...
(* Content-type: application/mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 6.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 145, 7]
NotebookDataLength[ 51807, 1659]
NotebookOptionsPosition[ 49044, 1566]
NotebookOutlinePosition[ 49407, 1582]
CellTagsIndexPosition[ 49364, 1579]
WindowFrame->Normal
ContainsDynamic->False*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{"Clear", "[",
RowBox[{"d", ",", "tm", ",", "m"}], "]"}]], "Input",
CellChangeTimes->{{3.4241980742571344`*^9, 3.424198074928099*^9}, {
3.424198111630875*^9, 3.424198112381955*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"tm", "[", "x_", "]"}], ":=", "x"}]], "Input",
CellChangeTimes->{{3.424198093104235*^9, 3.4241981152961454`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"m", "[", "x_", "]"}], ":=",
RowBox[{"d", "[", "x", "]"}]}]], "Input",
CellChangeTimes->{{3.424198093104235*^9, 3.4241981152961454`*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.424197939102792*^9, 3.4241979434390273`*^9}, {
3.424198082939619*^9, 3.424198084061232*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",", "b"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}]}], "]"}]}], "-",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b"}], "]"}]}]], "Output",
CellChangeTimes->{
3.424197943959776*^9, {3.424198070712037*^9, 3.4241981177697024`*^9},
3.4241981527399874`*^9, {3.424198220988123*^9, 3.4241982242928753`*^9}, {
3.4241984914269953`*^9, 3.424198497575837*^9}, {3.4241986744701986`*^9,
3.424198684594757*^9}, 3.4241987900664177`*^9, {3.4241989830138626`*^9,
3.4241990466954317`*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.424198928445397*^9, 3.4241989306886225`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "-",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b", ",", "c"}], "]"}]}]], "Output",
CellChangeTimes->{3.4241989309990687`*^9, 3.424199050130371*^9}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"d", "[",
RowBox[{"a", ":",
RowBox[{"t", "[", "___", "]"}]}], "]"}], ":=",
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{"k", "=",
RowBox[{"Length", "[", "a", "]"}]}], "}"}], ",",
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"i", "=", "1"}], "k"],
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"j", "=", "1"}],
RowBox[{"i", "-", "1"}]],
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}],
"]"}]}]],
RowBox[{"MapAt", "[",
RowBox[{"d", ",", "a", ",", "i"}], "]"}]}]}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.4241985045058017`*^9, 3.4241986214940224`*^9}, {
3.4241986537403903`*^9, 3.424198663494416*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"t", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.4241986645559425`*^9, 3.4241986670695567`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",", "b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{"t", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b", ",", "c"}], "]"}]}]], "Output",
CellChangeTimes->{3.424198667420061*^9, 3.4241987978676353`*^9}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"d", "[", "X_Plus", "]"}], ":=",
RowBox[{"d", "/@", "X"}]}]], "Input",
CellChangeTimes->{{3.4241988074414015`*^9, 3.424198812658904*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"d", "[",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n_."], " ", "X_"}], "]"}], ":=",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n"], " ",
RowBox[{"d", "[", "X", "]"}]}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"d", "[",
RowBox[{"s_\[Sigma]", " ", "X_"}], "]"}], ":=",
RowBox[{"s", " ",
RowBox[{"d", "[", "X", "]"}]}]}]}], "Input",
CellChangeTimes->{{3.424199070639862*^9, 3.424199126960848*^9}, {
3.424201311281747*^9, 3.4242013146165423`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"d", "[",
RowBox[{"d", "[", "_", "]"}], "]"}], ":=", "0"}]], "Input",
CellChangeTimes->{{3.4241988199694157`*^9, 3.4241988233342543`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"tm", "[",
RowBox[{"___", ",", "0", ",", "___"}], "]"}], ":=", "0"}]], "Input",
CellChangeTimes->{{3.424198831185544*^9, 3.424198836773579*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"tm", "[",
