8-teste[teste simples da interseção entre esferas com a AGC]EsferasAGCWolfram(jul-2018).nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.2' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     26761,        713]
NotebookOptionsPosition[     25730,        689]
NotebookOutlinePosition[     26073,        704]
CellTagsIndexPosition[     26030,        701]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{"carrega", " ", "o", " ", "pacote", " ", 
    RowBox[{"clifford", ".", "m"}]}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"<<", "\"\<clifford.m\>\""}], "\[IndentingNewLine]"}]}]], "Input",
 CellChangeTimes->{{3.7652802695654383`*^9, 
  3.765280292507471*^9}},ExpressionUUID->"9fef554c-1702-43b7-b301-\
6e540c06f21a"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{"modulo", " ", "erro"}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"erroMDE", "[", 
      RowBox[{"x_", ",", "A_", ",", "d_", ",", "m_"}], "]"}], ":=", 
     RowBox[{"Module", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"MDE", ",", "ii"}], "}"}], ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"MDE", "=", "0"}], ";", "\[IndentingNewLine]", 
        RowBox[{"For", "[", 
         RowBox[{
          RowBox[{"ii", "=", "1"}], ",", 
          RowBox[{"ii", "\[LessEqual]", "m"}], ",", 
          RowBox[{"ii", "++"}], ",", "\[IndentingNewLine]", 
          RowBox[{
           RowBox[{"MDE", "=", 
            RowBox[{"MDE", "+", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"1", "/", 
                RowBox[{"d", "[", 
                 RowBox[{"[", 
                  RowBox[{"ii", ",", "1"}], "]"}], "]"}]}], ")"}], "*", 
              RowBox[{"Abs", "[", 
               RowBox[{
                RowBox[{"Norm", "[", 
                 RowBox[{"x", "-", 
                  RowBox[{"A", "[", 
                   RowBox[{"[", 
                    RowBox[{";;", ",", "ii"}], "]"}], "]"}]}], "]"}], "-", 
                RowBox[{"d", "[", 
                 RowBox[{"[", 
                  RowBox[{"ii", ",", "1"}], "]"}], "]"}]}], "]"}]}]}]}], 
           ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", 
        RowBox[{"MDE", "=", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"1", "/", "m"}], ")"}], "*", "MDE"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"Return", "[", "MDE", "]"}], ";"}]}], "\[IndentingNewLine]", 
      "]"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input",
 CellChangeTimes->{{3.7652802867074633`*^9, 
  3.7652802898774676`*^9}},ExpressionUUID->"f80fbb55-5233-4ed1-9f70-\
471dbd87b2b2"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{
    "modulo", " ", "que", " ", "gera", " ", "matriz", " ", "nxm", " ", "de", 
     " ", "rank", " ", "k"}], ",", 
    RowBox[{
     RowBox[{
     "cujas", " ", "colunas", " ", "sao", " ", "os", " ", "centros", " ", 
      "das", " ", "m", " ", "esferas"}], ";", 
     RowBox[{"gera", " ", "vetor", " ", "com", " ", "os", " ", "raios"}]}]}], 
   "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"geraEsferas", "[", 
      RowBox[{"m_", ",", "n_", ",", "kk_"}], "]"}], ":=", 
     RowBox[{"Module", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
        "A", ",", "ii", ",", "jj", ",", "d", ",", "lambda", ",", "u", ",", 
         "v", ",", "Amin", ",", "Amax", ",", "xstar", ",", "di"}], "}"}], ",",
        "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"A", "=", 
         RowBox[{"Table", "[", 
          RowBox[{"0", ",", 
           RowBox[{"{", 
            RowBox[{"ii", ",", "n"}], "}"}], ",", 
           RowBox[{"{", 
            RowBox[{"jj", ",", "m"}], "}"}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"d", "=", 
