(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 63325, 1854] NotebookOptionsPosition[ 61089, 1814] NotebookOutlinePosition[ 61480, 1830] CellTagsIndexPosition[ 61437, 1827] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"matzeros", "=", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "1"}], "1", "\[Placeholder]", "1", "1", "1", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]"}, {"1", RowBox[{"-", "1"}], "1", "1", "\[Placeholder]", "1", "\[Placeholder]", "0", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]"}, {"\[Placeholder]", "1", RowBox[{"-", "1"}], "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]"}, {"1", "1", "1", RowBox[{"-", "1"}], "1", "\[Placeholder]", "1", "0", "0", "0", "0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0"}, {"1", "\[Placeholder]", "\[Placeholder]", "1", RowBox[{"-", "1"}], "1", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0"}, {"1", "1", "\[Placeholder]", "\[Placeholder]", "1", RowBox[{"-", "1"}], "1", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "0", "0", "0"}, {"\[Placeholder]", "\[Placeholder]", "1", "1", "\[Placeholder]", "1", RowBox[{"-", "1"}], "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0", "0"}, {"0", "0", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", RowBox[{"-", "1"}], "1", "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]"}, {"0", "\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "1", RowBox[{"-", "1"}], "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "1"}, {"\[Placeholder]", "0", "0", "0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", RowBox[{"-", "1"}], "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "1", RowBox[{"-", "1"}], "\[Placeholder]", "\[Placeholder]", "1", "1"}, {"0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", RowBox[{"-", "1"}], "1", "\[Placeholder]", "1"}, {"0", "0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "1", RowBox[{"-", "1"}], "1", "\[Placeholder]"}, {"\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "1", "1", "\[Placeholder]", "1", RowBox[{"-", "1"}], "1"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "0", "0", "0", "\[Placeholder]", "1", "\[Placeholder]", "1", "1", "\[Placeholder]", "1", RowBox[{"-", "1"}]} }, 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" -> {}}], ")"}]}], "\[IndentingNewLine]", RowBox[{"varstuff", "=", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "a11"}, { RowBox[{"-", "1"}], "1", "0"}, {"1", "1", "0"}, {"1", RowBox[{"-", "1"}], "0"}, {"a1", "1", "a12"}, {"1", "a7", "a13"}, {"a2", "1", "a14"}, {"0", "0", "1"}, {"a3", "0", "a15"}, {"0", "0", RowBox[{"-", "1"}]}, {"a4", "0", "1"}, {"a5", "a8", "a16"}, {"0", "a9", "a17"}, {"0", "a10", "1"}, {"a6", "0", "a18"} }, 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" -> {}}], ")"}]}], "\[IndentingNewLine]", RowBox[{"a", "=", "1"}], "\[IndentingNewLine]", RowBox[{"b", "=", "11"}], "\[IndentingNewLine]", RowBox[{"o", "=", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "1"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"n", "=", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "2"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"d", "=", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "3"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"q", "=", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "1"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "2"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"s", "=", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "3"}], "]"}], "]"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.831807518799519*^9, 3.831807594956044*^9}, { 3.8318076728397713`*^9, 3.831807701743909*^9}, {3.831807964346015*^9, 3.831807983417666*^9}, {3.8318080161942463`*^9, 3.831808018286193*^9}, { 3.831808048507024*^9, 3.831808049498742*^9}, {3.831808167039514*^9, 3.8318081853134823`*^9}, {3.831808248068654*^9, 3.831808271264772*^9}, { 3.831809298769846*^9, 3.8318094912990503`*^9}, {3.831817104091901*^9, 3.83181710652077*^9}, {3.8318177838030863`*^9, 3.831817881551998*^9}, { 3.831817925941033*^9, 3.831817928931918*^9}, {3.8318182203609247`*^9, 3.8318182359756727`*^9}, {3.8318183896631527`*^9, 3.831818450411126*^9}, 3.831818499908147*^9, {3.831818542464649*^9, 3.831818610607449*^9}, 3.831819420323295*^9, 3.8318196814511757`*^9, {3.8318197239910173`*^9, 3.831819813512734*^9}, {3.831819843678256*^9, 3.83181988326925*^9}, { 3.83181992077528*^9, 3.831819944340735*^9}, 3.8318202962086*^9, { 3.8318204011042128`*^9, 3.831820402666539*^9}, {3.831820493045451*^9, 3.8318204956924543`*^9}, {3.831821323942285*^9, 3.831821325133766*^9}, { 3.832067458363123*^9, 3.832067460179153*^9}, {3.832067519350775*^9, 