RowBox[{"X___", ",", "Y_Plus", ",", "Z__"}], "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"tm", "[",
RowBox[{"X", ",", "#", ",", "Z"}], "]"}], "&"}], "/@",
"Y"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"X__", ",", "Y_Plus", ",", "Z___"}], "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"tm", "[",
RowBox[{"X", ",", "#", ",", "Z"}], "]"}], "&"}], "/@",
"Y"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"X___", ",",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n_."], "Y_"}], ",", "Z___"}], "]"}], ":=",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n"],
RowBox[{"tm", "[",
RowBox[{"X", ",", "Y", ",", "Z"}], "]"}]}]}]}], "Input",
CellChangeTimes->{{3.4242002106090574`*^9, 3.4242002710960336`*^9}, {
3.4242009022035217`*^9, 3.4242009251565266`*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"t", "[",
RowBox[{"X___", ",", "Y_Plus", ",", "Z__"}], "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"t", "[",
RowBox[{"X", ",", "#", ",", "Z"}], "]"}], "&"}], "/@",
"Y"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"t", "[",
RowBox[{"X__", ",", "Y_Plus", ",", "Z___"}], "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"t", "[",
RowBox[{"X", ",", "#", ",", "Z"}], "]"}], "&"}], "/@",
"Y"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"t", "[",
RowBox[{"X___", ",",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n_."], "Y_"}], ",", "Z___"}], "]"}], ":=",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n"],
RowBox[{"t", "[",
RowBox[{"X", ",", "Y", ",", "Z"}], "]"}]}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"t", "[",
RowBox[{"X___", ",",
RowBox[{"s_\[Sigma]", " ", "Y_"}], ",", "Z___"}], "]"}], ":=",
RowBox[{"s", " ",
RowBox[{"t", "[",
RowBox[{"X", ",", "Y", ",", "Z"}], "]"}]}]}]}], "Input",
CellChangeTimes->{{3.424201175196066*^9, 3.4242012093451695`*^9}, {
3.424201303861077*^9, 3.424201306564965*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"t", "[",
RowBox[{"X__", ",",
RowBox[{"t", "[", "Y__", "]"}], ",", "Z___"}], "]"}], ":=",
RowBox[{"t", "[",
RowBox[{"X", ",", "Y", ",", "Z"}], "]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"t", "[",
RowBox[{"X___", ",",
RowBox[{"t", "[", "Y__", "]"}], ",", "Z__"}], "]"}], ":=",
RowBox[{"t", "[",
RowBox[{"X", ",", "Y", ",", "Z"}], "]"}]}]}], "Input",
CellChangeTimes->{{3.42420197886168*^9, 3.424201999771747*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"deg", "[",
RowBox[{"d", "[", "X_", "]"}], "]"}], ":=",
RowBox[{
RowBox[{"deg", "[", "X", "]"}], "-", "1"}]}]], "Input",
CellChangeTimes->{{3.4241991779742017`*^9, 3.4241991852346416`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"deg", "[", "a_m", "]"}], ":=",
RowBox[{
RowBox[{"Length", "[", "a", "]"}], "-", "2", "+",
RowBox[{"Plus", "@@",
RowBox[{"(",
RowBox[{"deg", "/@",
RowBox[{"List", "@@", "a"}]}], ")"}]}]}]}]], "Input",
CellChangeTimes->{{3.4242003314828653`*^9, 3.4242003740440655`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"deg", "[", "a_tm", "]"}], ":=",
RowBox[{
RowBox[{"Length", "[", "a", "]"}], "-", "1", "+",
RowBox[{"Plus", "@@",
RowBox[{"(",
RowBox[{"deg", "/@",
RowBox[{"List", "@@", "a"}]}], ")"}]}]}]}]], "Input",
CellChangeTimes->{{3.4242003910885744`*^9, 3.4242003932016125`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"d", "[",
RowBox[{"a", ":",
RowBox[{"HoldPattern", "[",
RowBox[{"tm", "[", "___", "]"}], "]"}]}], "]"}], ":=",
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{"k", "=",
RowBox[{"Length", "[", "a", "]"}]}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"l", "=", "1"}],
RowBox[{"k", "-", "1"}]],
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"l", ",",
RowBox[{"List", "@@", "a"}]}], "]"}], " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"Take", "[",
RowBox[{"a", ",", "l"}], "]"}], ",",
RowBox[{"Drop", "[",
RowBox[{"a", ",", "l"}], "]"}]}], "]"}]}]}], "+",
"\[IndentingNewLine]",
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"l", "=", "1"}], "k"],
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"lp", "=", "0"}],
RowBox[{"l", "-", "1"}]],
