You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
548 lines
17 KiB
548 lines
17 KiB
(* Content-type: application/vnd.wolfram.mathematica *)
|
|
|
|
(*** Wolfram Notebook File ***)
|
|
(* http://www.wolfram.com/nb *)
|
|
|
|
(* CreatedBy='Mathematica 11.3' *)
|
|
|
|
(*CacheID: 234*)
|
|
(* Internal cache information:
|
|
NotebookFileLineBreakTest
|
|
NotebookFileLineBreakTest
|
|
NotebookDataPosition[ 158, 7]
|
|
NotebookDataLength[ 17609, 538]
|
|
NotebookOptionsPosition[ 15296, 492]
|
|
NotebookOutlinePosition[ 15631, 507]
|
|
CellTagsIndexPosition[ 15588, 504]
|
|
WindowFrame->Normal*)
|
|
|
|
(* Beginning of Notebook Content *)
|
|
Notebook[{
|
|
|
|
Cell[CellGroupData[{
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"r", "^", "k"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"r", ",", "th"}], "}"}], ",", "\"\<Polar\>\""}], "]"}], "//",
|
|
"Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"r", "^", "k"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"r", ",", "th"}], "}"}], ",", "\"\<Polar\>\""}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"r", ",", "th"}], "}"}], ",", "\"\<Polar\>\""}], "]"}], "//",
|
|
"Simplify"}]}], "Input",
|
|
CellChangeTimes->{{3.773994787267322*^9, 3.7739948721002197`*^9}, {
|
|
3.7739950060672483`*^9, 3.77399501194617*^9}},
|
|
CellLabel->"In[9]:=",ExpressionUUID->"0e204612-f4ad-4947-8512-0d390f7199a4"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
SuperscriptBox["k", "2"], " ",
|
|
SuperscriptBox["r",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}]]}]], "Output",
|
|
CellChangeTimes->{{3.7739948444033318`*^9, 3.773994872377877*^9}, {
|
|
3.773995007145669*^9, 3.773995012205846*^9}},
|
|
CellLabel->"Out[9]=",ExpressionUUID->"a5ab13a9-d7b2-4e5a-966e-05a797805dbf"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
SuperscriptBox[
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}], ")"}], "2"], " ",
|
|
SuperscriptBox["k", "2"], " ",
|
|
SuperscriptBox["r",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], "+", "k"}]]}]], "Output",
|
|
CellChangeTimes->{{3.7739948444033318`*^9, 3.773994872377877*^9}, {
|
|
3.773995007145669*^9, 3.77399501221817*^9}},
|
|
CellLabel->"Out[10]=",ExpressionUUID->"e5c5c912-0e26-410f-96fc-5c07bf8abd51"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"r", "^", "k"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"r", ",", "th", ",", "f"}], "}"}], ",", "\"\<Spherical\>\""}],
|
|
"]"}], " ", "//", " ", "Simplify"}], "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"r", "^", "k"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"r", ",", "th", ",", "f"}], "}"}], ",", "\"\<Spherical\>\""}],
|
|
"]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"r", ",", "th", ",", "f"}], "}"}], ",", "\"\<Spherical\>\""}],
|
|
"]"}], "//", "FullSimplify"}]}], "Input",
|
|
CellChangeTimes->{{3.773994912081747*^9, 3.773994933279908*^9}, {
|
|
3.773995020515245*^9, 3.773995023729156*^9}},
|
|
CellLabel->"In[11]:=",ExpressionUUID->"0b72d798-5753-48df-96e8-89e63672e9a0"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"k", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+", "k"}], ")"}], " ",
|
|
SuperscriptBox["r",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}]]}]], "Output",
|
|
CellChangeTimes->{{3.77399491650675*^9, 3.773994933609599*^9},
|
|
3.7739950240560417`*^9},
|
|
