833411850626,
 					"cell_origin": "server",
 					"cell_type": "latex_view",
 					"cells": [
 						{
-							"cell_id": 1379197150120835065,
+							"cell_id": 16874039423838371410,
 							"cell_origin": "server",
 							"cell_type": "input_form",
-							"source": "\\sin(x) A_{\\mu}(x)"
+							"source": "A_{\\mu}(x) \\cos(x) + \\sin(x) \\partial_{x}(A_{\\mu}(x))"
 						}
 					],
-					"source": "\\begin{dmath*}{}\\sin{x} A_{\\mu}\\left(x\\right)\\end{dmath*}"
-				},
+					"source": "\\begin{dmath*}{}A_{\\mu}\\left(x\\right) \\cos{x}+\\sin{x} \\partial_{x}\\left(A_{\\mu}\\left(x\\right)\\right)\\end{dmath*}"
+				}
+			],
+			"ignore_on_import": true,
+			"source": "diff($\\sin(x) A_{\\mu}(x)$, $x$);"
+		},
+		{
+			"cell_id": 549591636986061462,
+			"cell_origin": "client",
+			"cell_type": "input",
+			"cells": [
 				{
-					"cell_id": 7634624450130909684,
+					"cell_id": 8841772239434008615,
 					"cell_origin": "server",
 					"cell_type": "latex_view",
 					"cells": [
 						{
-							"cell_id": 1252059972554683227,
+							"cell_id": 4066297813555277329,
 							"cell_origin": "server",
 							"cell_type": "input_form",
-							"source": "A_{\\mu}(x) \\cos(x) + \\sin(x) \\partial_{x}(A_{\\mu}(x))"
+							"source": "-\\sin(y) \\cos(x)"
 						}
 					],
-					"source": "\\begin{dmath*}{}A_{\\mu}\\left(x\\right) \\cos{x}+\\sin{x} \\partial_{x}\\left(A_{\\mu}\\left(x\\right)\\right)\\end{dmath*}"
+					"source": "\\begin{dmath*}{}-\\sin{y} \\cos{x}\\end{dmath*}"
 				}
 			],
-			"ignore_on_import": true,
-			"source": "ex:=\\sin(x) A_{\\mu}(x);\ndiff(ex, $x$);"
+			"source": "diff($\\sin(x)\\cos(y)$, $x$, $y$);"
 		},
 		{
 			"cell_id": 6234003092100779795,
@@ -116,12 +124,12 @@
 			"cell_type": "input",
 			"cells": [
 				{
-					"cell_id": 12012117006062441490,
+					"cell_id": 17063052500213847361,
 					"cell_origin": "server",
 					"cell_type": "latex_view",
 					"cells": [
 						{
-							"cell_id": 316157390348515815,
+							"cell_id": 7172967486322218859,
 							"cell_origin": "server",
 							"cell_type": "input_form",
 							"source": " 27/2 "
@@ -154,12 +162,12 @@
 			"cell_type": "input",
 			"cells": [
 				{
-					"cell_id": 15728598564050855914,
+					"cell_id": 5978718279542050921,
 					"cell_origin": "server",
 					"cell_type": "latex_view",
 					"cells": [
 						{
-							"cell_id": 13682162971051715272,
+							"cell_id": 4267217324248610000,
 							"cell_origin": "server",
 							"cell_type": "input_form",
 							"source": " 1/3 (x)**3 y"
@@ -191,12 +199,12 @@
 			"cell_type": "input",
 			"cells": [
 				{
-					"cell_id": 4095815210246821736,
+					"cell_id": 9023252122610197719,
 					"cell_origin": "server",
 					"cell_type": "latex_view",
 					"cells": [
 						{
-							"cell_id": 13733098240311066994,
+							"cell_id": 2730904024514227788,
 							"cell_origin": "server",
 							"cell_type": "input_form",
 							"source": " 1/4 (y)**2"