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"l1", "=", "lp"}], ",",
RowBox[{"l2", "=",
RowBox[{"k", "-", "l", "+", "1"}]}], ",",
RowBox[{"l3", "=",
RowBox[{"l", "-", "1", "-", "lp"}]}]}], "}"}], ",",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"l2",
RowBox[{"(",
RowBox[{"k", "-", "1", "+",
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"j", "=", "1"}], "lp"],
RowBox[{"deg", "[",
RowBox[{
"a", "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}],
"]"}]}]}], ")"}]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"k", "-", "l"}], ")"}],
RowBox[{"(", "lp", ")"}]}]}]],
RowBox[{"tm", "@@",
RowBox[{"(",
RowBox[{
RowBox[{"Take", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",", "lp"}], "]"}], "~", "Join",
"~",
RowBox[{"{",
RowBox[{"m", "@@",
RowBox[{"Take", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"lp", "+", "1"}], ",",
RowBox[{"lp", "+", "k", "-", "l", "+", "1"}]}], "}"}]}],
"]"}]}], "}"}], "~", "Join", "~",
RowBox[{"Drop", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",",
RowBox[{"lp", "+", "k", "-", "l", "+", "1"}]}], "]"}]}],
")"}]}]}]}], "]"}]}]}]}]}], "\[IndentingNewLine]",
"]"}]}]], "Input",
CellChangeTimes->{{3.4241976743520994`*^9, 3.4241979358681407`*^9}, {
3.4241980205799503`*^9, 3.4241980693100204`*^9}, {3.4241981831937776`*^9,
3.424198219375805*^9}, {3.4241984876916237`*^9, 3.424198488572891*^9}, {
3.4241987823553295`*^9, 3.424198785980542*^9}, {3.4241989378989906`*^9,
3.424198966930736*^9}, {3.4241990027121873`*^9, 3.424199045193272*^9}, {
3.424200498352813*^9, 3.4242005144659824`*^9}, {3.4242006132580385`*^9,
3.424200613448312*^9}, {3.42420072089281*^9, 3.4242007272219105`*^9}, {
3.424200772507027*^9, 3.424200782811845*^9}, {3.4242012813687344`*^9,
3.424201292494733*^9}, {3.4242071329028273`*^9, 3.424207333311*^9}, {
3.4242075895995245`*^9, 3.424207624329464*^9}}],
Cell[BoxData[
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"k", "-", "l", "+", "1"}], ")"}],
RowBox[{"(",
RowBox[{"k", "-", "1", "+",
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"j", "=", "1"}], "lp"],
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}],
"]"}]}]}], ")"}]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"k", "-", "l"}], ")"}],
RowBox[{"(", "lp", ")"}]}]}]]], "Input"],
Cell[BoxData[
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"l1", "+", "l2"}], ")"}], "l3"}], "+",
RowBox[{"l2", " ",
RowBox[{"(",
RowBox[{"Plus", "@@",
RowBox[{"(",
RowBox[{"deg", "/@",
RowBox[{"Take", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",", "l1"}], "]"}]}], ")"}]}],
")"}]}]}]]], "Input"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Collect", "[",
RowBox[{
RowBox[{"d", "[",
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], "]"}], "]"}], ",",
RowBox[{"(",
RowBox[{"_tm", "|", "_d", "|", "_t"}], ")"}], ",", "Together"}],
"]"}]], "Input",
CellChangeTimes->{{3.424198799299694*^9, 3.424198802804734*^9}, {
3.4241991375360546`*^9, 3.4241991665077133`*^9}, {3.424199203320648*^9,
3.4241992055338306`*^9}}],
Cell[BoxData["0"], "Output",
CellChangeTimes->{{3.424198803315469*^9, 3.424198837724947*^9}, {
3.4241990626684*^9, 3.424199205944421*^9}, 3.424200074182886*^9,
3.4242001944958878`*^9, 3.424200409054408*^9, {3.4242004997448144`*^9,
3.4242005193029375`*^9}, 3.424200728914344*^9, 3.424200784414149*^9,
3.424200932707384*^9, 3.4242013241802945`*^9, 3.4242014646823263`*^9, {
3.4242073102378225`*^9, 3.424207336445507*^9}, {3.42420760386003*^9,
3.4242076281149073`*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.424200732269168*^9, 3.424200734181918*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"2", " ",
RowBox[{"deg", "[", "a", "]"}]}]}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",", "b"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}]}], "]"}]}], "-",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b"}], "]"}]}]], "Output",
CellChangeTimes->{3.4242007344122496`*^9, 3.424200785946352*^9,
3.4242009332481613`*^9, 3.4242011847097454`*^9, 3.424201395322592*^9,
3.42420146061648*^9, 3.4242074562277455`*^9, 3.4242076049616146`*^9}]
}, Open ]],
Cell[BoxData[
RowBox[{"Clear", "[", "\[Sigma]", "]"}]], "Input",