CellLabel->"Out[11]=",ExpressionUUID->"474cae3e-f8c6-42cd-a60f-9bc2167d62b3"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "k"}], ")"}], " ", "k", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+", "k"}], ")"}], " ",
|
|
SuperscriptBox["r",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], "+", "k"}]]}]], "Output",
|
|
CellChangeTimes->{{3.77399491650675*^9, 3.773994933609599*^9},
|
|
3.7739950241093187`*^9},
|
|
CellLabel->"Out[12]=",ExpressionUUID->"2d2db202-fef1-4c81-bb99-bc06c64ad71b"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"lap", "[",
|
|
RowBox[{"f_", ",", "v_", ",", "d_"}], "]"}], ":=",
|
|
RowBox[{
|
|
RowBox[{"D", "[",
|
|
RowBox[{"f", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"v", ",", "2"}], "}"}]}], "]"}], "+",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"d", "-", "1"}], ")"}], "/", "v"}], " ",
|
|
RowBox[{"D", "[",
|
|
RowBox[{"f", ",", "v"}], "]"}]}]}]}]], "Input",
|
|
CellChangeTimes->{{3.7739951880238047`*^9, 3.773995279951795*^9}},
|
|
CellLabel->"In[16]:=",ExpressionUUID->"38e3118c-e658-4684-8248-6598d3b19264"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"bih", "=",
|
|
RowBox[{
|
|
RowBox[{"lap", "[",
|
|
RowBox[{
|
|
RowBox[{"lap", "[",
|
|
RowBox[{
|
|
RowBox[{"r", "^", "k"}], ",", "r", ",", "d"}], "]"}], ",", "r", ",",
|
|
"d"}], "]"}], " ", "//", "FullSimplify"}]}]], "Input",
|
|
CellChangeTimes->{{3.773995239552339*^9, 3.7739952596127462`*^9}, {
|
|
3.773995323263743*^9, 3.773995353492358*^9}, {3.773996962358405*^9,
|
|
3.773996962893777*^9}, {3.773997001856657*^9,
|
|
3.7739970058145733`*^9}},ExpressionUUID->"9d1eb23a-bda0-4e25-b8e8-\
|
|
630323d206bf"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}], ")"}], " ", "k", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], "+", "d", "+", "k"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "d", "+", "k"}], ")"}], " ",
|
|
SuperscriptBox["r",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], "+", "k"}]]}]], "Output",
|
|
CellChangeTimes->{{3.773995250934018*^9, 3.773995286155744*^9}, {
|
|
3.773995320614431*^9, 3.7739953537596684`*^9}, {3.7739969693879623`*^9,
|
|
3.773996982573557*^9}},
|
|
CellLabel->"Out[36]=",ExpressionUUID->"45e170b9-2452-4676-87b1-d599304643af"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"biheq", "=",
|
|
RowBox[{
|
|
RowBox[{"lap", "[",
|
|
RowBox[{
|
|
RowBox[{"lap", "[",
|
|
RowBox[{
|
|
RowBox[{"f", "[", "r", "]"}], ",", "r", ",", "d"}], "]"}], ",", "r",
|
|
",", "d"}], "]"}], " ", "//", "FullSimplify"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.7739970142859488`*^9, 3.773997042094945*^9}},
|
|
CellLabel->"In[40]:=",ExpressionUUID->"cc9e4006-1dad-4241-900e-382d2d2c6de9"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
RowBox[{"$Assumptions", "=",
|
|
RowBox[{"{",
|
|
RowBox[{"d", ">", "0"}], "}"}]}], ";"}]], "Input",
|
|
CellChangeTimes->{{3.773997189633976*^9, 3.773997202656371*^9}},
|
|
CellLabel->"In[51]:=",ExpressionUUID->"901b4b59-c787-4abc-857f-45d86b9ba8cd"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"slv", "=",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"f", "[", "r", "]"}], "/.",
|
|
RowBox[{
|
|
RowBox[{"DSolve", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"biheq", "\[Equal]", "0"}], ",",
|
|
RowBox[{
|
|
RowBox[{"f", "[", "1", "]"}], "\[Equal]", "1"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"f", "'"}], "[", "1", "]"}], "\[Equal]", "1"}]}], "}"}],