         RowBox[{"Table", "[", 
          RowBox[{"0", ",", 
           RowBox[{"{", 
            RowBox[{"ii", ",", "m"}], "}"}], ",", 
           RowBox[{"{", 
            RowBox[{"jj", ",", "1"}], "}"}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"For", "[", 
         RowBox[{
          RowBox[{"ii", "=", "1"}], ",", 
          RowBox[{"ii", "\[LessEqual]", "kk"}], ",", 
          RowBox[{"ii", "++"}], ",", "\[IndentingNewLine]", 
          RowBox[{
           RowBox[{"SeedRandom", "[", "ii", "]"}], ";", 
           RowBox[{"lambda", "=", 
            RowBox[{"RandomReal", "[", 
             RowBox[{"{", 
              RowBox[{"0", ",", "10"}], "}"}], "]"}]}], ";", 
           "\[IndentingNewLine]", 
           RowBox[{"SeedRandom", "[", 
            RowBox[{"ii", "+", "1"}], "]"}], ";", 
           RowBox[{"u", "=", 
            RowBox[{"RandomReal", "[", 
             RowBox[{
              RowBox[{"{", 
               RowBox[{"0", ",", "1"}], "}"}], ",", "n"}], "]"}]}], ";", 
           "\[IndentingNewLine]", 
           RowBox[{"SeedRandom", "[", 
            RowBox[{"ii", "+", "2"}], "]"}], ";", 
           RowBox[{"v", "=", 
            RowBox[{"RandomReal", "[", 
             RowBox[{
              RowBox[{"{", 
               RowBox[{"0", ",", "1"}], "}"}], ",", "m"}], "]"}]}], ";", 
           "\[IndentingNewLine]", 
           RowBox[{"A", "=", 
            RowBox[{"A", "+", 
             RowBox[{"lambda", "*", 
              RowBox[{"Outer", "[", 
               RowBox[{"Times", ",", "u", ",", "v"}], "]"}]}]}]}], ";"}]}], 
         "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", 
        RowBox[{"Amin", "=", 
         RowBox[{"Min", "[", "A", "]"}]}], ";", 
        RowBox[{"Amax", "=", 
         RowBox[{"Max", "[", "A", "]"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"SeedRandom", "[", "123", "]"}], ";", 
        RowBox[{"xstar", "=", 
         RowBox[{"RandomReal", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{"Amin", ",", "Amax"}], "}"}], ",", "n"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"For", "[", 
         RowBox[{
          RowBox[{"ii", "=", "1"}], ",", 
          RowBox[{"ii", "\[LessEqual]", "m"}], ",", 
          RowBox[{"ii", "++"}], ",", "\[IndentingNewLine]", 
          RowBox[{
           RowBox[{"di", "=", 
            RowBox[{"Norm", "[", 
             RowBox[{"xstar", "-", 
              RowBox[{"A", "[", 
               RowBox[{"[", 
                RowBox[{";;", ",", "ii"}], "]"}], "]"}]}], "]"}]}], ";", 
           "\[IndentingNewLine]", 
           RowBox[{
            RowBox[{"d", "[", 
             RowBox[{"[", 
              RowBox[{"ii", ",", "1"}], "]"}], "]"}], "=", "di"}], ";"}]}], 
         "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", 
        RowBox[{"A", "=", 
         RowBox[{"Transpose", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0", ",", 
              RowBox[{"-", "0.1"}]}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"1.6", ",", "0.45", ",", "0.45"}], "}"}]}], "}"}], 
          "]"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"d", "=", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", "1.0", "}"}], ",", 
           RowBox[{"{", "0.7", "}"}], ",", 
           RowBox[{"{", "0.9", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"Return", "[", 
         RowBox[{"{", 
          RowBox[{"A", ",", "d"}], "}"}], "]"}], ";"}]}], 
      "\[IndentingNewLine]", "]"}]}], ";"}], "\n"}]}]], "Input",ExpressionUUID\
->"10e558f9-db6c-4957-87ab-4bcbc3344637"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