CellChangeTimes->{{3.424201810469544*^9, 3.4242018117614017`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"l_", ",", "a_List"}], "]"}], ":=",
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{"k", "=",
RowBox[{"Length", "[", "a", "]"}]}], "}"}], ",",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"k", "-", "l", "+", "1"}], ")"}],
RowBox[{"(",
RowBox[{"Plus", "@@",
RowBox[{"(",
RowBox[{"deg", "/@",
RowBox[{"Take", "[",
RowBox[{"a", ",", "l"}], "]"}]}], ")"}]}], ")"}]}], "+", "l"}]]}],
"]"}]}]], "Input",
CellChangeTimes->{{3.424206850386589*^9, 3.4242069563589697`*^9}, {
3.4242070973617215`*^9, 3.4242070975419807`*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.4242005789086466`*^9, 3.424200581302088*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"3", " ",
RowBox[{"deg", "[", "a", "]"}]}]}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"2", " ",
RowBox[{"(",
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}], ")"}]}]}]], " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"2", " ",
RowBox[{"(",
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}]}], ")"}]}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b", ",", "c"}], "]"}]}]], "Output",
CellChangeTimes->{
3.4242005816826353`*^9, 3.424200616232315*^9, 3.424200747741416*^9,
3.4242007892711325`*^9, 3.424200933939155*^9, 3.4242011853306384`*^9,
3.4242014129078784`*^9, 3.4242014668153934`*^9, 3.424201520983283*^9,
3.424201813834382*^9, 3.4242019528943405`*^9, {3.42420693098248*^9,
3.424206957600755*^9}, 3.4242070989840546`*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Collect", "[",
RowBox[{
RowBox[{"d", "[",
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}], "]"}], ",",
RowBox[{"(",
RowBox[{"_tm", "|", "_d", "|", "_t", "|", "_m"}], ")"}], ",",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Together", "[", "#", "]"}], "/.",
RowBox[{"{",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "_"}]], "\[Rule]", "1"}], "}"}]}], ")"}], "&"}]}],
"]"}]], "Input",
CellChangeTimes->{{3.424198799299694*^9, 3.424198802804734*^9}, {
3.4241991375360546`*^9, 3.4241991665077133`*^9}, {3.424199203320648*^9,
3.4241992221176767`*^9}, {3.4242004382664127`*^9,
3.4242004391877375`*^9}, {3.4242005411643724`*^9, 3.4242005437080307`*^9},
3.4242008174216113`*^9, {3.4242020485218463`*^9, 3.4242020686007185`*^9}}],\
Cell[BoxData["0"], "Output",
CellChangeTimes->{
3.4241992227786274`*^9, {3.42420019620835*^9, 3.4242002421444035`*^9},
3.4242002726983376`*^9, 3.4242003764174786`*^9, 3.424200409885603*^9,
3.424200440639826*^9, {3.424200503289912*^9, 3.424200544218765*^9}, {
3.424200814537464*^9, 3.4242008178021584`*^9}, 3.424200934660192*^9, {
3.4242011874136333`*^9, 3.42420121426224*^9}, 3.4242015234968977`*^9,
3.4242019690475683`*^9, 3.4242020049091344`*^9, 3.4242020689311934`*^9, {
3.4242069335261374`*^9, 3.424206960825392*^9}, 3.424207099955451*^9, {
3.4242076078457613`*^9, 3.4242076316199474`*^9}}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_", ",", "_"}], "}"}]}], "]"}], ":=",
RowBox[{"-", "1"}]}]], "Input",
CellChangeTimes->{{3.4242021358173714`*^9, 3.424202143248056*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"2", ",",
RowBox[{"{",
RowBox[{"a_", ",", "b_", ",", "_", ",", "_"}], "}"}]}], "]"}], ":=",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"3", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_", ",", "_"}], "}"}]}], "]"}], ":=",
RowBox[{"-", "1"}]}]}], "Input",
CellChangeTimes->{{3.424202215401808*^9, 3.4242022541975937`*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"1", ",", "a_List"}], "]"}], ":=",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{
RowBox[{"Length", "[", "a", "]"}],
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
"]"}]}], "+", "1"}]]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"2", ",", "a_List"}], "]"}], ":=",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Length", "[", "a", "]"}], "+", "1"}], ")"}],
RowBox[{"(",
RowBox[{
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
"]"}], "+",
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}],