|
|
",",
|
|
RowBox[{"f", "[", "r", "]"}], ",", "r"}], "]"}], "[",
|
|
RowBox[{"[", "1", "]"}], "]"}]}], " ", "//", "Simplify"}]}]], "Input",
|
|
CellChangeTimes->{{3.773997043495263*^9, 3.773997161710218*^9}},
|
|
CellLabel->"In[52]:=",ExpressionUUID->"7bbea44f-a092-4aee-96db-b390932cf3e5"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
FractionBox["1",
|
|
RowBox[{"2", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], "+", "d"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "d"}], ")"}]}]],
|
|
RowBox[{
|
|
SuperscriptBox["r",
|
|
RowBox[{"-", "d"}]], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], "+", "d"}], ")"}], " ",
|
|
SuperscriptBox["r", "2"], " ",
|
|
RowBox[{"C", "[", "1", "]"}]}], "-",
|
|
RowBox[{"2", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "d"}], ")"}], " ",
|
|
SuperscriptBox["r", "4"], " ",
|
|
RowBox[{"C", "[", "2", "]"}]}], "-",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"8", "-",
|
|
RowBox[{"6", " ", "d"}], "+",
|
|
SuperscriptBox["d", "2"]}], ")"}], " ",
|
|
SuperscriptBox["r",
|
|
RowBox[{"2", "+", "d"}]], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+",
|
|
RowBox[{"C", "[", "1", "]"}], "+",
|
|
RowBox[{"C", "[", "2", "]"}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
SuperscriptBox["r", "d"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"4", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"2", "+",
|
|
RowBox[{"C", "[", "2", "]"}]}], ")"}]}], "+",
|
|
RowBox[{
|
|
SuperscriptBox["d", "2"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
RowBox[{"C", "[", "1", "]"}], "+",
|
|
RowBox[{"C", "[", "2", "]"}]}], ")"}]}], "-",
|
|
RowBox[{"2", " ", "d", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"3", "+",
|
|
RowBox[{"2", " ",
|
|
RowBox[{"C", "[", "1", "]"}]}], "+",
|
|
RowBox[{"2", " ",
|
|
RowBox[{"C", "[", "2", "]"}]}]}], ")"}]}]}], ")"}]}]}],
|
|
")"}]}]}]], "Output",
|
|
CellChangeTimes->{{3.773997095418332*^9, 3.773997161985395*^9},
|
|
3.7739972039793158`*^9},
|
|
CellLabel->"Out[52]=",ExpressionUUID->"d8ff31cf-7d75-4eb7-8d37-39450a8e40e4"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"bihsol", "=",
|
|
RowBox[{
|
|
RowBox[{"slv", "/.",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"C", "[", "1", "]"}], "\[Rule]", "0"}], ",",
|
|
RowBox[{
|
|
RowBox[{"C", "[", "2", "]"}], "\[Rule]", "0"}]}], "}"}]}], "//",
|
|
"Simplify"}]}]], "Input",
|
|
CellChangeTimes->{{3.7739971753691893`*^9, 3.773997300205394*^9}, {
|
|
3.773997382501239*^9, 3.773997393518981*^9}, {3.7740792162587633`*^9,
|
|
3.774079217425703*^9}},
|
|
CellLabel->"In[65]:=",ExpressionUUID->"8167fb86-f924-4194-8bd3-e227911b3977"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
FractionBox["1", "2"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{"1", "+",
|
|
SuperscriptBox["r", "2"]}], ")"}]}]], "Output",
|
|
CellChangeTimes->{{3.773997178972314*^9, 3.7739973004831057`*^9}, {
|
|
3.773997390369925*^9, 3.7739973975037947`*^9}, 3.774079218811607*^9},
|
|
CellLabel->"Out[65]=",ExpressionUUID->"ebc5b8e0-5d0d-4854-88d5-22174051e964"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"bihc", " ", "=",
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{"Laplacian", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"x", "^", "i"}], " ",
|
|
RowBox[{"y", "^", "j"}], " ",
|
|
