492 lines
16 KiB
Mathematica
492 lines
16 KiB
Mathematica
(* Content-type: application/vnd.wolfram.mathematica *)
|
|
|
|
(*** Wolfram Notebook File ***)
|
|
(* http://www.wolfram.com/nb *)
|
|
|
|
(* CreatedBy='Mathematica 8.0' *)
|
|
|
|
(*CacheID: 234*)
|
|
(* Internal cache information:
|
|
NotebookFileLineBreakTest
|
|
NotebookFileLineBreakTest
|
|
NotebookDataPosition[ 157, 7]
|
|
NotebookDataLength[ 16383, 482]
|
|
NotebookOptionsPosition[ 15716, 454]
|
|
NotebookOutlinePosition[ 16071, 470]
|
|
CellTagsIndexPosition[ 16028, 467]
|
|
WindowFrame->Normal*)
|
|
|
|
(* Beginning of Notebook Content *)
|
|
Notebook[{
|
|
Cell["\<\
|
|
The derivative of CalibratedStereoCamera.project:\
|
|
\>", "Text",
|
|
CellChangeTimes->{{3.5349648356912127`*^9, 3.534964846480523*^9}, {
|
|
3.534983100980744*^9, 3.534983101484686*^9}, {3.535027340892766*^9,
|
|
3.535027363679287*^9}}],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"H1", "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["1", "z"],
|
|
RowBox[{
|
|
RowBox[{"(", GridBox[{
|
|
{"1", "0",
|
|
RowBox[{
|
|
RowBox[{"-", " ", "xL"}], "/", "z"}]},
|
|
{"1", "0",
|
|
RowBox[{
|
|
RowBox[{"-", " ", "xR"}], "/", "z"}]},
|
|
{"0", "1",
|
|
RowBox[{
|
|
RowBox[{"-", " ", "y"}], "/", "z"}]}
|
|
}], ")"}], ".",
|
|
RowBox[{"(", GridBox[{
|
|
{"0",
|
|
RowBox[{"-", "z"}], "y",
|
|
RowBox[{"-", "1"}], "0", "0", "R00", "R10", "R20"},
|
|
{"z", "0",
|
|
RowBox[{"-", "x"}], "0",
|
|
RowBox[{"-", "1"}], "0", "R01", "R11", "R21"},
|
|
{
|
|
RowBox[{"-", "y"}], "x", "0", "0", "0",
|
|
RowBox[{"-", "1"}], "R02", "R12", "R22"}
|
|
}], ")"}]}]}], "//", "FullSimplify"}], "//",
|
|
"MatrixForm"}]}]], "Input",
|
|
CellChangeTimes->{{3.5349631885090446`*^9, 3.5349632390951033`*^9}, {
|
|
3.53496344228561*^9, 3.534963552777855*^9}, {3.53496365487344*^9,
|
|
3.53496369917972*^9}, 3.534963801932398*^9, {3.5349638327702837`*^9,
|
|
3.534963833842349*^9}, {3.5349638684957743`*^9, 3.534963869306225*^9}, {
|
|
3.5349640018609343`*^9, 3.534964073635954*^9}, {3.534964139661661*^9,
|
|
3.534964141597094*^9}, {3.534964228457883*^9, 3.534964230497267*^9}, {
|
|
3.534964522693956*^9, 3.534964554934105*^9}, 3.534979649216166*^9, {
|
|
3.534979703414953*^9, 3.5349797245266523`*^9}, 3.534979754875834*^9, {
|
|
3.5349801268943996`*^9, 3.534980128188809*^9}, {3.534981330976294*^9,
|
|
3.5349813327600317`*^9}, 3.534981567474765*^9, {3.534982081101321*^9,
|
|
3.534982107106247*^9}, {3.534982164393888*^9, 3.534982164510919*^9}, {
|
|
3.534982374683118*^9, 3.534982376464725*^9}, {3.534985216789068*^9,
|
|
3.5349853102222767`*^9}, {3.535027369587408*^9, 3.535027381384465*^9}, {
|
|
3.535027443509613*^9, 3.535027464114572*^9}, {3.535027568452767*^9,
|
|
3.5350275759632196`*^9}}],
|
|
|
|
Cell[BoxData[
|
|
TagBox[
|
|
RowBox[{"(", "\[NoBreak]", GridBox[{
|
|
{
|
|
FractionBox[
|
|
RowBox[{"xL", " ", "y"}],
|
|
SuperscriptBox["z", "2"]],
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "-",
|
|
FractionBox[
|
|
RowBox[{"x", " ", "xL"}],
|
|
SuperscriptBox["z", "2"]]}],
|
|
FractionBox["y", "z"],
|
|
RowBox[{"-",