"]"}]}], ")"}]}]]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"3", ",", "a_List"}], "]"}], ":=",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"Length", "[", "a", "]"}], ")"}],
RowBox[{"(",
RowBox[{
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
"]"}], "+",
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}],
"]"}], "+",
RowBox[{"deg", "[",
RowBox[{"a", "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}],
"]"}]}], ")"}]}], "+", "1"}]]}]}], "Input",
CellChangeTimes->{{3.4242025340600157`*^9, 3.4242026162481966`*^9}, {
3.424202652159835*^9, 3.4242026904248576`*^9}, {3.424202735649888*^9,
3.424202777089475*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"\[Sigma]", "[",
RowBox[{"k_Integer", ",", "a_List"}], "]"}], ":=",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Length", "[", "a", "]"}], "+", "k", "+", "1"}], ")"}],
RowBox[{"(",
RowBox[{"Plus", "@@",
RowBox[{"(",
RowBox[{"deg", "/@",
RowBox[{"Take", "[",
RowBox[{"a", ",", "k"}], "]"}]}], ")"}]}], ")"}]}], "+",
"k"}]]}]], "Input",
CellChangeTimes->{{3.424202789427216*^9, 3.424202836054262*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Collect", "[",
RowBox[{
RowBox[{"d", "[",
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}], "]"}], "]"}], ",",
RowBox[{"(",
RowBox[{"_tm", "|", "_d", "|", "_t", "|", "_m"}], ")"}], ",",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Together", "[", "#", "]"}], "//.",
RowBox[{"{",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"n_Integer", " ", "x_"}]], "\[RuleDelayed]",
SuperscriptBox[
RowBox[{"(",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n"], ")"}], "x"]}], "}"}]}], ")"}],
"&"}]}], "]"}]], "Input",
CellChangeTimes->{{3.424198799299694*^9, 3.424198802804734*^9}, {
3.4241991375360546`*^9, 3.4241991665077133`*^9}, {3.424199203320648*^9,
3.4241992221176767`*^9}, {3.4242004382664127`*^9,
3.4242004391877375`*^9}, {3.4242005411643724`*^9, 3.4242005437080307`*^9},
3.4242008174216113`*^9, {3.4242020485218463`*^9, 3.424202081188819*^9}, {
3.424202169736144*^9, 3.4242021956233683`*^9}, {3.4242022722535567`*^9,
3.424202330757682*^9}, 3.4242025057092495`*^9}],
Cell[BoxData["0"], "Output",
CellChangeTimes->{
3.4242020826108637`*^9, 3.4242021449905615`*^9, 3.424202196805067*^9, {
3.4242022356809683`*^9, 3.424202255329221*^9}, {3.4242023014355183`*^9,
3.4242023313986034`*^9}, 3.424202506440301*^9, 3.424207107165819*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Collect", "[",
RowBox[{
RowBox[{"d", "[",
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{
"a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f", ",", "g"}],
"]"}], "]"}], "]"}], ",",
RowBox[{"(",
RowBox[{"_tm", "|", "_d", "|", "_t", "|", "_m"}], ")"}], ",",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Together", "[", "#", "]"}], "//.",
RowBox[{"{",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"n_Integer", " ", "x_"}]], "\[RuleDelayed]",
SuperscriptBox[
RowBox[{"(",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "n"], ")"}], "x"]}], "}"}]}], ")"}],
"&"}]}], "]"}]], "Input",
CellChangeTimes->{{3.424198799299694*^9, 3.424198802804734*^9}, {
3.4241991375360546`*^9, 3.4241991665077133`*^9}, {3.424199203320648*^9,
3.4241992221176767`*^9}, {3.4242004382664127`*^9,
3.4242004391877375`*^9}, {3.4242005411643724`*^9, 3.4242005437080307`*^9},
3.4242008174216113`*^9, {3.4242020485218463`*^9, 3.424202081188819*^9}, {
3.424202169736144*^9, 3.4242021956233683`*^9}, {3.4242022722535567`*^9,
3.424202330757682*^9}, {3.4242025057092495`*^9, 3.4242025139210577`*^9}, {
3.424202854761162*^9, 3.4242028737084064`*^9}}],
Cell[BoxData["0"], "Output",
CellChangeTimes->{
3.4242025147923107`*^9, 3.4242025962594547`*^9, 3.4242027035837793`*^9,
3.4242027793827724`*^9, {3.4242028405106707`*^9, 3.4242028777942815`*^9},
3.4242071121730194`*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"-",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "]"}]], "Input",
CellChangeTimes->{{3.4242016238211565`*^9, 3.424201638492253*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"-",
RowBox[{"m", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "b", "]"}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "]"}]}], ")"}]}],