RowBox[{"z", "^", "k"}]}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}], " ", "//",
|
|
"Simplify"}]}]], "Input",
|
|
CellChangeTimes->{{3.773995601099601*^9, 3.7739956712772007`*^9},
|
|
3.773996967288188*^9},
|
|
CellLabel->"In[34]:=",ExpressionUUID->"18a7a2b1-fd09-4e1b-a868-b7b11de2cf9c"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{
|
|
SuperscriptBox["x", "i"], " ",
|
|
SuperscriptBox["y", "j"], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "3"}], "+", "i"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "i"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "i"}], ")"}], " ", "i"}],
|
|
SuperscriptBox["x", "4"]], "+",
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "3"}], "+", "j"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "j"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "j"}], ")"}], " ", "j"}],
|
|
SuperscriptBox["y", "4"]], "+",
|
|
FractionBox[
|
|
RowBox[{"2", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "i"}], ")"}], " ", "i", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "j"}], ")"}], " ", "j"}],
|
|
RowBox[{
|
|
SuperscriptBox["x", "2"], " ",
|
|
SuperscriptBox["y", "2"]}]], "+",
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "3"}], "+", "k"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "k"}], ")"}], " ", "k"}],
|
|
SuperscriptBox["z", "4"]], "+",
|
|
FractionBox[
|
|
RowBox[{"2", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "i"}], ")"}], " ", "i", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "k"}], ")"}], " ", "k"}],
|
|
RowBox[{
|
|
SuperscriptBox["x", "2"], " ",
|
|
SuperscriptBox["z", "2"]}]], "+",
|
|
FractionBox[
|
|
RowBox[{"2", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "j"}], ")"}], " ", "j", " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "k"}], ")"}], " ", "k"}],
|
|
RowBox[{
|
|
SuperscriptBox["y", "2"], " ",
|
|
SuperscriptBox["z", "2"]}]]}], ")"}], " ",
|
|
SuperscriptBox["z", "k"]}]], "Output",
|
|
CellChangeTimes->{{3.773995622463397*^9, 3.773995672055132*^9},
|
|
3.773996967675263*^9},
|
|
CellLabel->"Out[34]=",ExpressionUUID->"caeada53-636d-4dfe-9e2f-da623d873561"]
|
|
}, Open ]],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"Limit", "[",
|
|
RowBox[{"bih", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"x", "\[Rule]", "0"}], "}"}]}], "]"}]], "Input",
|
|
CellChangeTimes->{{3.773995675238102*^9, 3.773995682196781*^9}},
|
|
CellLabel->"In[33]:=",ExpressionUUID->"7cf9521c-9b2c-4344-928d-d5fedd534ba7"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"ConditionalExpression", "[",
|
|
RowBox[{"ComplexInfinity", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "3"}], "+", "j"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "j"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "j"}], ")"}], " ", "j"}],
|
|
SuperscriptBox["y", "4"]], "|", "j", "|",
|
|
FractionBox["1",
|
|
SuperscriptBox["y", "2"]], "|",
|
|
FractionBox[
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "3"}], "+", "k"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "2"}], "+", "k"}], ")"}], " ",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], "+", "k"}], ")"}], " ", "k"}],
|
|
SuperscriptBox["z", "4"]], "|", "k", "|",
|
|
FractionBox["1",
|
|
SuperscriptBox["z", "2"]]}], ")"}], "\[Element]",
|
|
TemplateBox[{},
|
|
"Reals"]}], "&&",
|
|
RowBox[{"0", "<", "i", "<", "4"}], "&&",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"-", "6"}], "+",