   "modulo", " ", "interse\[CCedilla]\[ATilde]o", " ", "usando", " ", "AGC"}],
    "*)"}], 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"IntersEsferasAGC", "[", 
      RowBox[{"n_", ",", "m_", ",", "kk_", ",", "e0_", ",", "einf_"}], "]"}], 
     ":=", 
     RowBox[{"Module", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
        "epsilon", ",", "p", ",", "A", ",", "d", ",", "ii", ",", "TEsferas", 
         ",", "ri", ",", "Ci", ",", "ci", ",", "sigmai", ",", "sigma", ",", 
         "a", ",", "aa", ",", "inva", ",", "sigmaN", ",", "a2", ",", "pto1", 
         ",", "Ie", ",", "pto2", ",", "x1", ",", "x2", ",", "X", ",", "x", 
         ",", "y", ",", "z", ",", "pp", ",", "eqSigma", ",", "erro"}], "}"}], 
       ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"epsilon", "=", "5"}], ";", "\[IndentingNewLine]", 
        RowBox[{"p", "=", 
         RowBox[{"n", "+", "1"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{"gera", " ", "m", " ", "esferas", " ", "no", " ", 
          RowBox[{"R", "^", "n"}]}], "*)"}], "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"A", ",", "d"}], "}"}], "=", 
         RowBox[{"geraEsferas", "[", 
          RowBox[{"m", ",", "n", ",", "kk"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{
         "define", " ", "esferas", " ", "no", " ", "espaco", " ", 
          "conforme"}], "*)"}], "\[IndentingNewLine]", 
        RowBox[{"TEsferas", "=", 
         RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"For", "[", 
         RowBox[{
          RowBox[{"ii", "=", "1"}], ",", 
          RowBox[{"ii", "\[LessEqual]", "m"}], ",", 
          RowBox[{"ii", "++"}], ",", "\[IndentingNewLine]", 
          RowBox[{
           RowBox[{"ri", "=", 
            RowBox[{"d", "[", 
             RowBox[{"[", 
              RowBox[{"ii", ",", "1"}], "]"}], "]"}]}], ";", 
           RowBox[{"Ci", "=", 
            RowBox[{"ToBasis", "[", 
             RowBox[{"A", "[", 
              RowBox[{"[", 
               RowBox[{";;", ",", "ii"}], "]"}], "]"}], "]"}]}], ";", 
           "\[IndentingNewLine]", 
           RowBox[{"ci", "=", 
            RowBox[{"e0", "+", "Ci", "+", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"0.5", "*", 
                RowBox[{
                 RowBox[{"Norm", "[", 
                  RowBox[{"ToVector", "[", 
                   RowBox[{"Ci", ",", 
                    RowBox[{"p", "+", "1"}]}], "]"}], "]"}], "^", "2"}]}], 
               ")"}], "*", "einf"}]}]}], ";", "\[IndentingNewLine]", 
           RowBox[{"sigmai", "=", 
            RowBox[{"ci", "-", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"0.5", "*", 
                RowBox[{"ri", "^", "2"}]}], ")"}], "*", "einf"}]}]}], ";", 
           "\[IndentingNewLine]", 
           RowBox[{"TEsferas", "=", 
            RowBox[{"AppendTo", "[", 
             RowBox[{"TEsferas", ",", "sigmai"}], "]"}]}], ";"}]}], 
         "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{
         "computa", " ", "intersecao", " ", "usando", " ", "produto", " ", 
          "exterior"}], "*)"}], "\[IndentingNewLine]", 
        RowBox[{"sigma", "=", 
         RowBox[{"TEsferas", "[", 
          RowBox[{"[", 
           RowBox[{"1", ",", ";;"}], "]"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"For", "[", 
         RowBox[{
          RowBox[{"ii", "=", "2"}], ",", 
          RowBox[{"ii", "\[LessEqual]", "m"}], ",", 
          RowBox[{"ii", "++"}], ",", "\[IndentingNewLine]", 
          RowBox[{
           RowBox[{"sigma", "=", 
            RowBox[{"Chop", "[", 
             RowBox[{
              RowBox[{"OuterProduct", "[", 
               RowBox[{"sigma", ",", 
                RowBox[{"TEsferas", "[", 