|
|
FractionBox["1", "z"]}], "0",
|
|
FractionBox["xL",
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R02"}], " ", "xL"}], "+",
|
|
RowBox[{"R00", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R12"}], " ", "xL"}], "+",
|
|
RowBox[{"R10", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R22"}], " ", "xL"}], "+",
|
|
RowBox[{"R20", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]]},
|
|
{
|
|
FractionBox[
|
|
RowBox[{"xR", " ", "y"}],
|
|
SuperscriptBox["z", "2"]],
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "-",
|
|
FractionBox[
|
|
RowBox[{"x", " ", "xR"}],
|
|
SuperscriptBox["z", "2"]]}],
|
|
FractionBox["y", "z"],
|
|
RowBox[{"-",
|
|
FractionBox["1", "z"]}], "0",
|
|
FractionBox["xR",
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R02"}], " ", "xR"}], "+",
|
|
RowBox[{"R00", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R12"}], " ", "xR"}], "+",
|
|
RowBox[{"R10", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R22"}], " ", "xR"}], "+",
|
|
RowBox[{"R20", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]]},
|
|
{
|
|
RowBox[{"1", "+",
|
|
FractionBox[
|
|
SuperscriptBox["y", "2"],
|
|
SuperscriptBox["z", "2"]]}],
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
RowBox[{"x", " ", "y"}],
|
|
SuperscriptBox["z", "2"]]}],
|
|
RowBox[{"-",
|
|
FractionBox["x", "z"]}], "0",
|
|
RowBox[{"-",
|
|
FractionBox["1", "z"]}],
|
|
FractionBox["y",
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R02"}], " ", "y"}], "+",
|
|
RowBox[{"R01", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R12"}], " ", "y"}], "+",
|
|
RowBox[{"R11", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]],
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "R22"}], " ", "y"}], "+",
|
|
RowBox[{"R21", " ", "z"}]}],
|
|
SuperscriptBox["z", "2"]]}
|
|
},
|
|
GridBoxAlignment->{
|
|
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
|
|
"RowsIndexed" -> {}},
|
|
GridBoxSpacings->{"Columns" -> {
|
|
Offset[0.27999999999999997`], {
|
|
Offset[0.7]},
|
|
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
|
|
Offset[0.2], {
|
|
Offset[0.4]},
|
|
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
|
|
Function[BoxForm`e$,
|
|
MatrixForm[BoxForm`e$]]]], "Output",
|
|
CellChangeTimes->{
|
|
3.534979650069955*^9, {3.534979704654621*^9, 3.5349797249719963`*^9},
|
|
3.534979755407372*^9, 3.534980128803479*^9, 3.534981333789564*^9,
|
|
3.5349815682066193`*^9, 3.534982108180704*^9, 3.534982166031692*^9,
|
|
3.534982377250555*^9, {3.534985297869969*^9, 3.534985310666787*^9},
|
|
3.5350273834131517`*^9, {3.535027445678911*^9, 3.535027465353374*^9}, {
|
|
3.535027561035596*^9, 3.535027578459703*^9}, 3.535031349635189*^9}]
|
|
}, Open ]],
|
|
|
|
Cell["\<\
|
|
To get rid of (1/z) factors, work in terms of u=x/z and v=x/z.\
|
|
\>", "Text",
|
|
CellChangeTimes->{{3.534981922219325*^9, 3.534981963212936*^9}, {
|
|
3.534983115196439*^9, 3.534983121940318*^9}}],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"H2", "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
FractionBox["1", "z"],
|
|
RowBox[{