|
|
RowBox[{"11", " ", "i"}], "-",
|
|
RowBox[{"6", " ",
|
|
SuperscriptBox["i", "2"]}], "+",
|
|
SuperscriptBox["i", "3"]}], ")"}], " ",
|
|
SuperscriptBox["y", "j"], " ",
|
|
SuperscriptBox["z", "k"]}], "<", "0"}]}]}], "]"}]], "Output",
|
|
CellChangeTimes->{3.7739957020295143`*^9},
|
|
CellLabel->"Out[33]=",ExpressionUUID->"4941b575-a3b0-45b0-9d0c-33e69b7e52e3"]
|
|
}, Open ]],
|
|
|
|
Cell[BoxData[""], "Input",
|
|
CellChangeTimes->{{3.7739969559355297`*^9,
|
|
3.773996957924678*^9}},ExpressionUUID->"ea7630e8-5cd1-470e-bcee-\
|
|
c677a8c74e46"]
|
|
},
|
|
WindowSize->{808, 911},
|
|
WindowMargins->{{Automatic, 552}, {71, Automatic}},
|
|
FrontEndVersion->"11.3 for Linux x86 (64-bit) (March 6, 2018)",
|
|
StyleDefinitions->"Default.nb"
|
|
]
|
|
(* End of Notebook Content *)
|
|
|
|
(* Internal cache information *)
|
|
(*CellTagsOutline
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*CellTagsIndex
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*NotebookFileOutline
|
|
Notebook[{
|
|
Cell[CellGroupData[{
|
|
Cell[580, 22, 781, 21, 55, "Input",ExpressionUUID->"0e204612-f4ad-4947-8512-0d390f7199a4"],
|
|
Cell[1364, 45, 337, 8, 37, "Output",ExpressionUUID->"a5ab13a9-d7b2-4e5a-966e-05a797805dbf"],
|
|
Cell[1704, 55, 441, 12, 37, "Output",ExpressionUUID->"e5c5c912-0e26-410f-96fc-5c07bf8abd51"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[2182, 72, 843, 22, 78, "Input",ExpressionUUID->"0b72d798-5753-48df-96e8-89e63672e9a0"],
|
|
Cell[3028, 96, 347, 9, 37, "Output",ExpressionUUID->"474cae3e-f8c6-42cd-a60f-9bc2167d62b3"],
|
|
Cell[3378, 107, 501, 15, 37, "Output",ExpressionUUID->"2d2db202-fef1-4c81-bb99-bc06c64ad71b"]
|
|
}, Open ]],
|
|
Cell[3894, 125, 552, 16, 31, "Input",ExpressionUUID->"38e3118c-e658-4684-8248-6598d3b19264"],
|
|
Cell[CellGroupData[{
|
|
Cell[4471, 145, 535, 13, 31, "Input",ExpressionUUID->"9d1eb23a-bda0-4e25-b8e8-630323d206bf"],
|
|
Cell[5009, 160, 616, 17, 37, "Output",ExpressionUUID->"45e170b9-2452-4676-87b1-d599304643af"]
|
|
}, Open ]],
|
|
Cell[5640, 180, 440, 11, 31, "Input",ExpressionUUID->"cc9e4006-1dad-4241-900e-382d2d2c6de9"],
|
|
Cell[6083, 193, 272, 6, 31, "Input",ExpressionUUID->"901b4b59-c787-4abc-857f-45d86b9ba8cd"],
|
|
Cell[CellGroupData[{
|
|
Cell[6380, 203, 738, 20, 31, "Input",ExpressionUUID->"7bbea44f-a092-4aee-96db-b390932cf3e5"],
|
|
Cell[7121, 225, 2027, 64, 111, "Output",ExpressionUUID->"d8ff31cf-7d75-4eb7-8d37-39450a8e40e4"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[9185, 294, 546, 14, 31, "Input",ExpressionUUID->"8167fb86-f924-4194-8bd3-e227911b3977"],
|
|
Cell[9734, 310, 365, 8, 53, "Output",ExpressionUUID->"ebc5b8e0-5d0d-4854-88d5-22174051e964"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[10136, 323, 653, 18, 31, "Input",ExpressionUUID->"18a7a2b1-fd09-4e1b-a868-b7b11de2cf9c"],
|
|
Cell[10792, 343, 2356, 78, 109, "Output",ExpressionUUID->"caeada53-636d-4dfe-9e2f-da623d873561"]
|
|
}, Open ]],
|
|
Cell[CellGroupData[{
|
|
Cell[13185, 426, 283, 6, 31, "Input",ExpressionUUID->"7cf9521c-9b2c-4344-928d-d5fedd534ba7"],
|
|
Cell[13471, 434, 1652, 50, 126, "Output",ExpressionUUID->"4941b575-a3b0-45b0-9d0c-33e69b7e52e3"]
|
|
}, Open ]],
|
|
Cell[15138, 487, 154, 3, 31, "Input",ExpressionUUID->"ea7630e8-5cd1-470e-bcee-c677a8c74e46"]
|
|
}
|
|
]
|
|
*)
|
|
|
|
(* End of internal cache information *)
|
|
|
|
|