                 RowBox[{"[", 
                  RowBox[{"ii", ",", ";;"}], "]"}], "]"}]}], "]"}], ",", 
              RowBox[{"10", "^", 
               RowBox[{"(", 
                RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";"}]}], "]"}], 
        ";", "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{"normaliza", " ", "sigma"}], "*)"}], "\[IndentingNewLine]", 
        RowBox[{"a", "=", 
         RowBox[{"Chop", "[", 
          RowBox[{
           RowBox[{"InnerProduct", "[", 
            RowBox[{"einf", ",", "sigma"}], "]"}], ",", 
           RowBox[{"10", "^", 
            RowBox[{"(", 
             RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{
          RowBox[{"calcula", " ", "inversa", " ", "de", " ", "a"}], ",", 
          RowBox[{"obs", ":", 
           RowBox[{"o", " ", "programa", " ", "da", " ", "erro"}]}], ",", 
          RowBox[{"as", " ", "vezes"}]}], "*)"}], "\[IndentingNewLine]", 
        RowBox[{"aa", "=", 
         RowBox[{"Chop", "[", 
          RowBox[{
           RowBox[{"GeometricProduct", "[", 
            RowBox[{"a", ",", "a"}], "]"}], ",", 
           RowBox[{"10", "^", 
            RowBox[{"(", 
             RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"inva", "=", 
         RowBox[{"Chop", "[", 
          RowBox[{
           RowBox[{"GeometricProduct", "[", 
            RowBox[{"a", ",", 
             RowBox[{"MultivectorInverse", "[", "aa", "]"}]}], "]"}], ",", 
           RowBox[{"10", "^", 
            RowBox[{"(", 
             RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"sigmaN", "=", 
         RowBox[{"-", 
          RowBox[{"Chop", "[", 
           RowBox[{
            RowBox[{"GeometricProduct", "[", 
             RowBox[{"sigma", ",", "inva"}], "]"}], ",", 
            RowBox[{"10", "^", 
             RowBox[{"(", 
              RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{"(*", 
          RowBox[{"obtem", ":", 
           RowBox[{"sigmaN", "^", "2"}]}], "*)"}], 
         RowBox[{
          RowBox[{"Print", "[", 
           RowBox[{"\"\<\[Sigma]_n^2 = \>\"", ",", 
            RowBox[{"Style", "[", 
             RowBox[{
              RowBox[{"Chop", "[", 
               RowBox[{
                RowBox[{"GeometricProduct", "[", 
                 RowBox[{"sigmaN", ",", "sigmaN"}], "]"}], ",", 
                RowBox[{"10", "^", 
                 RowBox[{"(", 
                  RowBox[{"-", "2"}], ")"}]}]}], "]"}], ",", "Red"}], "]"}]}],
            "]"}], ";", "\[IndentingNewLine]", 
          RowBox[{"(*", 
           RowBox[{
            RowBox[{"obtem", ":", 
             RowBox[{"einf", ".", "sigmaN"}]}], "=", 
            RowBox[{"-", "1"}]}], "*)"}], 
          RowBox[{"Print", "[", 
           RowBox[{"\"\<e\[Infinity].\[Sigma]_n = \>\"", ",", 
            RowBox[{"Style", "[", 
             RowBox[{
              RowBox[{"Chop", "[", 
               RowBox[{
                RowBox[{"InnerProduct", "[", 
                 RowBox[{"einf", ",", "sigmaN"}], "]"}], ",", 
                RowBox[{"10", "^", 
                 RowBox[{"(", 
                  RowBox[{"-", "2"}], ")"}]}]}], "]"}], ",", "Red"}], "]"}]}],
            "]"}], ";"}], "*)"}], 
        RowBox[{"(*", 
         RowBox[{"obtem", ":", 
          RowBox[{
          "extrais", " ", "pontos", " ", "do", " ", "par", " ", "de", " ", 
           "ptos"}]}], "*)"}], "\[IndentingNewLine]", 
        RowBox[{"a2", "=", 
         RowBox[{"Chop", "[", 
          RowBox[{
           RowBox[{"InnerProduct", "[", 
            RowBox[{"einf", ",", 
             RowBox[{"Dual", "[", 
              RowBox[{"sigma", ",", 