3.832067521770728*^9}}, CellLabel-> "In[595]:=",ExpressionUUID->"b9956451-1eb1-4b6d-8ea0-8e5e4f91ba63"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"bil", "[", RowBox[{"a_", ",", "b_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"1", "/", "2"}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "3"}], "]"}], "]"}], "^", "2"}], "+", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "2"}], "]"}], "]"}], "^", "2"}], "-", "1"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "1"}], "]"}], "]"}], "+", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "2"}], "]"}], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "1"}], "]"}], "]"}], "+", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "2"}], "]"}], "]"}]}], ")"}]}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "3"}], "]"}], "]"}], "^", "2"}], "+", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "2"}], "]"}], "]"}], "^", "2"}], "-", "1"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "1"}], "]"}], "]"}], "+", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "2"}], "]"}], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "1"}], "]"}], "]"}], "+", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "2"}], "]"}], "]"}]}], ")"}]}]}]}], ")"}]}], "-", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "3"}], "]"}], "]"}], "*", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "3"}], "]"}], "]"}]}], "-", RowBox[{ RowBox[{"vars", "[", RowBox[{"[", RowBox[{"a", ",", "2"}], "]"}], "]"}], "*", RowBox[{"vars", "[", RowBox[{"[", RowBox[{"b", ",", "2"}], "]"}], "]"}]}]}], "==", RowBox[{"matzeros", "[", RowBox[{"[", RowBox[{"a", ",", "b"}], "]"}], "]"}]}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"bil", "[", RowBox[{"1", ",", "3"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "4"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "7"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "5"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "8"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "4"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "7"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "5"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "8"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"7", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"7", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"8", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"8", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"9", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"9", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"10", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"11", ",", "12"}], "]"}]}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.8320676035083227`*^9, 3.832067605480812*^9}, { 3.8320677888264303`*^9, 3.832067789040926*^9}, {3.832067857489883*^9, 3.832067876719578*^9}, {3.832068232353291*^9, 3.832068310167591*^9}, { 3.8320697967508307`*^9, 3.8320698123324327`*^9}}, CellLabel->"In[20]:=",ExpressionUUID->"6d6c1f85-a342-4808-8fa2-2cf8c0132147"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"vars", "=", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "a11"}, {"1", "1", "0"}, {"a1", "1", "a12"}, {"1", "a7", "a13"}, {"a2", "1", "a14"}, {"0", "0", "1"}, {"a3", "0", "a15"}, {"a4", "0", "1"}, {"a5", "a8", "a16"}, {"0", "a9", "a17"}, {"0", "a10", "1"}, {"a6", "0", "a18"} }, 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" -> {}}], ")"}]}]], "Input", CellChangeTimes->{ 3.832070076720479*^9},ExpressionUUID->"d414d2ba-4acb-46d3-a25c-\ b7b10cffd621"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", RowBox[{"a11", " ", "a12"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "+", "a1"}], ")"}], " ", SuperscriptBox["a11", "2"]}], "+", FractionBox[ RowBox[{"2", " ", SuperscriptBox["a12", "2"]}], RowBox[{"1", "+", "a1"}]]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a11"}], " ", "a13"}], "-", "a7", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["1", "2"], " ", SuperscriptBox["a11", "2"], " ", RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}]}], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}]}], RowBox[{"1", "+", "a7"}]]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a11"}], " ", "a15"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a15", "2"]}], ")"}]}], "a3"], "+", FractionBox[ RowBox[{ SuperscriptBox["a11", "2"], " ", "a3"}], "2"]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a11"}], " ", "a16"}], "-", "a8", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["1", "2"], " ", SuperscriptBox["a11", "2"], " ", RowBox[{"(", RowBox[{"a5", "+", "a8"}], ")"}]}], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a16", "2"], "+", SuperscriptBox["a8", "2"]}], ")"}]}], RowBox[{"a5", "+", "a8"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a11"}], " ", "a17"}], "-", "a9", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["a11", "2"], " ", "a9"}], "2"], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a17", "2"], "+", SuperscriptBox["a9", "2"]}], ")"}]}], "a9"]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", FractionBox[ SuperscriptBox["a14", "2"], RowBox[{"1", "+", "a2"}]]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a12"}], " ", "a13"}], "-", "a7", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["a12", "2"], " ", RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}]}], RowBox[{"1", "+", "a1"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a1"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}]}], RowBox[{"1", "+", "a7"}]]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a12"}], " ", "a15"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a1"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a15", "2"]}], ")"}]}], "a3"], "+", FractionBox[ RowBox[{ SuperscriptBox["a12", "2"], " ", "a3"}], RowBox[{"1", "+", "a1"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a12"}], " ", "a16"}], "-", "a8", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["a12", "2"], " ", RowBox[{"(", RowBox[{"a5", "+", "a8"}], ")"}]}], RowBox[{"1", "+", "a1"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a1"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a16", "2"], "+", SuperscriptBox["a8", "2"]}], ")"}]}], RowBox[{"a5", "+", "a8"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a12"}], " ", "a18"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a1"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}]}], "a6"], "+", FractionBox[ RowBox[{ SuperscriptBox["a12", "2"], " ", "a6"}], RowBox[{"1", "+", "a1"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a13"}], " ", "a14"}], "-", "a7", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["a14", "2"], " ", RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}]}], RowBox[{"1", "+", "a2"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}]}], RowBox[{"1", "+", "a7"}]]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a13"}], " ", "a16"}], "-", RowBox[{"a7", " ", "a8"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"a5", "+", "a8"}], ")"}]}], RowBox[{"1", "+", "a7"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a16", "2"], "+", SuperscriptBox["a8", "2"]}], ")"}]}], RowBox[{"a5", "+", "a8"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a13"}], " ", "a17"}], "-", RowBox[{"a7", " ", "a9"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}], " ", "a9"}], RowBox[{"1", "+", "a7"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a17", "2"], "+", SuperscriptBox["a9", "2"]}], ")"}]}], "a9"]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "a13"}], "-", RowBox[{"a10", " ", "a7"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"a10", " ", RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}]}], "+", FractionBox[ RowBox[{"a10", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}]}], RowBox[{"1", "+", "a7"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a13"}], " ", "a18"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "a7"}], ")"}]}], "a6"], "+", FractionBox[ RowBox[{"a6", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a13", "2"], "+", SuperscriptBox["a7", "2"]}], ")"}]}], RowBox[{"1", "+", "a7"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "a14"}], "+", FractionBox[ RowBox[{ SuperscriptBox["a14", "2"], " ", "a4"}], RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "a2"}], ")"}]}]]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "a10"}], "-", "a14", "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"a10", " ", SuperscriptBox["a14", "2"]}], RowBox[{"1", "+", "a2"}]], "+", RowBox[{"a10", " ", RowBox[{"(", RowBox[{"1", "+", "a2"}], ")"}]}]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a14"}], " ", "a18"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "a2"}], ")"}]}], "a6"], "+", FractionBox[ RowBox[{ SuperscriptBox["a14", "2"], " ", "a6"}], RowBox[{"1", "+", "a2"}]]}], ")"}]}]}], "\[Equal]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a15"}], " ", "a16"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a15", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"a5", "+", "a8"}], ")"}]}], "a3"], "+", FractionBox[ RowBox[{"a3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a16", "2"], "+", SuperscriptBox["a8", "2"]}], ")"}]}], RowBox[{"a5", "+", "a8"}]]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a15"}], " ", "a18"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}], " ", "a3"}], "a6"], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a15", "2"]}], ")"}], " ", "a6"}], "a3"]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", FractionBox[ RowBox[{"a10", " ", "a4"}], "2"]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "a18"}], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}], " ", "a4"}], RowBox[{"2", " ", "a6"}]]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a16"}], " ", "a17"}], "-", RowBox[{"a8", " ", "a9"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a16", "2"], "+", SuperscriptBox["a8", "2"]}], ")"}], " ", "a9"}], RowBox[{"a5", "+", "a8"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"a5", "+", "a8"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a17", "2"], "+", SuperscriptBox["a9", "2"]}], ")"}]}], "a9"]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "a16"}], " ", "a18"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"a5", "+", "a8"}], ")"}]}], "a6"], "+", FractionBox[ RowBox[{"a6", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a16", "2"], "+", SuperscriptBox["a8", "2"]}], ")"}]}], RowBox[{"a5", "+", "a8"}]]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "a17"}], "-", RowBox[{"a10", " ", "a9"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"a10", " ", "a9"}], "+", FractionBox[ RowBox[{"a10", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a17", "2"], "+", SuperscriptBox["a9", "2"]}], ")"}]}], "a9"]}], ")"}]}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{"-", "a18"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"a10", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["a18", "2"]}], ")"}]}], "a6"], "+", RowBox[{"a10", " ", "a6"}]}], ")"}]}]}], "\[Equal]", "1"}]}]], "Output",\ CellChangeTimes->{{3.832069790668619*^9, 