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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 106369, 3508]*) (*NotebookOutlinePosition[ 110174, 3610]*) (* CellTagsIndexPosition[ 109556, 3592]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["An Introduction to Names and Contexts", "Title"], Cell[CellGroupData[{ Cell["\<\ Bernd Thaller Institute of Mathematics University of Graz Austria\ \>", "Subsubsection"], Cell["\<\ You should start a new kernel session before evaluating the \ commands in this notebook. Since this notebook frequently switches contexts, \ the output critically depends on the order in which previous inputs are \ executed. If you get confused and can't reproduce some output, it is better \ to quit the kernel and evaluate all input cells in the order of the notebook.\ \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "The full name of a symbol in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Section"], Cell[TextData[{ "The name of a ", StyleBox["Mathematica", FontSlant->"Italic"], " symbol consists of a context and a short name. Normally, you can only see \ the short name of a symbol. The full name looks like ", StyleBox["context`shortname", FontSlant->"Italic"], ", for example, ", StyleBox["System`Sin", "Output"], ". The character ` separates the context from the short name." }], "Text"], Cell[TextData[{ "In order to write ", StyleBox["Mathematica", FontSlant->"Italic"], " packages you need to know about contexts." }], "Text"], Cell[TextData[{ "At any time during a ", StyleBox["Mathematica", FontSlant->"Italic"], " session, there is a currently active context. For a new kernel session, \ the name of this context is ", StyleBox["Global`", "Output"], ". (Don't forget the ` at the end of the context name). The name of the \ current context is stored in the variable ", StyleBox["$Context", "Output"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Context\)], "Input", CellLabel->"In[1]:="], Cell[BoxData[ \("Global`"\)], "Output", CellLabel->"Out[1]="] }, Open ]], Cell[TextData[{ "If you create a symbol during a ", StyleBox["Mathematica", FontSlant->"Italic"], " session, then the symbol is internally stored with its full name, i.e., \ with the name of the context in front. But whenever the context of the symbol \ coincides with the current context, ", StyleBox["Mathematica", FontSlant->"Italic"], " only displays the short name, and you can't see the context name." }], "Text"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " provides easy ways to define new contexts and to switch to other \ contexts. A context thus provides an environment, where the names of symbols \ have a local meaning so that they don't conflict with the names of other \ symbols." }], "Text"], Cell["Let us consider an example: Define a new function", "Text"], Cell[BoxData[ \(func[x_] := x^2\)], "Input", CellLabel->"In[2]:="], Cell["\<\ You can see the context by asking the kernel to display the \ definitions known for the symbol func\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?func\)\)], "Input", CellLabel->"In[3]:="], Cell["Global`func", "Print", CellTags->"Info3290493981-8161803"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(func[x_] := x\^2\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "func"], Editable->False]], "Print", CellTags->"Info3290493981-8161803"] }, Open ]], Cell["You can also ask directly for the context:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Context[func]\)], "Input", CellLabel->"In[4]:="], Cell[BoxData[ \("Global`"\)], "Output", CellLabel->"Out[4]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Switching the context", "Section"], Cell[CellGroupData[{ Cell["Switching the context with Begin[] .. End[]", "Subsubsection"], Cell[TextData[{ "You can start a new context (with name ", StyleBox["a`", "Output"], ") with" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\"]\)], "Input", CellLabel->"In[5]:="], Cell[BoxData[ \("a`"\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell[TextData[{ "This command resets the value of the variable ", StyleBox["$Context", "Output"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Context\)], "Input", CellLabel->"In[6]:="], Cell[BoxData[ \("a`"\)], "Output", CellLabel->"Out[6]="] }, Open ]], Cell["\<\ From now on all new symbols are defined within the new context. For \ example, we can define a new function:\ \>", "Text"], Cell[BoxData[ \(cube[x_] := x^3\)], "Input", CellLabel->"In[7]:="], Cell[CellGroupData[{ Cell[BoxData[ \(Context[cube]\)], "Input", CellLabel->"In[8]:="], Cell[BoxData[ \("a`"\)], "Output", CellLabel->"Out[8]="] }, Open ]], Cell["You end the current context with", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(End[]\)], "Input", CellLabel->"In[9]:="], Cell[BoxData[ \("a`"\)], "Output", CellLabel->"Out[9]="] }, Open ]], Cell[TextData[{ "Now ", StyleBox["$Context", "Output"], " is reset to its original value." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Context\)], "Input", CellLabel->"In[10]:="], Cell[BoxData[ \("Global`"\)], "Output", CellLabel->"Out[10]="] }, Open ]], Cell["Now, let us try to do something similar in another context:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\"]\)], "Input", CellLabel->"In[11]:="], Cell[BoxData[ \("b`"\)], "Output", CellLabel->"Out[11]="] }, Open ]], Cell[BoxData[ \(cube[x_] := \((x + 1)\)^3\)], "Input", CellLabel->"In[12]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[13]:="], Cell["b`cube", "Print", CellTags->"Info3290493981-8699254"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(cube[x_] := \((x + 1)\)\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "cube"], Editable->False]], "Print", CellTags->"Info3290493981-8699254"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(End[]\)], "Input", CellLabel->"In[14]:="], Cell[BoxData[ \("b`"\)], "Output", CellLabel->"Out[14]="] }, Open ]], Cell[TextData[{ "Let us now switch back to context \"", StyleBox["a`", "Output"], "\"" }], "Text"], Cell[BoxData[ \(\(Begin["\"];\)\)], "Input", CellLabel->"In[15]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[16]:="], Cell["a`cube", "Print", CellTags->"Info3290493981-8208164"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(cube[x_] := x\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "cube"], Editable->False]], "Print", CellTags->"Info3290493981-8208164"] }, Open ]], Cell[BoxData[ \(\(End[];\)\)], "Input", CellLabel->"In[17]:="], Cell[TextData[{ "We see that the definitions made within the context ", StyleBox["b`", "Output"], " do not conflict with the definitions made in ", StyleBox["a`", "Output"], "." }], "Text"], Cell[TextData[{ "We are now back in the context ", StyleBox["Global`", "Output"], ". We can still refer to the functions defined above by specifying the full \ name:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a`cube[2]\)], "Input", CellLabel->"In[18]:="], Cell[BoxData[ \(8\)], "Output", CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(b`cube[2]\)], "Input", CellLabel->"In[19]:="], Cell[BoxData[ \(27\)], "Output", CellLabel->"Out[19]="] }, Open ]], Cell[TextData[{ "You can see that the short name \"", StyleBox["cube", "Output"], "\" is unknown in the context ", StyleBox["Global`", "Output"], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[20]:="], Cell[BoxData[ RowBox[{\(Information::"notfound"\), \(\(:\)\(\ \)\), "\<\"Symbol \ \\!\\(\\\"cube\\\"\\) not found. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::notfound\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[20]:="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Switching the context by setting $Context", "Subsubsection"], Cell["\<\ In principle, we could also switch the context by manually changing \ the variable $Context:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Context\)], "Input", CellLabel->"In[21]:="], Cell[BoxData[ \("Global`"\)], "Output", CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \($Context = \ "\"\)], "Input", CellLabel->"In[22]:="], Cell[BoxData[ \("mycontext`"\)], "Output", CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(q = 5\)], "Input", CellLabel->"In[23]:="], Cell[BoxData[ \(5\)], "Output", CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?q\)\)], "Input", CellLabel->"In[24]:="], Cell["mycontext`q", "Print", CellTags->"Info3290493982-2323044"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(q = 5\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "q"], Editable->False]], "Print", CellTags->"Info3290493982-2323044"] }, Open ]], Cell["\<\ Switch back to global in the same way (End[] would not work in this \ situation)\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Context\ = \ "\"\)], "Input", CellLabel->"In[25]:="], Cell[BoxData[ \("Global`"\)], "Output", CellLabel->"Out[25]="] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["The context path", "Section"], Cell[TextData[{ "The built-in functions of Mathematica are usually defined in a context \ called ", StyleBox["System`", "Output"], ". You can check this, for example, as follows:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Context[Sin]\)], "Input", CellLabel->"In[26]:="], Cell[BoxData[ \("System`"\)], "Output", CellLabel->"Out[26]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Context[Pi]\)], "Input", CellLabel->"In[27]:="], Cell[BoxData[ \("System`"\)], "Output", CellLabel->"Out[27]="] }, Open ]], Cell[TextData[{ "Although our presently active context is ", StyleBox["Global`", "Output"], ", ", StyleBox["Mathematica", FontSlant->"Italic"], " can