|
|
RowBox[{"(", GridBox[{
|
|
{"1", "0",
|
|
RowBox[{
|
|
RowBox[{"-", " ", "xL"}], "/", "z"}]},
|
|
{"1", "0",
|
|
RowBox[{
|
|
RowBox[{"-", " ", "xR"}], "/", "z"}]},
|
|
{"0", "1",
|
|
RowBox[{
|
|
RowBox[{"-", " ", "y"}], "/", "z"}]}
|
|
}], ")"}], ".",
|
|
RowBox[{"(", GridBox[{
|
|
{"0",
|
|
RowBox[{"-", "z"}], "y",
|
|
RowBox[{"-", "1"}], "0", "0", "R00", "R10", "R20"},
|
|
{"z", "0",
|
|
RowBox[{"-", "x"}], "0",
|
|
RowBox[{"-", "1"}], "0", "R01", "R11", "R21"},
|
|
{
|
|
RowBox[{"-", "y"}], "x", "0", "0", "0",
|
|
RowBox[{"-", "1"}], "R02", "R12", "R22"}
|
|
}], ")"}]}]}], "/.",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"xL", "\[Rule]",
|
|
RowBox[{"z", " ", "uL"}]}], ",",
|
|
RowBox[{"xR", "\[Rule]",
|
|
RowBox[{"z", " ", "uR"}]}], ",",
|
|
RowBox[{"y", "\[Rule]",
|
|
RowBox[{"z", " ", "v"}]}]}], "}"}]}], "//", "FullSimplify"}], " ", "//",
|
|
"MatrixForm", " "}]}]], "Input",
|
|
CellChangeTimes->{{3.534981575562448*^9, 3.534981660163035*^9}, {
|
|
3.534981699433219*^9, 3.534981715884362*^9}, {3.534981811953741*^9,
|
|
3.534981812758938*^9}, {3.534981967549185*^9, 3.534981970084591*^9}, {
|
|
3.5349821168936243`*^9, 3.5349821229726763`*^9}, {3.5349821691614027`*^9,
|
|
3.534982169838853*^9}, {3.5349823818506517`*^9, 3.5349823882411737`*^9}, {
|
|
3.534982418562274*^9, 3.534982445450313*^9}, {3.5349824987688103`*^9,
|
|
3.5349825453911533`*^9}, 3.5349853401371813`*^9, {3.5349854168944473`*^9,
|
|
3.534985505039978*^9}, {3.5349855515891447`*^9, 3.5349855522595778`*^9}, {
|
|
3.534985594640473*^9, 3.534985605102441*^9}, {3.534985635544286*^9,
|
|
3.5349856556893806`*^9}, {3.534985722650296*^9, 3.534985735961334*^9}, {
|
|
3.5349862396524563`*^9, 3.534986241578967*^9}, {3.534986277578917*^9,
|
|
3.5349863148397903`*^9}, {3.534986786489544*^9, 3.534986789124526*^9}, {
|
|
3.5349868534541187`*^9, 3.534986854897138*^9}, {3.53502738808462*^9,
|
|
3.5350274696107397`*^9}, {3.535027581254743*^9, 3.535027584027256*^9}, {
|
|
3.5350276166332808`*^9, 3.535027627938361*^9}, {3.535027699887917*^9,
|
|
3.535027701552945*^9}, {3.535027782110402*^9, 3.5350277854136066`*^9}}],
|
|
|
|
Cell[BoxData[
|
|
TagBox[
|
|
RowBox[{"(", "\[NoBreak]", GridBox[{
|
|
{
|
|
RowBox[{"uL", " ", "v"}],
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"uL", " ", "x"}], "+", "z"}], "z"]}], "v",
|
|
RowBox[{"-",
|
|
FractionBox["1", "z"]}], "0",
|
|
FractionBox["uL", "z"],
|
|
FractionBox[
|
|
RowBox[{"R00", "-",
|
|
RowBox[{"R02", " ", "uL"}]}], "z"],
|
|
FractionBox[
|
|
RowBox[{"R10", "-",
|
|
RowBox[{"R12", " ", "uL"}]}], "z"],
|
|
FractionBox[
|
|
RowBox[{"R20", "-",
|
|
RowBox[{"R22", " ", "uL"}]}], "z"]},
|
|
{
|
|
RowBox[{"uR", " ", "v"}],
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"uR", " ", "x"}], "+", "z"}], "z"]}], "v",
|
|
RowBox[{"-",
|
|
FractionBox["1", "z"]}], "0",
|
|
FractionBox["uR", "z"],
|
|
FractionBox[
|
|
RowBox[{"R00", "-",
|
|
RowBox[{"R02", " ", "uR"}]}], "z"],
|
|
FractionBox[
|
|
RowBox[{"R10", "-",
|
|
RowBox[{"R12", " ", "uR"}]}], "z"],
|
|
FractionBox[
|
|
RowBox[{"R20", "-",
|
|