3.832069813664901*^9}}, CellLabel->"Out[21]=",ExpressionUUID->"b8883fc0-3737-4e0d-bb40-5e10d682ff05"] }, Open ]], Cell[BoxData[ RowBox[{"(", GridBox[{ {"1", "1", RowBox[{"2", " ", SqrtBox["5"]}]}, {"1", "1", "0"}, { FractionBox["27", "5"], "1", FractionBox["24", SqrtBox["5"]]}, {"1", FractionBox["3", "2"], FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"]}, { FractionBox["13", "5"], "1", FractionBox["6", SqrtBox["5"]]}, {"0", "0", "1"}, { FractionBox["8", SqrtBox["5"]], "0", "7"}, { FractionBox["6", SqrtBox["5"]], "0", "1"}, { FractionBox["8", SqrtBox["5"]], SqrtBox["5"], "10"}, {"0", SqrtBox["5"], "4"}, {"0", FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"], "1"}, { FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]], "0", FractionBox["13", "5"]} }, 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]", ")"}]], "Input", CellChangeTimes->{{3.832067797029974*^9, 3.8320678250887947`*^9}, 3.83206786184661*^9, 3.832068908563352*^9, {3.832069004927162*^9, 3.832069063221637*^9}},ExpressionUUID->"07c417e3-ab27-4df6-bac8-\ 407abe9b7e72"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"bil", "[", RowBox[{"1", ",", "3"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "4"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "7"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "5"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "8"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "4"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "7"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "5"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "8"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"7", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"7", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"8", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"8", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"9", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"9", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"10", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"11", ",", "12"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.832067284149284*^9, 3.832067410227961*^9}, { 3.832067450877516*^9, 3.8320675172287073`*^9}, {3.832067574189147*^9, 3.832067636902478*^9}, {3.83206809001365*^9, 3.832068095934476*^9}, { 3.832068328544753*^9, 3.8320686347614307`*^9}, {3.832068670190175*^9, 3.83206868825493*^9}, {3.832068752719368*^9, 3.8320687603657846`*^9}, { 3.832069594176708*^9, 3.832069596341961*^9}, {3.8320698732190323`*^9, 3.8320700238496428`*^9}, 3.832070194760044*^9, {3.832071008128688*^9, 3.832071010781746*^9}},ExpressionUUID->"afd53ed6-b287-4977-8a5a-\ f73dda451b35"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a1", "\[Rule]", FractionBox["27", "5"]}], ",", RowBox[{"a10", "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"]}]}], ",", RowBox[{"a11", "\[Rule]", RowBox[{ RowBox[{"-", "2"}], " ", SqrtBox["5"]}]}], ",", RowBox[{"a12", "\[Rule]", RowBox[{"-", FractionBox["24", SqrtBox["5"]]}]}], ",", RowBox[{"a13", "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"]}]}], ",", RowBox[{"a14", "\[Rule]", RowBox[{"-", FractionBox["6", SqrtBox["5"]]}]}], ",", RowBox[{"a15", "\[Rule]", "7"}], ",", RowBox[{"a16", "\[Rule]", "10"}], ",", RowBox[{"a17", "\[Rule]", "4"}], ",", RowBox[{"a18", "\[Rule]", FractionBox["13", "5"]}], ",", RowBox[{"a2", "\[Rule]", FractionBox["13", "5"]}], ",", RowBox[{"a3", "\[Rule]", RowBox[{"-", FractionBox["8", SqrtBox["5"]]}]}], ",", RowBox[{"a4", "\[Rule]", RowBox[{"-", FractionBox["6", SqrtBox["5"]]}]}], ",", RowBox[{"a5", "\[Rule]", RowBox[{"-", FractionBox["8", SqrtBox["5"]]}]}], ",", RowBox[{"a6", "\[Rule]", RowBox[{"-", FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]]}]}], ",", RowBox[{"a7", "\[Rule]", FractionBox["3", "2"]}], ",", RowBox[{"a8", "\[Rule]", RowBox[{"-", SqrtBox["5"]}]}], ",", RowBox[{"a9", "\[Rule]", RowBox[{"-", SqrtBox["5"]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"a1", "\[Rule]", FractionBox["27", "5"]}], ",", RowBox[{"a10", "\[Rule]", FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"]}], ",", RowBox[{"a11", "\[Rule]", RowBox[{"2", " ", SqrtBox["5"]}]}], ",", RowBox[{"a12", "\[Rule]", FractionBox["24", SqrtBox["5"]]}], ",", RowBox[{"a13", "\[Rule]", FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"]}], ",", RowBox[{"a14", "\[Rule]", FractionBox["6", SqrtBox["5"]]}], ",", RowBox[{"a15", "\[Rule]", "7"}], ",", RowBox[{"a16", "\[Rule]", "10"}], ",", RowBox[{"a17", "\[Rule]", "4"}], ",", RowBox[{"a18", "\[Rule]", FractionBox["13", "5"]}], ",", RowBox[{"a2", "\[Rule]", FractionBox["13", "5"]}], ",", RowBox[{"a3", "\[Rule]", FractionBox["8", SqrtBox["5"]]}], ",", RowBox[{"a4", "\[Rule]", FractionBox["6", SqrtBox["5"]]}], ",", RowBox[{"a5", "\[Rule]", FractionBox["8", SqrtBox["5"]]}], ",", RowBox[{"a6", "\[Rule]", FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]]}], ",", RowBox[{"a7", "\[Rule]", FractionBox["3", "2"]}], ",", RowBox[{"a8", "\[Rule]", SqrtBox["5"]}], ",", RowBox[{"a9", "\[Rule]", SqrtBox["5"]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.83206988252102*^9, 3.832069907460369*^9}, 3.832069976565806*^9, 3.832070204430662*^9, 3.832070269764318*^9, 3.832070411800643*^9, 