find the definition of the symbols ", StyleBox["Sin", "Output"], " or ", StyleBox["Pi", "Output"], ". The reason for this is that there is always a currently active \"context \ search path\". The context search path is a list of contexts which is \ searched by ", StyleBox["Mathematica", FontSlant->"Italic"], " everytime when a symbol is encountered that is unknown in the current \ context. ", StyleBox["Global`", "Output"], " and ", StyleBox["System`", "Output"], " are both on the currently active context search path. So you only have to \ type the short name of ", StyleBox["Pi", "Output"], " (instead of ", StyleBox["System`Pi", "Output"], ") and ", StyleBox["Mathematica", FontSlant->"Italic"], " looks through all contexts of the context search path to find the \ definition of that symbol. The currently active context search path is stored \ in the variable ", StyleBox["$ContextPath", "Output"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($ContextPath\)], "Input", CellLabel->"In[28]:="], Cell[BoxData[ \({"Global`", "System`"}\)], "Output", CellLabel->"Out[28]="] }, Open ]], Cell["You can add your own contexts to the context search path", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($ContextPath\ = Append[%, "\"]\)], "Input", CellLabel->"In[29]:="], Cell[BoxData[ \({"Global`", "System`", "a`"}\)], "Output", CellLabel->"Out[29]="] }, Open ]], Cell[TextData[{ "Now, the definition of the symbol \"", StyleBox["cube", "Output"], "\" made above in the context ", StyleBox["a`", "Output"], " is now also accessible from within the current context ", StyleBox["Global`", "Output"], ", because the context ", StyleBox["a`", "Output"], " is on the currently active context path:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[30]:="], Cell["a`cube", "Print", CellTags->"Info3290493982-5241507"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(cube[x_] := x\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "cube"], Editable->False]], "Print", CellTags->"Info3290493982-5241507"] }, Open ]], Cell["\<\ Hence we can call the function cube without specifying the context \ name:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cube[2]\)], "Input", CellLabel->"In[31]:="], Cell[BoxData[ \(8\)], "Output", CellLabel->"Out[31]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Shadowing", "Section"], Cell[TextData[{ "Still, there is another function cube defined in the context ", StyleBox["b`", "Output"], ". Hence there is a new possible source of conflicts, if we also add the \ context ", StyleBox["b`", "Output"], " to the current context path:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($ContextPath\ = \ {"\", "\", "\", \ "\"}\ \)], "Input", CellLabel->"In[32]:="], Cell[BoxData[ \({"Global`", "System`", "a`", "b`"}\)], "Output", CellLabel->"Out[32]="] }, Open ]], Cell[TextData[{ "In this case, ", StyleBox["Mathematica", FontSlant->"Italic"], " uses the definition which comes first in the context path." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[33]:="], Cell["a`cube", "Print", CellTags->"Info3290493982-7199547"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(cube[x_] := x\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "cube"], Editable->False]], "Print", CellTags->"Info3290493982-7199547"] }, Open ]], Cell[TextData[{ "Thus, the definition of ", StyleBox["cube", "Output"], " made in the context ", StyleBox["b`", "Output"], " is \"shadowed\" by the definition in a`. You would have to type the full \ name ", StyleBox["b`cube", "Output"], " if you want to access the function defined in the context ", StyleBox["b`", "Output"], ". Instead, we could also redefine the context path:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($ContextPath\ = \ {"\", "\", "\", \ "\"}\ \)], "Input", CellLabel->"In[34]:="], Cell[BoxData[ \({"Global`", "System`", "b`", "a`"}\)], "Output", CellLabel->"Out[34]="] }, Open ]], Cell[TextData[{ "Now the symbol \"", StyleBox["cube", "Output"], "\" is first detected in the context ", StyleBox["b`", "Output"], ", and the definition in a` is shadowed:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[35]:="], Cell["b`cube", "Print", CellTags->"Info3290493982-8643221"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(cube[x_] := \((x + 1)\)\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "cube"], Editable->False]], "Print", CellTags->"Info3290493982-8643221"] }, Open ]], Cell[TextData[{ "Lets have a look on the behavior of ", StyleBox["Mathematica", FontSlant->"Italic"], " if you try to redefine a symbol. Given the present definition of the \ context path, if you redefine \"", StyleBox["cube", "Output"], "\", then it will automatically be redefined in the context ", StyleBox["b`", "Output"], ":" }], "Text"], Cell[BoxData[ \(cube[x_] := \((x - 1)\)^3\)], "Input", CellLabel->"In[36]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[37]:="], Cell["b`cube", "Print", CellTags->"Info3290493982-9361274"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(cube[x_] := \((x - 1)\)\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "cube"], Editable->False]], "Print", CellTags->"Info3290493982-9361274"] }, Open ]], Cell[TextData[{ "If you explicitly try to define a symbol \"", StyleBox["cube", "Output"], "\" in the context ", StyleBox["Global`", "Output"], ", this definition would \"shadow\" the definition in ", StyleBox["b`", "Output"], " because ", StyleBox["Global`", "Output"], " is the current context and the context path is only searched when a \ symbol is not found in the current context. In this case, ", StyleBox["Mathematica", FontSlant->"Italic"], " displays a warning message:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Global`cube\)], "Input", CellLabel->"In[38]:="], Cell[BoxData[ RowBox[{\(cube::"shdw"\), \(\(:\)\(\ \)\), "\<\"Symbol \\!\\(\\\"cube\\\"\ \\) appears in multiple contexts \\!\\({\\\"Global`\\\", \\\"b`\\\", \\\"a`\\\ \"}\\); definitions in context \\!\\(\\\"Global`\\\"\\) may shadow or be \ shadowed by other definitions. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::shdw\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[38]:="], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(cube\\)\\\" is similar to existing symbol \\\ \"\\!\\(b`cube\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[38]:="], Cell[BoxData[ \(cube\)], "Output", CellLabel->"Out[38]="] }, Open ]], Cell["\<\ Notice that just typing \"Global`cube\" in the input cell has \ created the symbol cube in the global context. From now on, this symbol \ exists, although there are no definitions associated with it.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cube[3]\)], "Input", CellLabel->"In[39]:="], Cell[BoxData[ \(cube[3]\)], "Output", CellLabel->"Out[39]="] }, Open ]], Cell["\<\ You might try to change the search order in the context path by \ redefining it:\ \>", "Text"], Cell[BoxData[ \(\($ContextPath\ = \ {"\", \ "\", "\", \ "\"};\)\)], "Input", CellLabel->"In[40]:="], Cell["\<\ Now, whenever the context path is searched for \"cube\", this \ symbol is encountered first in the context b`. Still, when you now call cube \ you will not get the cube from context b`, because the current context \ (Global`) is searched first:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cube[3]\)], "Input", CellLabel->"In[41]:="], Cell[BoxData[ \(cube[3]\)], "Output", CellLabel->"Out[41]="] }, Open ]], Cell[TextData[{ "When ", StyleBox["Mathematica", FontSlant->"Italic"], " finds a symbol in the current context, the context path is not searched." }], "Text"], Cell["\<\ We can always add symbol definitions in the various contexts by \ explicitly specifying the full name:\ \>", "Text"], Cell[BoxData[ \(b`sq[x_] := x^2\)], "Input", CellLabel->"In[42]:="], Cell[TextData[{ "Since ", StyleBox["b`", "Output"], " comes first, a definition of ", StyleBox["a`sq", "Output"], " would now be shadowed by the previous definition:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a`sq\)], "Input", CellLabel->"In[43]:="], Cell[BoxData[ RowBox[{\(a`sq::"shdw"\), \(\(:\)\(\ \)\), "\<\"Symbol \ \\!\\(\\\"sq\\\"\\) appears in multiple contexts \\!\\({\\\"a`\\\", \ \\\"b`\\\"}\\); definitions in context \\!\\(\\\"a`\\\"\\) may shadow or be \ shadowed by other definitions. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::shdw\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[43]:="], Cell[BoxData[ \(a`sq\)], "Output", CellLabel->"Out[43]="] }, Open ]], Cell[TextData[{ "Note: By switching the context using ", StyleBox["Begin", "Output"], " you do not change the context path. Therefore, you still cannot redefine \ the built-in functions without having a conflict. On the other hand, all \ built-in ", StyleBox["Mathematica", FontSlant->"Italic"], " commands work as usual within the new context." }], "Text"], Cell["\<\ The list of all currently existing contexts can be obtained by the \ command Contexts[]:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Contexts[]\)], "Input", CellLabel->"In[44]:="], Cell[BoxData[ \({"a`", "Algebra`", "Algebra`Algebraics`Private`", "Algebraics`Private`", "Algebra`SymmetricPolynomials`", "b`", "BoxForm`", "BrowserCategoryLoad`", "Compile`", "Conversion`", "Debug`", "Developer`", "DSolve`", "Experimental`", "Factor`", "FE`", "FindMinimum`", "FindRoot`", "Format`", "FrontEnd`", "Global`", "GroebnerGCD`", "GroebnerWalk`", "HypergeometricLogDump`", "Integrate`", "Integrate`Elliptic`", "Internal`", "Internal`ProcessEquations`", "Limit`", "LinearAlgebra`", "LinearAlgebra`BLAS`", "LinearAlgebra`Implementations`", "LinearAlgebra`LAPACK`", "LinearAlgebra`LinearSolve`", "LinearAlgebra`Private`", "MathLink`Information`", "MLFS`", "MultivariateResultant`", "mycontext`", "NDSolve`", "NDSolve`BDF`", "NDSolve`BDF`Newton`", "NDSolve`Chasing`", "NDSolve`Chasing`Implementation`", "NDSolve`FiniteDifferenceDerivativeFunction`", "NDSolve`IDA`", "NDSolve`IDA`Newton`", "NDSolve`MethodOfLines`", "NDSolve`Private`", "NDSolve`StateData`", "NIntegrate`OscNInt`", "NMinimize`", "NumberTheory`", "NumberTheory`AlgebraicNumberFields`", "NumericalMath`", "Optimization`", "Optimization`LinearProgramming`", "Optimization`LinearProgramming`Private`", "Optimization`LineSearch`", "Optimization`MPSData`", "Quantifier`", "Reduce`", "RSolve`", "Simplify`", "Solve`", "SparseArray`", "SymbolicProduct`", "SymbolicSum`", "System`", "System`ComplexExpand`", "System`Convert`CommonDump`", "System`Convert`HTMLDump`", "System`Convert`MathMLDump`", "System`Convert`MLStringDataDump`", "System`Convert`NotebookMLDump`", "System`Convert`SVGDump`", "System`Convert`TeXDump`", "System`Convert`XMLDump`", "System`CrossDump`", "System`Dump`", "System`Dump`ArgumentCount`", "System`FactorDump`", "System`FEDump`", "System`IntegerPartitionsDump`", "System`InterpolatingFunction`", "System`LanguageEnhancements`", "System`LaplaceTransformDump`", "System`Private`", "XML`", "XML`MathML`", "XML`MathML`Symbols`", "XML`NotebookML`", "XML`Parser`", "XML`SVG`"}\)], "Output", CellLabel->"Out[44]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Removing symbols", "Section"], Cell[TextData[{ "During this session so far, the symbol ", StyleBox["cube", "Output"], " has been defined in several contexts. The present state is" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($ContextPath\)], "Input", CellLabel->"In[45]:="], Cell[BoxData[ \({"b`", "Global`", "System`", "a`"}\)], "Output", CellLabel->"Out[45]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?cube\)\)], "Input", CellLabel->"In[46]:="], Cell["Global`cube", "Print", CellTags->"Info3290493983-7871130"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?a`cube\)\)], "Input", CellLabel->"In[47]:="], Cell["a`cube", "Print", CellTags->"Info3290493983-4951396"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(a`cube[x_] := x\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "a`cube"], Editable->False]], "Print", CellTags->"Info3290493983-4951396"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?b`cube\)\)], "Input", CellLabel->"In[48]:="], Cell["b`cube", "Print", CellTags->"Info3290493983-9263945"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(b`cube[x_] := \((x - 1)\)\^3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "b`cube"], Editable->False]], "Print", CellTags->"Info3290493983-9263945"] }, Open ]], Cell[TextData[{ "The presence of the symbol ", StyleBox["cube", "Output"], " in the global context shadows all definitions in the other contexts. If \ you try to evaluate" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cube[4]\)], "Input", CellLabel->"In[49]:="], Cell[BoxData[ \(cube[4]\)], "Output", CellLabel->"Out[49]="] }, Open ]], Cell[TextData[{ "you will get nothing (only the input is echoed), because no definition is \ associated to the symbol ", StyleBox["cube", "Output"], " in the global context. The command ", StyleBox["Remove[", "Output"], StyleBox["symbolname", FontSlant->"Italic"], StyleBox["]", "Output"], " completely removes the symbol ", StyleBox["symbolname", FontSlant->"Italic"], " from the active context." }], "Text"], Cell[BoxData[ \(Remove[cube]\)], "Input", CellLabel->"In[50]:="], Cell["\<\ The symbol cube still remains in contexts a` and b`. The context b` \ is searched first:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cube[3]\)], "Input", CellLabel->"In[51]:="], Cell[BoxData[ \(8\)], "Output", CellLabel->"Out[51]="] }, Open ]], Cell[BoxData[ \(Remove[b`cube]\)], "Input", CellLabel->"In[52]:="], Cell["A symbol \"cube\" is still in context a`:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cube[3]\)], "Input", CellLabel->"In[53]:="], Cell[BoxData[ \(27\)], "Output", CellLabel->"Out[53]="] }, Open ]], Cell[TextData[{ StyleBox["Remove", "Output"], " is more radical than ", StyleBox["Clear", "Output"], ". The command ", StyleBox["Clear", "Output"], " only removes the definitions associated with a symbol, but not the symbol \ itself. The command ", StyleBox["Remove", "Output"], " completely removes the whole symbol from the session." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Finding the names of symbols", "Section"], Cell["\<\ The command Names allows you to list all names defined in a given \ context. Use Names[\"context`*\"]. \ \>", "Text"], Cell[CellGroupData[{ Cell["Names[\"Global`*\"]", "Input", CellLabel->"In[54]:="], Cell[BoxData[ \({"func", "x"}\)], "Output", CellLabel->"Out[54]="] }, Open ]], Cell[CellGroupData[{ Cell["Names[\"Developer`*\"]", "Input", CellLabel->"In[55]:="], Cell[BoxData[ \({"Developer`BesselSimplify", "Developer`BitLength", "Developer`BitShiftLeft", "Developer`BitShiftRight", "Developer`BoxesToMathML", "Developer`ClearCache", "Developer`CompensatedAdd", "Developer`ContextFreeForm", "Developer`FibonacciSimplify", "Developer`FileInformation", "Developer`FourierListConvolve", "Developer`FromPackedArray", "Developer`GammaSimplify", "Developer`HermiteNormalForm", "Developer`HessenbergDecomposition", "Developer`InequalityInstance", "Developer`LinearExpressionToMatrix", "Developer`LinearExpressionToSparseMatrix", "Developer`MachineComplexQ", "Developer`MachineIntegerQ", "Developer`MachineRealQ", "Developer`MathMLToBoxes", "Developer`NotebookInformation", "Developer`PackedArrayForm", "Developer`PackedArrayQ", "Developer`PolyGammaSimplify", "Developer`PolyLogSimplify", "Developer`PolynomialDivision", "Developer`PseudoFunctionsSimplify", "Developer`ReplaceAllUnheld", "Developer`SetSystemOptions", "Developer`SparseLinearSolve", "Developer`SystemOptions", "Developer`ToPackedArray", "Developer`TrigToRadicals", "Developer`ZeroQ", "Developer`ZetaSimplify", "Developer`$MaxMachineInteger", "Developer`$SymbolShadowingFunction", "Developer`$SymbolSystemShadowing"}\)], "Output", CellLabel->"Out[55]="] }, Open ]], Cell["\<\ Note that only the short name is displayed, when the context is \ already on the context path.\ \>", "Text"], Cell["A=5;B=3;", "Input", CellLabel->"In[56]:="], Cell[CellGroupData[{ Cell["Names[\"Global`*\"]", "Input", CellLabel->"In[57]:="], Cell[BoxData[ \({"A", "B", "func", "x"}\)], "Output", CellLabel->"Out[57]="] }, Open ]], Cell[TextData[{ "Names[] gives a list of all names which are in use in the current ", StyleBox["Mathematica", FontSlant->"Italic"], " session (all names in all contexts, whether they are on the search path \ or not). This is a very long list:" }], "Text"], Cell[CellGroupData[{ Cell["Length[Names[]]", "Input", CellLabel->"In[58]:="], Cell[BoxData[ \(4283\)], "Output", CellLabel->"Out[58]="] }, Open ]], Cell[TextData[{ "Names[\"System`*\"] lists all built-in ", StyleBox["Mathematica", FontSlant->"Italic"], " functions." }], "Text"], Cell[CellGroupData[{ Cell["Length[Names[\"System`*\"]]", "Input", CellLabel->"In[59]:="], Cell[BoxData[ \(1920\)], "Output", CellLabel->"Out[59]="] }, Open ]], Cell["\<\ If you define a new symbol, you might wish to know whether the name \ of the symbol is already in use. This can be done as follows\ \>", "Text"], Cell[CellGroupData[{ Cell["NameQ /@ {\"RGB\", \"RGB*\", \"BinaryExport\", \"*`BinaryExport\"}", \ "Input", CellLabel->"In[60]:="], Cell[BoxData[ \({False, True, False, True}\)], "Output", CellLabel->"Out[60]="] }, Open ]], Cell["\<\ (Here \"*\" is a metacharacter meaning zero or more characters. In \ the result above we obtain \"True\" for the existing symbols \"RGBColor\" and \ \"Experimental`BinaryExport\")\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Parsing the input", "Section"], Cell[TextData[{ "When you enter a ", StyleBox["Mathematica", FontSlant->"Italic"], " input, the system tries to interpret the characters according to the \ syntax defined by ", StyleBox["Mathematica", FontSlant->"Italic"], ". The textual form of the input has to be interpreted as a ", StyleBox["Mathematica", FontSlant->"Italic"], " expression that can be evaluated by the kernel. This process of \ interpreting the input is called \"parsing\". Parsing translates the input \ expression into an internal form which is understood by the ", StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[" kernel. ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], StyleBox[" always parses a complete input cell before evaluating the \ expressions.", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[TextData[{ "$Context and $ContextPath influence the way how Mathematica parses symbols \ in input cells. If a short name is found in an input cell, it is interpreted \ as belonging to the active context. If there exists no symbol with that name \ in the active context, then ", StyleBox["Mathematica", FontSlant->"Italic"], " searches the context path whether it can find the symbol. If the symbol \ does not exist in any context, then it is finally added to the active \ context." }], "Text"], Cell[TextData[{ StyleBox["The ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontSlant->"Italic"], " front end always parses complete lines of input before sending them to \ the kernel. As a consequence, you cannot change the context in a single line \ of input." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\"]; \ A = 3; End[]\)], "Input", CellLabel->"In[61]:="], Cell[BoxData[ \("d`"\)], "Output", CellLabel->"Out[61]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?A\)\)], "Input", CellLabel->"In[62]:="], Cell["Global`A", "Print", CellTags->"Info3290494011-2762691"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(A = 3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "A"], Editable->False]], "Print", CellTags->"Info3290494011-2762691"] }, Open ]], Cell["\<\ This shows that the constant A has been defined in the global \ context and not in the context d`.\ \>", "Text"], Cell[BoxData[{ \(\(Begin["\"];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(B = 3;\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(End[];\)\)}], "Input", CellLabel->"In[68]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(?B\)\)], "Input", CellLabel->"In[71]:="], Cell[BoxData[ RowBox[{\(Information::"notfound"\), \(\(:\)\(\ \)\), "\<\"Symbol \ \\!\\(\\\"B\\\"\\) not found. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::notfound\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[71]:="] }, Open ]], Cell["\<\ Thus, B is not in the global context. But it is in the context \ e`:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?e`B\)\)], "Input", CellLabel->"In[72]:="], Cell["e`B", "Print", CellTags->"Info3290494080-9333815"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(e`B = 3\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "e`B"], Editable->False]], "Print", CellTags->"Info3290494080-9333815"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Hierarchical context names", "Section"], Cell["\<\ Symbols may have a combined context name like \ \"context1`context2`\". This simulates a hierarchical behavior of contexts, \ which is, however, only partly reflected by the Begin command. Look at the \ following example:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\"]\)], "Input", CellLabel->"In[73]:="], Cell[BoxData[ \("c1`"\)], "Output", CellLabel->"Out[73]="] }, Open ]], Cell["Let us start another context within c1`:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\"]\)], "Input", CellLabel->"In[74]:="], Cell[BoxData[ \("c2`"\)], "Output", CellLabel->"Out[74]="] }, Open ]], Cell["\<\ This just switches from the context c1` to the context c2`. If we \ leave that context ...\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(End[]\)], "Input", CellLabel->"In[75]:="], Cell[BoxData[ \("c2`"\)], "Output", CellLabel->"Out[75]="] }, Open ]], Cell["... then we are back in the context c1`,", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Context\)], "Input", CellLabel->"In[76]:="], Cell[BoxData[ \("c1`"\)], "Output", CellLabel->"Out[76]="] }, Open ]], Cell["which we are no going to leave.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(End[]\)], "Input", CellLabel->"In[77]:="], Cell[BoxData[ \("c1`"\)], "Output", CellLabel->"Out[77]="] }, Open ]], Cell["\<\ For a true hierarchical behavior of context names we can do the \ following:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\"]\)], "Input", CellLabel->"In[78]:="], Cell[BoxData[ \("c1`"\)], "Output", CellLabel->"Out[78]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Begin["\<`c2`\>"]\)], "Input", CellLabel->"In[79]:="], Cell[BoxData[ \("c1`c2`"\)], "Output", CellLabel->"Out[79]="] }, Open ]], Cell["\<\ The extra ` at the beginning of \"`c2`\" above declares c2` as a \ sub-context of c1`.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(End[]\)], "Input", CellLabel->"In[80]:="], Cell[BoxData[ \("c1`c2`"\)], "Output", CellLabel->"Out[80]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(End[]\)], "Input", CellLabel->"In[81]:="], Cell[BoxData[ \("c1`"\)], "Output", CellLabel->"Out[81]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Contexts of packages", "Section"], Cell[CellGroupData[{ Cell["Loading packages", "Subsubsection"], Cell[TextData[{ "Packages are collections of ", StyleBox["Mathematica", FontSlant->"Italic"], " commands which are defined for a special purpose. For example, the \ standard package ", StyleBox["Graphics3D.m", "Output"], " (which comes together with any ", StyleBox["Mathematica-", FontSlant->"Italic"], "distribution) contains useful functions for 3 dimensional graphics. You \ can load this package with one of the following commands\n\n ", StyleBox["<"Italic"], " session)\nor with\n\n ", StyleBox["Needs[\"Graphics`Graphics3D`\"]", "Output"], "\n\n(which loads the package only if it has not already been loaded)" }], "Text"], Cell[TextData[{ "Both commands tell ", StyleBox["Mathematica", FontSlant->"Italic"], " to read the file \"Graphics3D.m\" which is in the sub-directory \ \"Graphics\" (which is inside the ", StyleBox["Mathematica", FontSlant->"Italic"], " 4.0 files/AddOns/Standard Packages/ directory)." }], "Text"], Cell["\<\ Note that the filename is specified with the syntax of a context \ name.