               RowBox[{"p", "+", "1"}]}], "]"}]}], "]"}], ",", 
           RowBox[{"10", "^", 
            RowBox[{"(", 
             RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"pto1", "=", 
         RowBox[{"Chop", "[", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"GeometricProduct", "[", 
             RowBox[{
              RowBox[{
               RowBox[{"Sqrt", "[", 
                RowBox[{"InnerProduct", "[", 
                 RowBox[{
                  RowBox[{"Dual", "[", 
                   RowBox[{"sigma", ",", 
                    RowBox[{"p", "+", "1"}]}], "]"}], ",", 
                  RowBox[{"Dual", "[", 
                   RowBox[{"sigma", ",", 
                    RowBox[{"p", "+", "1"}]}], "]"}]}], "]"}], "]"}], "+", 
               RowBox[{"Dual", "[", 
                RowBox[{"sigma", ",", 
                 RowBox[{"p", "+", "1"}]}], "]"}]}], ",", 
              RowBox[{"MultivectorInverse", "[", "a2", "]"}]}], "]"}]}], ",", 
           RowBox[{"10", "^", 
            RowBox[{"(", 
             RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"Ie", "=", 
         RowBox[{"OuterProduct", "[", 
          RowBox[{"einf", ",", "e0"}], "]"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"pto2", "=", 
         RowBox[{"Chop", "[", 
          RowBox[{
           RowBox[{"GeometricProduct", "[", 
            RowBox[{
             RowBox[{
              RowBox[{"Sqrt", "[", 
               RowBox[{"InnerProduct", "[", 
                RowBox[{
                 RowBox[{"Dual", "[", 
                  RowBox[{"sigma", ",", 
                   RowBox[{"p", "+", "1"}]}], "]"}], ",", 
                 RowBox[{"Dual", "[", 
                  RowBox[{"sigma", ",", 
                   RowBox[{"p", "+", "1"}]}], "]"}]}], "]"}], "]"}], "-", 
              RowBox[{"Dual", "[", 
               RowBox[{"sigma", ",", 
                RowBox[{"p", "+", "1"}]}], "]"}]}], ",", 
             RowBox[{"MultivectorInverse", "[", "a2", "]"}]}], "]"}], ",", 
           RowBox[{"10", "^", 
            RowBox[{"(", 
             RowBox[{"-", "epsilon"}], ")"}]}]}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"x1", "=", 
         RowBox[{"GeometricProduct", "[", 
          RowBox[{
           RowBox[{"OuterProduct", "[", 
            RowBox[{"pto1", ",", "Ie"}], "]"}], ",", "Ie"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"x2", "=", 
         RowBox[{"GeometricProduct", "[", 
          RowBox[{
           RowBox[{"OuterProduct", "[", 
            RowBox[{"pto2", ",", "Ie"}], "]"}], ",", "Ie"}], "]"}]}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"Print", "[", 
         RowBox[{"\"\<Solu\[CCedilla]\[OTilde]es: x1 = \>\"", ",", 
          RowBox[{"Style", "[", 
           RowBox[{
            RowBox[{"MatrixForm", "[", "x1", "]"}], ",", "Red"}], "]"}], ",", 
          "\"\<,  x2 = \>\"", ",", 
          RowBox[{"Style", "[", 
           RowBox[{
            RowBox[{"MatrixForm", "[", "x2", "]"}], ",", "Red"}], "]"}]}], 
         "]"}], ";", "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{
          RowBox[{"Print", "[", "\"\<Solucoes: \>\"", "]"}], ";", 
          "\[IndentingNewLine]", 
          RowBox[{"Print", "[", 
           RowBox[{"\"\<x_1 =\>\"", ",", 
            RowBox[{"Style", "[", 
             RowBox[{"x1", ",", "Red"}], "]"}], ",", "\"\< \[Element] R^\>\"",
             ",", 
            RowBox[{"Style", "[", 
             RowBox[{"n", ",", "Red"}], "]"}]}], "]"}], ";", 
          "\[IndentingNewLine]", 
          RowBox[{"Print", "[", 
           RowBox[{"\"\<x_2 =\>\"", ",", 
            RowBox[{"Style", "[", 