"+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}]], "Output",
CellChangeTimes->{{3.4242016302504015`*^9, 3.424201639203275*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Collect", "[",
RowBox[{
RowBox[{"d", "[",
RowBox[{"-",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "]"}], ",",
RowBox[{"(",
RowBox[{"_tm", "|", "_d", "|", "_t", "|", "_m"}], ")"}], ",",
"Together"}], "]"}]], "Input",
CellChangeTimes->{{3.4242016637085123`*^9, 3.4242016950435696`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{
RowBox[{"-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]]}], " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"t", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "]"}]}], "-",
RowBox[{"t", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}]], "Output",
CellChangeTimes->{{3.4242016665425873`*^9, 3.424201695384059*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Collect", "[",
RowBox[{
RowBox[{"d", "[",
RowBox[{"d", "[",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}], "]"}], "]"}], ",",
RowBox[{"(",
RowBox[{"_tm", "|", "_d", "|", "_t", "|", "_m"}], ")"}], ",",
"Together"}], "]"}]], "Input",
CellChangeTimes->{{3.424200829108416*^9, 3.4242008345862927`*^9},
3.4242009398075933`*^9}],
Cell[BoxData[
RowBox[{
RowBox[{
RowBox[{"-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"3", " ",
RowBox[{"deg", "[", "a", "]"}]}]]}], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c", ",", "d"}], "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"2", " ",
RowBox[{"deg", "[", "a", "]"}]}], "+",
RowBox[{"2", " ",
RowBox[{"deg", "[", "b", "]"}]}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",",
RowBox[{"m", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", " ",
RowBox[{"deg", "[", "a", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}], ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}], "+",
RowBox[{"deg", "[", "c", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c", ",",
RowBox[{"d", "[", "d", "]"}]}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",",
RowBox[{"d", "[", "c", "]"}], ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "b", "]"}], ",", "c", ",", "d"}], "]"}]}], "]"}]}],
"+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{
RowBox[{"m", "[",
RowBox[{"b", ",", "c", ",", "d"}], "]"}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"b", ",",
RowBox[{"tm", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"b", ",", "c"}], "]"}], ",", "d"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"2", " ",
RowBox[{"(",
RowBox[{"2", "+",
RowBox[{"deg", "[", "b", "]"}]}], ")"}]}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"b", ",",
RowBox[{"m", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}], ",", "d"}], "]"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "b", "]"}], "+",
RowBox[{"deg", "[", "c", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c", ",",
RowBox[{"d", "[", "d", "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"b", ",",
RowBox[{"d", "[", "c", "]"}], ",", "d"}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "b", "]"}], ",", "c", ",", "d"}], "]"}]}]}],
"]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], ",",
RowBox[{"tm", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], ",", "d"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"2", " ",
RowBox[{"deg", "[", "a", "]"}]}], "+",
RowBox[{"2", " ",
RowBox[{"deg", "[", "b", "]"}]}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",",
RowBox[{"m", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}], "+",
RowBox[{"deg", "[", "c", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",",
RowBox[{"tm", "[",
RowBox[{"c", ",",
RowBox[{"d", "[", "d", "]"}]}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",",
RowBox[{
RowBox[{"m", "[",
RowBox[{"c", ",", "d"}], "]"}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"deg", "[", "c", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"c", ",",
RowBox[{"d", "[", "d", "]"}]}], "]"}]}], "-",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "c", "]"}], ",", "d"}], "]"}]}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "c", "]"}], ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}]}], "]"}], ",",