RowBox[{"R22", " ", "uR"}]}], "z"]},
|
|
{
|
|
RowBox[{"1", "+",
|
|
SuperscriptBox["v", "2"]}],
|
|
RowBox[{"-",
|
|
FractionBox[
|
|
RowBox[{"v", " ", "x"}], "z"]}],
|
|
RowBox[{"-",
|
|
FractionBox["x", "z"]}], "0",
|
|
RowBox[{"-",
|
|
FractionBox["1", "z"]}],
|
|
FractionBox["v", "z"],
|
|
FractionBox[
|
|
RowBox[{"R01", "-",
|
|
RowBox[{"R02", " ", "v"}]}], "z"],
|
|
FractionBox[
|
|
RowBox[{"R11", "-",
|
|
RowBox[{"R12", " ", "v"}]}], "z"],
|
|
FractionBox[
|
|
RowBox[{"R21", "-",
|
|
RowBox[{"R22", " ", "v"}]}], "z"]}
|
|
},
|
|
GridBoxAlignment->{
|
|
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
|
|
"RowsIndexed" -> {}},
|
|
GridBoxSpacings->{"Columns" -> {
|
|
Offset[0.27999999999999997`], {
|
|
Offset[0.7]},
|
|
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
|
|
Offset[0.2], {
|
|
Offset[0.4]},
|
|
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
|
|
Function[BoxForm`e$,
|
|
MatrixForm[BoxForm`e$]]]], "Output",
|
|
CellChangeTimes->{
|
|
3.534981661750978*^9, {3.534981700471121*^9, 3.5349817167574883`*^9},
|
|
3.534981813153152*^9, 3.5349819705942793`*^9, {3.534982117522484*^9,
|
|
3.534982124251252*^9}, 3.534982170293386*^9, 3.534982388956635*^9,
|
|
3.534982446240321*^9, {3.534982502305121*^9, 3.534982546180998*^9},
|
|
3.534985341687833*^9, {3.534985429323271*^9, 3.534985505574792*^9},
|
|
3.534985553224812*^9, {3.534985595114938*^9, 3.534985605471074*^9}, {
|
|
3.534985637118844*^9, 3.534985656675743*^9}, {3.534985725554123*^9,
|
|
3.534985736368793*^9}, 3.5349862441909113`*^9, 3.534986284242839*^9,
|
|
3.534986315973349*^9, 3.5349868083087063`*^9, 3.5349868556678743`*^9, {
|
|
3.535027409664824*^9, 3.535027470084853*^9}, {3.535027561117285*^9,
|
|
3.535027585819845*^9}, {3.535027620794636*^9, 3.535027628250724*^9},
|
|
3.535027702304246*^9, 3.535027785836504*^9, 3.535031349716421*^9}]
|
|
}, Open ]],
|
|
|
|
Cell["Finally, avoid divides.", "Text",
|
|
CellChangeTimes->{{3.534983093980698*^9, 3.5349831123126383`*^9}}],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"FullSimplify", "[",
|
|
RowBox[{
|
|
RowBox[{"H2", "/.",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"1", "/", "z"}], "\[Rule]", "d"}], "}"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"z", " ", "d"}], " ", "\[Equal]", "1"}], ",", " ",
|
|
RowBox[{
|
|
RowBox[{"d", " ", "x"}], " ", "\[Equal]", " ", "uL"}]}], "}"}]}],
|
|
"]"}]], "Input",
|
|
CellChangeTimes->{{3.534982548021124*^9, 3.534982548331835*^9}, {
|
|
3.534985672071082*^9, 3.5349856752309647`*^9}, {3.53498575691752*^9,
|
|
3.534985773748554*^9}, {3.534985930341876*^9, 3.534985932316481*^9}, {
|
|
3.534986318557267*^9, 3.534986330749145*^9}, 3.534986878092679*^9, {
|
|
3.535027890326747*^9, 3.5350279684574137`*^9}, {3.535029655571067*^9,
|
|
3.5350296880567923`*^9}, 3.535029764887192*^9, {3.535030004090427*^9,
|
|
3.535030121269846*^9}, {3.535030273225251*^9, 3.5350302878805017`*^9}, {
|
|
3.535030326279409*^9, 3.535030326575099*^9}}],
|
|
|
|
Cell[BoxData[
|
|
TagBox[
|
|
RowBox[{"(", "\[NoBreak]", GridBox[{
|
|
{
|
|
RowBox[{"uL", " ", "v"}],