             RowBox[{"x2", ",", "Red"}], "]"}], ",", "\"\< \[Element] R^\>\"",
             ",", 
            RowBox[{"Style", "[", 
             RowBox[{"n", ",", "Red"}], "]"}]}], "]"}], ";"}], "*)"}], 
        RowBox[{"(*", 
         RowBox[{
         "calcula", " ", "erro", " ", "da", " ", "solu\[CCedilla]\[ATilde]o", 
          " ", "encontrada"}], "*)"}], 
        RowBox[{"erro", "=", 
         RowBox[{"erroMDE", "[", 
          RowBox[{
           RowBox[{"ToVector", "[", 
            RowBox[{"x1", "[", 
             RowBox[{"[", 
              RowBox[{"2", ";;"}], "]"}], "]"}], "]"}], ",", "A", ",", "d", 
           ",", "m"}], "]"}]}], ";", "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{
          RowBox[{"Print", "[", 
           RowBox[{"\"\<erro = \>\"", ",", 
            RowBox[{"Style", "[", 
             RowBox[{"erro", ",", "Red"}], "]"}]}], "]"}], ";"}], "*)"}], 
        "\[IndentingNewLine]", 
        RowBox[{"Print", "[", 
         RowBox[{"\"\<Erro de x1 = \>\"", ",", 
          RowBox[{"Style", "[", 
           RowBox[{"erro", ",", "Red"}], "]"}]}], "]"}], ";", 
        "\[IndentingNewLine]", 
        RowBox[{"Print", "[", 
         RowBox[{"\"\<Erro de x2 = \>\"", ",", 
          RowBox[{"Style", "[", 
           RowBox[{
            RowBox[{"erroMDE", "[", 
             RowBox[{
              RowBox[{"ToVector", "[", 
               RowBox[{"x2", "[", 
                RowBox[{"[", 
                 RowBox[{"2", ";;"}], "]"}], "]"}], "]"}], ",", "A", ",", "d",
               ",", "m"}], "]"}], ",", "Red"}], "]"}]}], "]"}], ";", 
        "\[IndentingNewLine]", " ", "\[IndentingNewLine]", 
        RowBox[{"Return", "[", "erro", "]"}], ";"}]}], "\[IndentingNewLine]", 
      "]"}]}], ";"}], "\n"}]}]], "Input",ExpressionUUID->"4076adc6-de74-4024-\
a1f1-f423503db120"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"n", "=", "3"}], ";", 
  RowBox[{"m", "=", "3"}], ";", 
  RowBox[{"kk", "=", "2"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"m", "=", "n"}], ";", 
   RowBox[{"kk", "=", "m"}], ";"}], "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{"define", " ", "assinatura", " ", "de", " ", 
     RowBox[{"R", "^", "p"}]}], ",", 
    RowBox[{"q", " ", "e", " ", "base", " ", "nula"}]}], 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"$SetSignature", "=", 
   RowBox[{"n", "+", "1"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"p", "=", 
   RowBox[{"n", "+", "1"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e0", "=", 
   RowBox[{"0.5", "*", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"e", "[", 
       RowBox[{"p", "+", "1"}], "]"}], "-", 
      RowBox[{"e", "[", "p", "]"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"einf", "=", 
   RowBox[{
    RowBox[{"e", "[", 
     RowBox[{"p", "+", "1"}], "]"}], "+", 
    RowBox[{"e", "[", "p", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"eerro", "=", 
   RowBox[{"IntersEsferasAGC", "[", 
    RowBox[{"n", ",", "m", ",", "kk", ",", "e0", ",", "einf"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]"}], "Input",ExpressionUUID->"3c2c9517-1dbc-489b-\
aef0-987b6690c3f6"],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Solu\[CCedilla]\[OTilde]es: x1 = \"\>", "\[InvisibleSpace]", 
   StyleBox[
    TagBox[
     RowBox[{"0.`", "\[VeryThinSpace]", "+", 
      RowBox[{"0.7016051660056601`", " ", 
       TagBox[
        SubscriptBox["e", "1"],
        DisplayForm]}], "+", 
      RowBox[{"0.408355883160165`", " ", 
       TagBox[
        SubscriptBox["e", "2"],
        DisplayForm]}], "+", 
      RowBox[{"0.483948339943399`", " ", 
       TagBox[
        SubscriptBox["e", "3"],