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Package context", "Subsubsection"], Cell["Loading a Mathematica package usually creates new contexts.", "Text"], Cell[BoxData[ \(\(listold\ = \ Contexts[];\)\)], "Input", CellLabel->"In[82]:="], Cell[BoxData[ \(<< Graphics`Graphics3D`\)], "Input", CellLabel->"In[83]:="], Cell[BoxData[ \(\(listnew\ = \ Contexts[];\)\)], "Input", CellLabel->"In[84]:="], Cell["\<\ We can see that loading the package has created a whole bunch of \ new contexts:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Complement[listnew, listold]\)], "Input", CellLabel->"In[85]:="], Cell[BoxData[ \({"Graphics`Common`GraphicsCommon`", "Graphics`Graphics3D`", "Graphics`Graphics3D`Private`", "Graphics`Spline`Private`", "Utilities`FilterOptions`", "Utilities`FilterOptions`Private`"}\)], "Output", CellLabel->"Out[85]="] }, Open ]], Cell["The context path has also been changed:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($ContextPath\)], "Input", CellLabel->"In[86]:="], Cell[BoxData[ \({"Graphics`Graphics3D`", "Utilities`FilterOptions`", "Graphics`Common`GraphicsCommon`", "b`", "Global`", "System`", "a`"}\)], "Output", CellLabel->"Out[86]="] }, Open ]], Cell[TextData[{ "The new ", StyleBox["Mathematica", FontSlant->"Italic"], " commands provided by the package are usually created within the context \ of the package. In this case the package context is Graphics`Graphics3D`. \ Adding this context to the context path enables the user to access these \ symbols within the currently active context. " }], "Text"], Cell["\<\ The list above shows that the Graphic3D-package in turn needs the \ packages Utilities`FilterOptions` and Graphics`Common`GraphicsCommon` whose \ contexts have been added too. There are also private contexts within each of \ the packages. These are not added to $ContextPath, because they only serve to \ define symbols which are used within the package but which are hidden from \ the user.\ \>", "Text"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Problems with shadowing", "Section"], Cell["\<\ There is a frequently occurring problem if a package is loaded too \ late. For example, you might want to create a filled plot of a function and \ type in the command\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(FilledPlot[1/\((1 + x^2)\), {x, \(-4\), 4}]\)], "Input", CellLabel->"In[87]:="], Cell[BoxData[ \(FilledPlot[1\/\(1 + x\^2\), {x, \(-4\), 4}]\)], "Output", CellLabel->"Out[87]="] }, Open ]], Cell["\<\ Then you realize that you haven't loaded the package \ Graphics`FilledPlot` which defines that command. You want to correct your \ mistake and load the package:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(<< Graphics`FilledPlot`\)], "Input", CellLabel->"In[88]:="], Cell[BoxData[ RowBox[{\(FilledPlot::"shdw"\), \(\(:\)\(\ \)\), "\<\"Symbol \ \\!\\(\\\"FilledPlot\\\"\\) appears in multiple contexts \ \\!\\({\\\"Graphics`FilledPlot`\\\", \\\"Global`\\\"}\\); definitions in \ context \\!\\(\\\"Graphics`FilledPlot`\\\"\\) may shadow or be shadowed by \ other definitions. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::shdw\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[88]:="] }, Open ]], Cell["\<\ You obtain an error message and the command still does not \ work:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(FilledPlot[1/\((1 + x^2)\), {x, \(-4\), 4}]\)], "Input", CellLabel->"In[89]:="], Cell[BoxData[ \(FilledPlot[1\/\(1 + x\^2\), {x, \(-4\), 4}]\)], "Output", CellLabel->"Out[89]="] }, Open ]], Cell[TextData[{ "The problem is that by typing the command ", StyleBox["FilledPlot", "Output"], " for the first time you have created the symbol ", StyleBox["FilledPlot", "Output"], " in the (currently active) global context. The short name ", StyleBox["FilledPlot", "Output"], " is automatically assumed to belong to the active context and the right \ definition is not found. (The context path is only searched, when the symbol \ is not found in the active context). Indeed," }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?FilledPlot\)\)], "Input", CellLabel->"In[72]:="], Cell[BoxData[ \("Global`FilledPlot"\)], "Print", CellLabel->"From In[72]:="] }, Open ]], Cell[TextData[{ "In order to access the command ", StyleBox["FilledPlot", "Output"], " provided by the package, you could try to specify the full name by adding \ the package context:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Graphics`FilledPlot`FilledPlot[ 1/\((1 + x^2)\), {x, \(-4\), 4}]\)], "Input", CellLabel->"In[90]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0 1 0 0.618034 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin 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