RowBox[{"tm", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", " ",
RowBox[{"deg", "[", "a", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}], ",", "d"}], "]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",", "b"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}]}], "]"}]}], "-",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b"}], "]"}]}], ",",
RowBox[{"tm", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "-",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b"}], "]"}], ",",
RowBox[{"tm", "[",
RowBox[{"c", ",", "d"}], "]"}]}], "]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}], ",", "d"}],
"]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}], ",", "d"}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ", "\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}], ",", "d"}], "]"}]}],
"-",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b", ",", "c"}], "]"}], ",", "d"}],
"]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{"a", ",",
RowBox[{"tm", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{"\[Sigma]", " ",
RowBox[{"t", "[",
RowBox[{
RowBox[{"tm", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+",
RowBox[{"2", " ",
RowBox[{"(",
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}]}], ")"}]}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",", "b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "+",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"tm", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "+",
RowBox[{"tm", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b", ",", "c"}], "]"}]}], ",",
"d"}], "]"}]}]}]], "Output",
CellChangeTimes->{{3.424200829779381*^9, 3.424200835517632*^9}, {
3.4242009367532015`*^9, 3.4242009403483715`*^9}}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"d", "[",
RowBox[{"a", ":",
RowBox[{"HoldPattern", "[",
RowBox[{"m", "[", "___", "]"}], "]"}]}], "]"}], ":=",
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{"k", "=",
RowBox[{"Length", "[", "a", "]"}]}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"r", "=", "0"}], "k"],
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"s", "=", "1"}],
RowBox[{"k", "-", "r"}]],
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{"t", "=",
RowBox[{"k", "-", "r", "-", "s"}]}], "}"}], ",",
RowBox[{"If", "[",
RowBox[{
RowBox[{
RowBox[{"t", "<", "0"}], "\[Or]",
RowBox[{
RowBox[{"r", "+", "t"}], "\[Equal]", "0"}]}], ",", "0", ",",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+", "r", "+",
RowBox[{"s", " ", "t"}]}]],
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"s",
RowBox[{"(",
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"j", "=", "1"}], "r"],
RowBox[{"deg", "[",
RowBox[{
"a", "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}],
"]"}]}], ")"}]}]],
RowBox[{"m", "@@",
RowBox[{"(",
RowBox[{
RowBox[{"Take", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",", "r"}], "]"}], "~", "Join",
"~",
RowBox[{"{",
RowBox[{"m", "@@",
RowBox[{"Take", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"r", "+", "1"}], ",",
RowBox[{"r", "+", "s"}]}], "}"}]}], "]"}]}], "}"}], "~",
"Join", "~",
RowBox[{"Drop", "[",
RowBox[{
RowBox[{"List", "@@", "a"}], ",",
RowBox[{"r", "+", "s"}]}], "]"}]}], ")"}]}]}]}], "]"}]}],
"]"}]}]}]}], "\[IndentingNewLine]", "]"}]}]], "Input",
CellChangeTimes->{{3.4241996616096354`*^9, 3.424199684522582*^9}, {
3.4241997338535166`*^9, 3.4241998383938384`*^9}, {3.4241998737747135`*^9,
3.424199918098448*^9}, {3.424199948492152*^9, 3.424199948542224*^9}, {
3.424199990071941*^9, 3.4242000045327344`*^9}, {3.4242000530124445`*^9,
3.4242000564173408`*^9}, {3.4242001313150387`*^9, 3.4242001706716304`*^9}}],\
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.4241999216135025`*^9, 3.424199923626397*^9}, {
3.424200009630064*^9, 3.424200011002037*^9}, 3.4242000641184144`*^9}],
Cell[BoxData[
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ",
RowBox[{"m", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}]}], "]"}]}], "+",