        DisplayForm]}]}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]],
    StripOnInput->False,
    LineColor->RGBColor[1, 0, 0],
    FrontFaceColor->RGBColor[1, 0, 0],
    BackFaceColor->RGBColor[1, 0, 0],
    GraphicsColor->RGBColor[1, 0, 0],
    FontColor->RGBColor[1, 0, 0]], "\[InvisibleSpace]", "\<\",  x2 = \"\>", 
   "\[InvisibleSpace]", 
   StyleBox[
    TagBox[
     RowBox[{"0.`", "\[VeryThinSpace]", "+", 
      RowBox[{"0.7197618161184198`", " ", 
       TagBox[
        SubscriptBox["e", "1"],
        DisplayForm]}], "+", 
      RowBox[{"0.5657135174707495`", " ", 
       TagBox[
        SubscriptBox["e", "2"],
        DisplayForm]}], "+", 
      RowBox[{"0.3023818388158016`", " ", 
       TagBox[
        SubscriptBox["e", "3"],
        DisplayForm]}]}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]],
    StripOnInput->False,
    LineColor->RGBColor[1, 0, 0],
    FrontFaceColor->RGBColor[1, 0, 0],
    BackFaceColor->RGBColor[1, 0, 0],
    GraphicsColor->RGBColor[1, 0, 0],
    FontColor->RGBColor[1, 0, 0]]}],
  SequenceForm["Solu\[CCedilla]\[OTilde]es: x1 = ", 
   Style[
    MatrixForm[
    0. + 0.7016051660056601 Clifford`e[1] + 0.408355883160165 Clifford`e[2] + 
     0.483948339943399 Clifford`e[3]], 
    RGBColor[1, 0, 0]], ",  x2 = ", 
   Style[
    MatrixForm[
    0. + 0.7197618161184198 Clifford`e[1] + 0.5657135174707495 Clifford`e[2] + 
     0.3023818388158016 Clifford`e[3]], 
    RGBColor[1, 0, 0]]],
  Editable->False]], "Print",ExpressionUUID->"d034a0c0-ecde-4842-8538-\
74b39c2595a8"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Erro de x1 = \"\>", "\[InvisibleSpace]", 
   StyleBox["1.4274296030894868`*^-16",
    StripOnInput->False,
    LineColor->RGBColor[1, 0, 0],
    FrontFaceColor->RGBColor[1, 0, 0],
    BackFaceColor->RGBColor[1, 0, 0],
    GraphicsColor->RGBColor[1, 0, 0],
    FontColor->RGBColor[1, 0, 0]]}],
  SequenceForm["Erro de x1 = ", 
   Style[1.4274296030894868`*^-16, 
    RGBColor[1, 0, 0]]],
  Editable->False]], "Print",ExpressionUUID->"43f4038c-3b46-4632-9769-\
dc4640c5148e"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Erro de x2 = \"\>", "\[InvisibleSpace]", 
   StyleBox["8.987519723156029`*^-17",
    StripOnInput->False,
    LineColor->RGBColor[1, 0, 0],
    FrontFaceColor->RGBColor[1, 0, 0],
    BackFaceColor->RGBColor[1, 0, 0],
    GraphicsColor->RGBColor[1, 0, 0],
    FontColor->RGBColor[1, 0, 0]]}],
  SequenceForm["Erro de x2 = ", 
   Style[8.987519723156029*^-17, 
    RGBColor[1, 0, 0]]],
  Editable->False]], "Print",ExpressionUUID->"37bb7dfd-20b1-40ea-b617-\
b34b85a8e6bd"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1366, 696},
WindowMargins->{{-8, Automatic}, {Automatic, -8}},
FrontEndVersion->"11.3 for Microsoft Windows (32-bit) (March 6, 2018)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 380, 9, 97, "Input",ExpressionUUID->"9fef554c-1702-43b7-b301-6e540c06f21a"],
Cell[941, 31, 1903, 49, 293, "Input",ExpressionUUID->"f80fbb55-5233-4ed1-9f70-471dbd87b2b2"],
Cell[2847, 82, 4924, 127, 629, "Input",ExpressionUUID->"10e558f9-db6c-4957-87ab-4bcbc3344637"],
Cell[7774, 211, 13425, 332, 1413, "Input",ExpressionUUID->"4076adc6-de74-4024-a1f1-f423503db120"],
Cell[CellGroupData[{
Cell[21224, 547, 1345, 40, 228, "Input",ExpressionUUID->"3c2c9517-1dbc-489b-aef0-987b6690c3f6"],
Cell[CellGroupData[{
Cell[22594, 591, 2061, 62, 28, "Print",ExpressionUUID->"d034a0c0-ecde-4842-8538-74b39c2595a8"],
Cell[24658, 655, 522, 14, 28, "Print",ExpressionUUID->"43f4038c-3b46-4632-9769-dc4640c5148e"],
Cell[25183, 671, 519, 14, 28, "Print",ExpressionUUID->"37bb7dfd-20b1-40ea-b617-b34b85a8e6bd"]
}, Open  ]]
}, Open  ]]
}
]
*)