3.832070943915667*^9}, CellLabel->"Out[34]=",ExpressionUUID->"2fa96c23-acd6-4c4a-9a0a-5bee0a0dd517"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"RootApproximant", "[", RowBox[{"NSolve", "[", RowBox[{ RowBox[{"bil", "[", RowBox[{"1", ",", "3"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "4"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "7"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"1", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "5"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "8"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"2", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "4"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "7"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"3", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "5"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"4", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "8"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"5", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"7", ",", "9"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"7", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"8", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"8", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"9", ",", "10"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"9", ",", "12"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"10", ",", "11"}], "]"}], "&&", RowBox[{"bil", "[", RowBox[{"11", ",", "12"}], "]"}]}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.832074529944628*^9, 3.8320745363529787`*^9}, { 3.832074782348741*^9, 3.8320747879554043`*^9}}, CellLabel->"In[41]:=",ExpressionUUID->"8d27c355-b0e8-4254-94d4-cbfdd3ad0826"], Cell[BoxData[ TemplateBox[{ "RootApproximant", "blnotn", "\"The value of the argument \\!\\(\\*RowBox[{\\\"a1\\\", \\\"\[Rule]\\\", \ \\\"5.4`\\\"}]\\) in position \\!\\(\\*RowBox[{\\\"1\\\"}]\\) is not a \ number.\"", 2, 41, 12, 31696493496564779713, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.832074805241248*^9}, CellLabel-> "During evaluation of \ In[41]:=",ExpressionUUID->"56473541-5f4c-4432-a33d-cbb5f88fe550"], Cell[BoxData[ TemplateBox[{ "RootApproximant", "blnotn", "\"The value of the argument \\!\\(\\*RowBox[{\\\"a10\\\", \ \\\"\[Rule]\\\", RowBox[{\\\"-\\\", \\\"1.490711984999859`\\\"}]}]\\) in \ position \\!\\(\\*RowBox[{\\\"1\\\"}]\\) is not a number.\"", 2, 41, 13, 31696493496564779713, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.83207480524988*^9}, CellLabel-> "During evaluation of \ In[41]:=",ExpressionUUID->"304c5d99-263a-4649-bf1d-46dff562b2a7"], Cell[BoxData[ TemplateBox[{ "RootApproximant", "blnotn", "\"The value of the argument \\!\\(\\*RowBox[{\\\"a11\\\", \ \\\"\[Rule]\\\", RowBox[{\\\"-\\\", \\\"4.472135954999577`\\\"}]}]\\) in \ position \\!\\(\\*RowBox[{\\\"1\\\"}]\\) is not a number.\"", 2, 41, 14, 31696493496564779713, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.8320748052566013`*^9}, CellLabel-> "During evaluation of \ In[41]:=",ExpressionUUID->"e394b350-77c7-49c7-923b-9ab48092fe2f"], Cell[BoxData[ TemplateBox[{ "General", "stop", "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"RootApproximant\\\", \\\ \"::\\\", \\\"blnotn\\\"}], \\\"MessageName\\\"]\\) will be suppressed during \ this calculation.\"", 2, 41, 15, 31696493496564779713, "Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.83207480526341*^9}, CellLabel-> "During evaluation of \ In[41]:=",ExpressionUUID->"ffa3f13e-0381-473e-997f-185d867233cd"] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RootApproximant", "[", RowBox[{"a1", "\[Rule]", "5.4`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a10", "\[Rule]", RowBox[{"-", "1.490711984999859`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a11", "\[Rule]", RowBox[{"-", "4.472135954999577`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a12", "\[Rule]", RowBox[{"-", "10.733126291998984`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a13", "\[Rule]", RowBox[{"-", "3.354101966249683`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a14", "\[Rule]", RowBox[{"-", "2.683281572999746`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a15", "\[Rule]", "7.`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a16", "\[Rule]", "10.`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a17", "\[Rule]", "4.`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a18", "\[Rule]", "2.6`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a2", "\[Rule]", "2.6`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a3", "\[Rule]", RowBox[{"-", "3.5777087639996616`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a4", "\[Rule]", RowBox[{"-", "2.683281572999746`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a5", "\[Rule]", RowBox[{"-", "3.5777087639996616`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a6", "\[Rule]", RowBox[{"-", "2.146625258399797`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a7", "\[Rule]", "1.5`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a8", "\[Rule]", RowBox[{"-", "2.2360679774997885`"}]}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a9", "\[Rule]", RowBox[{"-", "2.2360679774997885`"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RootApproximant", "[", RowBox[{"a1", "\[Rule]", "5.4`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a10", "\[Rule]", "1.4907119849998598`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a11", "\[Rule]", "4.47213595499958`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a12", "\[Rule]", "10.73312629199899`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a13", "\[Rule]", "3.3541019662496847`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a14", "\[Rule]", "2.6832815729997477`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a15", "\[Rule]", "7.