RowBox[{"m", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b"}], "]"}]}]], "Output",
CellChangeTimes->{{3.424199923936843*^9, 3.424199949763981*^9}, {
3.4242000053739443`*^9, 3.424200011452685*^9}, {3.4242000598322515`*^9,
3.424200064418846*^9}, 3.4242001734556336`*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"d", "[",
RowBox[{"m", "[",
RowBox[{"a", ",", "b", ",", "c"}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.4242000997796926`*^9, 3.4242000998497934`*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", " ",
RowBox[{"deg", "[", "a", "]"}]}]], " ",
RowBox[{"m", "[",
RowBox[{"a", ",",
RowBox[{"m", "[",
RowBox[{"b", ",", "c"}], "]"}]}], "]"}]}], "-",
RowBox[{"m", "[",
RowBox[{
RowBox[{"m", "[",
RowBox[{"a", ",", "b"}], "]"}], ",", "c"}], "]"}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{
RowBox[{"deg", "[", "a", "]"}], "+",
RowBox[{"deg", "[", "b", "]"}]}]], " ",
RowBox[{"m", "[",
RowBox[{"a", ",", "b", ",",
RowBox[{"d", "[", "c", "]"}]}], "]"}]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"deg", "[", "a", "]"}]], " ",
RowBox[{"m", "[",
RowBox[{"a", ",",
RowBox[{"d", "[", "b", "]"}], ",", "c"}], "]"}]}], "-",
RowBox[{"m", "[",
RowBox[{
RowBox[{"d", "[", "a", "]"}], ",", "b", ",", "c"}], "]"}]}]], "Output",
CellChangeTimes->{3.4242001001702547`*^9, 3.42420017736125*^9}]
}, Open ]]
},
WindowSize->{1007, 555},
WindowMargins->{{34, Automatic}, {32, Automatic}},
ShowSelection->True,
FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (June 19, 2007)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[568, 21, 209, 4, 31, "Input"],
Cell[780, 27, 148, 3, 31, "Input"],
Cell[931, 32, 175, 4, 31, "Input"],
Cell[CellGroupData[{
Cell[1131, 40, 224, 5, 31, "Input"],
Cell[1358, 47, 878, 24, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[2273, 76, 185, 4, 31, "Input"],
Cell[2461, 82, 1530, 50, 50, "Output"]
}, Open ]],
Cell[4006, 135, 908, 27, 54, "Input"],
Cell[CellGroupData[{
Cell[4939, 166, 186, 4, 31, "Input"],
Cell[5128, 172, 719, 23, 30, "Output"]
}, Open ]],
Cell[5862, 198, 175, 4, 31, "Input"],
Cell[6040, 204, 586, 18, 52, "Input"],
Cell[6629, 224, 177, 4, 31, "Input"],
Cell[6809, 230, 183, 4, 31, "Input"],
Cell[6995, 236, 977, 32, 72, "Input"],
Cell[7975, 270, 1206, 39, 92, "Input"],
Cell[9184, 311, 490, 13, 52, "Input"],
Cell[9677, 326, 234, 6, 31, "Input"],
Cell[9914, 334, 332, 9, 31, "Input"],
Cell[10249, 345, 333, 9, 31, "Input"],
Cell[10585, 356, 3647, 95, 216, "Input"],
Cell[14235, 453, 564, 19, 40, "Input"],
Cell[14802, 474, 435, 16, 31, "Input"],
Cell[CellGroupData[{
Cell[15262, 494, 454, 12, 31, "Input"],
Cell[15719, 508, 489, 7, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[16245, 520, 173, 4, 31, "Input"],
Cell[16421, 526, 887, 27, 30, "Output"]
}, Open ]],
Cell[17323, 556, 133, 2, 31, "Input"],
Cell[17459, 560, 770, 24, 33, "Input"],
Cell[CellGroupData[{
Cell[18254, 588, 185, 4, 31, "Input"],
Cell[18442, 594, 2301, 73, 50, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[20780, 672, 934, 24, 33, "Input"],
Cell[21719, 699, 621, 9, 30, "Output"]
}, Open ]],
Cell[22355, 711, 266, 7, 31, "Input"],
Cell[22624, 720, 607, 18, 52, "Input"],
Cell[23234, 740, 1818, 54, 72, "Input"],
Cell[25055, 796, 592, 19, 31, "Input"],
Cell[CellGroupData[{
Cell[25672, 819, 1246, 31, 33, "Input"],
Cell[26921, 852, 271, 4, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[27229, 861, 1368, 34, 33, "Input"],
Cell[28600, 897, 229, 4, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[28866, 906, 253, 7, 31, "Input"],
Cell[29122, 915, 1177, 40, 33, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[30336, 960, 418, 12, 31, "Input"],
Cell[30757, 974, 1389, 48, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[32183, 1027, 412, 11, 31, "Input"],
Cell[32598, 1040, 11493, 371, 235, "Output"]
}, Open ]],
Cell[44106, 1414, 2771, 74, 167, "Input"],
Cell[CellGroupData[{
Cell[46904, 1493, 248, 5, 31, "Input"],
Cell[47155, 1500, 537, 15, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[47729, 1520, 186, 4, 31, "Input"],
Cell[47918, 1526, 1110, 37, 30, "Output"]
}, Open ]]
}
]
*)
(* End of internal cache information *)