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "-",
|
|
SuperscriptBox["uL", "2"]}], "v",
|
|
RowBox[{"-", "d"}], "0",
|
|
RowBox[{"d", " ", "uL"}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R00", "-",
|
|
RowBox[{"R02", " ", "uL"}]}], ")"}]}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R10", "-",
|
|
RowBox[{"R12", " ", "uL"}]}], ")"}]}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R20", "-",
|
|
RowBox[{"R22", " ", "uL"}]}], ")"}]}]},
|
|
{
|
|
RowBox[{"uR", " ", "v"}],
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "-",
|
|
RowBox[{"uL", " ", "uR"}]}], "v",
|
|
RowBox[{"-", "d"}], "0",
|
|
RowBox[{"d", " ", "uR"}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R00", "-",
|
|
RowBox[{"R02", " ", "uR"}]}], ")"}]}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R10", "-",
|
|
RowBox[{"R12", " ", "uR"}]}], ")"}]}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R20", "-",
|
|
RowBox[{"R22", " ", "uR"}]}], ")"}]}]},
|
|
{
|
|
RowBox[{"1", "+",
|
|
SuperscriptBox["v", "2"]}],
|
|
RowBox[{
|
|
RowBox[{"-", "uL"}], " ", "v"}],
|
|
RowBox[{"-", "uL"}], "0",
|
|
RowBox[{"-", "d"}],
|
|
RowBox[{"d", " ", "v"}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R01", "-",
|
|
RowBox[{"R02", " ", "v"}]}], ")"}]}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R11", "-",
|
|
RowBox[{"R12", " ", "v"}]}], ")"}]}],
|
|
RowBox[{"d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"R21", "-",
|
|
RowBox[{"R22", " ", "v"}]}], ")"}]}]}
|
|
},
|
|
GridBoxAlignment->{
|
|
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
|
|
"RowsIndexed" -> {}},
|
|
GridBoxSpacings->{"Columns" -> {
|
|
Offset[0.27999999999999997`], {
|
|
Offset[0.7]},
|
|
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
|
|
Offset[0.2], {
|
|
Offset[0.4]},
|
|
Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
|
|
Function[BoxForm`e$,
|
|
MatrixForm[BoxForm`e$]]]], "Output",
|
|
CellChangeTimes->{{3.535030258510765*^9, 3.535030288430678*^9},
|
|
3.535030327829464*^9, 3.535031349766954*^9}]
|
|
}, Open ]]
|
|
},
|
|
WindowSize->{738, 817},
|
|
WindowMargins->{{Automatic, 217}, {Automatic, 0}},
|
|
FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (October 5, \
|
|
2011)",
|
|
StyleDefinitions->"Default.nb"
|
|
]
|
|
(* End of Notebook Content *)
|
|
|
|
(* Internal cache information *)
|
|
(*CellTagsOutline
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*CellTagsIndex
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*NotebookFileOutline
|
|
Notebook[{
|
|
Cell[557, 20, 239, 5, 26, "Text"],
|
|
Cell[CellGroupData[{
|
|
Cell[821, 29, 1945, 44, 61, "Input"],
|
|
Cell[2769, 75, 3751, 119, 109, "Output"]
|
|
}, Open ]],
|
|
Cell[6535, 197, 201, 4, 26, "Text"],
|
|
Cell[CellGroupData[{
|
|
Cell[6761, 205, 2402, 54, 80, "Input"],
|
|
Cell[9166, 261, 3050, 84, 99, "Output"]
|
|
}, Open ]],
|
|
Cell[12231, 348, 107, 1, 26, "Text"],
|
|
Cell[CellGroupData[{
|
|
Cell[12363, 353, 950, 21, 27, "Input"],
|
|
Cell[13316, 376, 2384, 75, 79, "Output"]
|
|
}, Open ]]
|
|
}
|
|
]
|
|
*)
|
|
|
|
(* End of internal cache information *)
|