`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a16", "\[Rule]", "10.`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a17", "\[Rule]", "4.`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a18", "\[Rule]", "2.6`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a2", "\[Rule]", "2.6`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a3", "\[Rule]", "3.577708763999664`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a4", "\[Rule]", "2.6832815729997477`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a5", "\[Rule]", "3.577708763999664`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a6", "\[Rule]", "2.1466252583997982`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a7", "\[Rule]", "1.5`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a8", "\[Rule]", "2.23606797749979`"}], "]"}], ",", RowBox[{"RootApproximant", "[", RowBox[{"a9", "\[Rule]", "2.23606797749979`"}], "]"}]}], "}"}]}], "}"}]],\ "Input", CellChangeTimes->{{3.832107989040124*^9, 3.83210798904531*^9}},ExpressionUUID->"7d35b7ff-e080-4389-8596-\ 12c0fca29756"], Cell[BoxData[{ RowBox[{"matzeros", "=", RowBox[{"(", "\[NoBreak]", GridBox[{ {"\[Placeholder]", "\[Placeholder]", "1", "1", "\[Placeholder]", "0", "0", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]"}, {"\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]"}, {"1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0"}, {"1", "\[Placeholder]", "1", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "0", "0", "0"}, {"\[Placeholder]", "1", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0", "0"}, {"0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]"}, {"0", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "1"}, {"\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", "1", "1"}, {"0", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "1"}, {"0", "\[Placeholder]", "\[Placeholder]", "0", "\[Placeholder]", "1", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "1", "\[Placeholder]"}, {"\[Placeholder]", "0", "\[Placeholder]", "0", "0", "\[Placeholder]", "\[Placeholder]", "1", "\[Placeholder]", "1", "\[Placeholder]", "1"}, {"\[Placeholder]", "\[Placeholder]", "0", "0", "0", "\[Placeholder]", "1", "1", "1", "\[Placeholder]", "1", "\[Placeholder]"} }, 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" -> {}}], ")"}]}], "\[IndentingNewLine]", RowBox[{"vars", "=", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "a11"}, {"1", "1", "0"}, {"a1", "1", "a12"}, {"1", "a7", "a13"}, {"a2", "1", "a14"}, {"0", "0", "1"}, {"a3", "0", "a15"}, {"a4", "0", "1"}, {"a5", "a8", "a16"}, {"0", "a9", "a17"}, {"0", "a10", "1"}, {"a6", "0", "a18"} }, 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" -> {}}], ")"}]}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.831820405438169*^9, 3.83182046989646*^9}, { 3.831820558054164*^9, 3.83182091796528*^9}, {3.831820967771565*^9, 3.831820989061385*^9}, {3.831821049347245*^9, 3.8318210752980537`*^9}, { 3.831821111086649*^9, 3.831821229642725*^9}, {3.8318212669123917`*^9, 3.831821267598941*^9}, {3.831821432229517*^9, 3.831821444069852*^9}, { 3.83182156975242*^9, 3.83182162013104*^9}, {3.83182176340163*^9, 3.83182178387678*^9}, {3.831821864070838*^9, 3.831821864144848*^9}, { 3.8318218999237328`*^9, 3.8318219002495203`*^9}, {3.831821968960537*^9, 3.8318219971633673`*^9}, {3.8318220633867207`*^9, 3.831822064833501*^9}, { 3.831823094143306*^9, 3.8318231240548153`*^9}, {3.831823530378996*^9, 3.831823604069244*^9}, {3.831823639615611*^9, 3.831823696776061*^9}, { 3.8320675099523*^9, 3.832067549941819*^9}, 3.832069138114016*^9, { 3.8320697418454227`*^9, 3.83206975572313*^9}, {3.8320700866134357`*^9, 3.8320701819606857`*^9}, {3.832070301660103*^9, 3.832070302088328*^9}, { 3.8320704316877003`*^9, 3.832070450376793*^9}, {3.832071190635412*^9, 3.832071197297544*^9}},ExpressionUUID->"fe95b6b4-36d8-4b3e-bcff-\ 59c63171bd33"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MatrixForm", "[", RowBox[{"vars", "/.", RowBox[{"{", RowBox[{ RowBox[{"a1", "\[Rule]", FractionBox["27", "5"]}], ",", RowBox[{"a10", "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"]}]}], ",", RowBox[{"a11", "\[Rule]", RowBox[{ RowBox[{"-", "2"}], " ", SqrtBox["5"]}]}], ",", RowBox[{"a12", "\[Rule]", RowBox[{"-", FractionBox["24", SqrtBox["5"]]}]}], ",", RowBox[{"a13", "\[Rule]", RowBox[{"-", FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"]}]}], ",", RowBox[{"a14", "\[Rule]", RowBox[{"-", FractionBox["6", SqrtBox["5"]]}]}], ",", RowBox[{"a15", "\[Rule]", "7"}], ",", RowBox[{"a16", "\[Rule]", "10"}], ",", RowBox[{"a17", "\[Rule]", "4"}], ",", RowBox[{"a18", "\[Rule]", FractionBox["13", "5"]}], ",", RowBox[{"a2", "\[Rule]", FractionBox["13", "5"]}], ",", RowBox[{"a3", "\[Rule]", RowBox[{"-", FractionBox["8", SqrtBox["5"]]}]}], ",", RowBox[{"a4", "\[Rule]", RowBox[{"-", FractionBox["6", SqrtBox["5"]]}]}], ",", RowBox[{"a5", "\[Rule]", RowBox[{"-", FractionBox["8", SqrtBox["5"]]}]}], ",", RowBox[{"a6", "\[Rule]", RowBox[{"-", FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]]}]}], ",", RowBox[{"a7", "\[Rule]", FractionBox["3", "2"]}], ",", RowBox[{"a8", "\[Rule]", RowBox[{"-", SqrtBox["5"]}]}], ",", RowBox[{"a9", "\[Rule]", RowBox[{"-", SqrtBox["5"]}]}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.832071203390505*^9, 3.832071215169805*^9}, { 3.8320712717089663`*^9, 3.832071288966185*^9}, {3.832071518133173*^9, 3.8320715436453857`*^9}}, CellLabel->"In[39]:=",ExpressionUUID->"6cf3b807-be68-4d68-ad02-70d267d6eff1"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", RowBox[{ RowBox[{"-", "2"}], " ", SqrtBox["5"]}]}, {"1", "1", "0"}, { FractionBox["27", "5"], "1", RowBox[{"-", FractionBox["24", SqrtBox["5"]]}]}, {"1", FractionBox["3", "2"], RowBox[{"-", FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"]}]}, { FractionBox["13", "5"], "1", RowBox[{"-", FractionBox["6", SqrtBox["5"]]}]}, {"0", "0", "1"}, { RowBox[{"-", FractionBox["8", SqrtBox["5"]]}], "0", "7"}, { RowBox[{"-", FractionBox["6", SqrtBox["5"]]}], "0", "1"}, { RowBox[{"-", FractionBox["8", SqrtBox["5"]]}], RowBox[{"-", SqrtBox["5"]}], "10"}, {"0", RowBox[{"-", SqrtBox["5"]}], "4"}, {"0", RowBox[{"-", FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"]}], "1"}, { RowBox[{"-", FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]]}], "0", FractionBox["13", "5"]} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.832071544211069*^9}, CellLabel-> "Out[39]//MatrixForm=",ExpressionUUID->"ea395fc8-7203-4bfa-8173-\ b7d3647a415c"] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"a11", ",", "a12", ",", "a1"}], "]"}]], "Input", CellChangeTimes->{{3.831821344265843*^9, 3.831821380994482*^9}}, CellLabel-> "In[489]:=",ExpressionUUID->"ab8292a5-714c-499f-aec5-c2b87a6d3c15"], Cell[BoxData[ RowBox[{"mat", "=", RowBox[{"(", GridBox[{ { RowBox[{"-", "1"}], "1", "9", "1", "1", "1", "7", "0", "0", RowBox[{"2", " ", SqrtBox["5"]}], RowBox[{"4", " ", SqrtBox["5"]}], "0", "0", FractionBox[ RowBox[{"4", " ", SqrtBox["5"]}], "3"], FractionBox["4", SqrtBox["5"]]}, {"1", RowBox[{"-", "1"}], "1", "1", FractionBox["27", "5"], "1", FractionBox["13", "5"], "0", FractionBox["8", SqrtBox["5"]], "0", FractionBox["6", SqrtBox["5"]], FractionBox["8", SqrtBox["5"]], "0", "0", FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]]}, {"9", "1", RowBox[{"-", "1"}], "1", "17", FractionBox["7", "2"], "1", RowBox[{"2", " ", SqrtBox["5"]}], RowBox[{"6", " ", SqrtBox["5"]}], "0", "0", RowBox[{"7", " ", SqrtBox["5"]}], RowBox[{"3", " ", SqrtBox["5"]}], "0", FractionBox["6", SqrtBox["5"]]}, {"1", "1", "1", RowBox[{"-", "1"}], "1", FractionBox["3", "2"], "1", "0", "0", "0", "0", SqrtBox["5"], SqrtBox["5"], FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"], "0"}, {"1", FractionBox["27", "5"], "17", "1", RowBox[{"-", "1"}], "1", "9", FractionBox["8", SqrtBox["5"]], "0", FractionBox["24", SqrtBox["5"]], RowBox[{"6", " ", SqrtBox["5"]}], "0", FractionBox["8", SqrtBox["5"]], FractionBox[ RowBox[{"8", " ", SqrtBox["5"]}], "3"], "0"}, {"1", "1", FractionBox["7", "2"], FractionBox["3", "2"], "1", RowBox[{"-", "1"}], "1", SqrtBox["5"], SqrtBox["5"], FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"], FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"], "0", "0", "0", "0"}, {"7", FractionBox["13", "5"], "1", "1", "9", "1", RowBox[{"-", "1"}], FractionBox["12", SqrtBox["5"]], RowBox[{"4", " ", SqrtBox["5"]}], FractionBox["6", SqrtBox["5"]], "0", RowBox[{"4", " ", SqrtBox["5"]}], FractionBox["12", SqrtBox["5"]], "0", "0"}, {"0", "0", RowBox[{"2", " ", SqrtBox["5"]}], "0", FractionBox["8", SqrtBox["5"]], SqrtBox["5"], FractionBox["12", SqrtBox["5"]], RowBox[{"-", "1"}], "1", "1", "5", "3", "1", FractionBox["7", "3"], FractionBox["11", "5"]}, {"0", FractionBox["8", SqrtBox["5"]], RowBox[{"6", " ", SqrtBox["5"]}], "0", "0", SqrtBox["5"], RowBox[{"4", " ", SqrtBox["5"]}], "1", RowBox[{"-", "1"}], "7", "11", "1", "3", FractionBox["17", "3"], "1"}, { RowBox[{"2", " ", SqrtBox["5"]}], "0", "0", "0", FractionBox["24", SqrtBox["5"]], FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"], FractionBox["6", SqrtBox["5"]], "1", "7", RowBox[{"-", "1"}], "1", "10", "4", "1", FractionBox["13", "5"]}, { RowBox[{"4", " ", SqrtBox["5"]}], FractionBox["6", SqrtBox["5"]], "0", "0", RowBox[{"6", " ", SqrtBox["5"]}], FractionBox[ RowBox[{"3", " ", SqrtBox["5"]}], "2"], "0", "5", "11", "1", RowBox[{"-", "1"}], "14", "8", "1", "1"}, {"0", FractionBox["8", SqrtBox["5"]], RowBox[{"7", " ", SqrtBox["5"]}], SqrtBox["5"], "0", "0", RowBox[{"4", " ", SqrtBox["5"]}], "3", "1", "10", "14", RowBox[{"-", "1"}], "1", FractionBox["13", "3"], "1"}, {"0", "0", RowBox[{"3", " ", SqrtBox["5"]}], SqrtBox["5"], FractionBox["8", SqrtBox["5"]], "0", FractionBox["12", SqrtBox["5"]], "1", "3", "4", "8", "1", RowBox[{"-", "1"}], "1", FractionBox["11", "5"]}, { FractionBox[ RowBox[{"4", " ", SqrtBox["5"]}], "3"], "0", "0", FractionBox[ RowBox[{"2", " ", SqrtBox["5"]}], "3"], FractionBox[ RowBox[{"8", " ", SqrtBox["5"]}], "3"], "0", "0", FractionBox["7", "3"], FractionBox["17", "3"], "1", "1", FractionBox["13", "3"], "1", RowBox[{"-", "1"}], "1"}, { FractionBox["4", SqrtBox["5"]], FractionBox["24", RowBox[{"5", " ", SqrtBox["5"]}]], FractionBox["6", SqrtBox["5"]], "0", "0", "0", "0", FractionBox["11", "5"], "1", FractionBox["13", "5"], "1", "1", FractionBox["11", "5"], "1", RowBox[{"-", "1"}]} }, 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]", ")"}]}]], "Input", CellChangeTimes->{{3.831809538032175*^9, 3.831809538033771*^9}, 3.83181712916037*^9, {3.831817172849091*^9, 3.8318171810397167`*^9}, 3.831817237309411*^9}, CellLabel->"In[52]:=",ExpressionUUID->"5623f2b2-154d-42f9-a02f-11e8114855a3"], Cell[BoxData[{ RowBox[{"a", "=", "1"}], "\[IndentingNewLine]", RowBox[{"b", "=", "11"}], "\[IndentingNewLine]", RowBox[{"o", "=", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"2", ",", "a"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"n", "=", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"4", ",", "a"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"d", "=", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"10", ",", "a"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"q", "=", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"2", ",", "b"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"r", "=", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"4", ",", "b"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"s", "=", RowBox[{"mat", "[", RowBox[{"[", RowBox[{"10", ",", "b"}], "]"}], "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"1", "/", "2"}], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"d", "^", "2"}], "+", RowBox[{"n", "^", "2"}], "-", "1"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"q", "+", "r"}], ")"}], "/", RowBox[{"(", RowBox[{"o", "+", "n"}], ")"}]}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"s", "^", "2"}], "+", RowBox[{"r", "^", "2"}], "-", "1"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"o", "+", "n"}], ")"}], "/", RowBox[{"(", RowBox[{"q", "+", "r"}], ")"}]}]}]}], ")"}]}], "-", RowBox[{"d", "*", "s"}], "-", RowBox[{"n", "*", "r"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mat", "[", RowBox[{"[", RowBox[{"a", ",", "b"}], "]"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.831807518799519*^9, 3.831807594956044*^9}, { 3.8318076728397713`*^9, 3.831807701743909*^9}, {3.831807964346015*^9, 3.831807983417666*^9}, {3.8318080161942463`*^9, 3.831808018286193*^9}, { 3.831808048507024*^9, 3.831808049498742*^9}, {3.831808167039514*^9, 3.8318081853134823`*^9}, {3.831808248068654*^9, 3.831808271264772*^9}, { 3.8318095740710697`*^9, 3.8318096292919397`*^9}, {3.831816955139246*^9, 3.831817019688861*^9}, {3.831817059268959*^9, 3.831817092877222*^9}, { 3.831817135516425*^9, 3.8318172064984827`*^9}, {3.8318172559252768`*^9, 3.831817420540907*^9}, {3.8318175396098413`*^9, 3.831817566952179*^9}, { 3.831817705992889*^9, 3.83181771726031*^9}, {3.831819525149275*^9, 3.8318195541654053`*^9}, {3.83181969027396*^9, 3.831819690355661*^9}}, CellLabel-> "In[285]:=",ExpressionUUID->"2c9a1c60-bd62-4409-95a8-b2322e02b465"] }, WindowSize->{1440, 847}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"12.3 for Mac OS X x86 (64-bit) (May 11, 2021)", StyleDefinitions->"Default.nb", ExpressionUUID->"bc380211-a271-447c-9f05-196ef5612776" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 7044, 148, 786, "Input",ExpressionUUID->"b9956451-1eb1-4b6d-8ea0-8e5e4f91ba63"], Cell[7605, 170, 5045, 149, 178, "Input",ExpressionUUID->"6d6c1f85-a342-4808-8fa2-2cf8c0132147"], Cell[CellGroupData[{ Cell[12675, 323, 892, 28, 215, "Input",ExpressionUUID->"d414d2ba-4acb-46d3-a25c-b7b10cffd621"], Cell[13570, 353, 14779, 502, 468, "Output",ExpressionUUID->"b8883fc0-3737-4e0d-bb40-5e10d682ff05"] }, Open ]], Cell[28364, 858, 1514, 55, 315, "Input",ExpressionUUID->"07c417e3-ab27-4df6-bac8-407abe9b7e72"], Cell[CellGroupData[{ Cell[29903, 917, 2548, 67, 73, "Input",ExpressionUUID->"afd53ed6-b287-4977-8a5a-f73dda451b35"], Cell[32454, 986, 3433, 111, 156, "Output",ExpressionUUID->"2fa96c23-acd6-4c4a-9a0a-5bee0a0dd517"] }, Open ]], Cell[CellGroupData[{ Cell[35924, 1102, 2251, 62, 73, "Input",ExpressionUUID->"8d27c355-b0e8-4254-94d4-cbfdd3ad0826"], Cell[38178, 1166, 456, 10, 28, "Message",ExpressionUUID->"56473541-5f4c-4432-a33d-cbb5f88fe550"], Cell[38637, 1178, 495, 11, 28, "Message",ExpressionUUID->"304c5d99-263a-4649-bf1d-46dff562b2a7"], Cell[39135, 1191, 498, 11, 28, "Message",ExpressionUUID->"e394b350-77c7-49c7-923b-9ab48092fe2f"], Cell[39636, 1204, 461, 10, 28, "Message",ExpressionUUID->"ffa3f13e-0381-473e-997f-185d867233cd"] }, Open ]], Cell[40112, 1217, 4151, 93, 220, "Input",ExpressionUUID->"7d35b7ff-e080-4389-8596-12c0fca29756"], Cell[44266, 1312, 4510, 87, 482, "Input",ExpressionUUID->"fe95b6b4-36d8-4b3e-bcff-59c63171bd33"], Cell[CellGroupData[{ Cell[48801, 1403, 2018, 64, 106, "Input",ExpressionUUID->"6cf3b807-be68-4d68-ad02-70d267d6eff1"], Cell[50822, 1469, 1719, 67, 318, "Output",ExpressionUUID->"ea395fc8-7203-4bfa-8173-b7d3647a415c"] }, Open ]], Cell[52556, 1539, 245, 5, 30, "Input",ExpressionUUID->"ab8292a5-714c-499f-aec5-c2b87a6d3c15"], Cell[52804, 1546, 5528, 191, 451, "Input",ExpressionUUID->"5623f2b2-154d-42f9-a02f-11e8114855a3"], Cell[58335, 1739, 2750, 73, 283, "Input",ExpressionUUID->"2c9a1c60-bd62-4409-95a8-b2322e02b465"] } ] *)