(* 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[ 12050, 442] NotebookOptionsPosition[ 10309, 375] NotebookOutlinePosition[ 10669, 391] CellTagsIndexPosition[ 10626, 388] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[{ RowBox[{"e0", " ", "\:70ba\:6a62\:5713\:6a19\:6e96\:5f0f\:ff0c", " ", "e1", " ", "\:70ba\:67d0\:4e00\:6a62\:5713\:4e4b\:4e00\:822c\:5f0f"}], "\ \[IndentingNewLine]", RowBox[{"\:6c42\:9577\:8ef8", " ", "a", " ", "\:8207\:77ed\:8ef8", " ", "b", " "}]}], "Input", CellChangeTimes->{{3.43717395615625*^9, 3.437174092875*^9}, { 3.43717412721875*^9, 3.437174130609375*^9}, {3.437174366078125*^9, 3.437174406953125*^9}, 3.437174733359375*^9}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"e0", "=", RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["x", "2"], SuperscriptBox["a", "2"]], "+", FractionBox[ SuperscriptBox["y", "2"], SuperscriptBox["b", "2"]]}], "\[Equal]", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"e1", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"3", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"4", " ", SuperscriptBox["y", "2"]}]}], "==", "48"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Do", "[", RowBox[{ RowBox[{"DivideBy", "[", RowBox[{ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "i"}], "]"}], "]"}], ",", RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"Length", "[", RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}]}], "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "=", "1"}], ";"}], "\[IndentingNewLine]", "e1"}], "Input", CellChangeTimes->{{3.437171398984375*^9, 3.437171418671875*^9}, { 3.437171460984375*^9, 3.437171541359375*^9}, {3.437171575703125*^9, 3.437171597234375*^9}, {3.437171673875*^9, 3.437171734015625*^9}, { 3.437171889421875*^9, 3.43717190853125*^9}, {3.437172004484375*^9, 3.437172052515625*^9}, {3.43717361746875*^9, 3.437173701421875*^9}, { 3.43717375734375*^9, 3.437173770328125*^9}, {3.437173917*^9, 3.43717392178125*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["x", "2"], "16"], "+", FractionBox[ SuperscriptBox["y", "2"], "12"]}], "\[Equal]", "1"}], "}"}]], "Output", CellChangeTimes->{ 3.437173251421875*^9, 3.43717362859375*^9, {3.4371736781875*^9, 3.437173702515625*^9}, {3.437173764796875*^9, 3.437173780390625*^9}, 3.437173935671875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}], "/.", RowBox[{"Solve", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"e0", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "i"}], "]"}], "]"}], "\[Equal]", RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "i"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{ 3.43717314009375*^9, 3.437173170734375*^9, 3.437173360109375*^9, { 3.437173426828125*^9, 3.437173444078125*^9}, {3.437173486484375*^9, 3.437173503703125*^9}, 3.437173573796875*^9, {3.437173882765625*^9, 3.43717388796875*^9}, {3.43717480065625*^9, 3.43717480159375*^9}, { 3.43717488834375*^9, 3.43717489515625*^9}, {3.43717501896875*^9, 3.437175072796875*^9}, 3.43717517390625*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", RowBox[{ RowBox[{"-", "2"}], " ", SqrtBox["3"]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", RowBox[{"2", " ", SqrtBox["3"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", RowBox[{ RowBox[{"-", "2"}], " ", SqrtBox["3"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", RowBox[{"2", " ", SqrtBox["3"]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.4371735049375*^9, 3.43717357728125*^9, 3.43717389015625*^9, 3.437173938390625*^9, 3.4371748053125*^9, 3.43717489803125*^9, { 3.43717503903125*^9, 3.43717507471875*^9}, 3.43717517821875*^9}] }, Open ]], Cell[BoxData["\:9644\:9304\:ff1a\:5206\:89e3\:52d5\:4f5c"], "Input", CellFrame->{{0, 0}, {0, 0.5}}, CellChangeTimes->{{3.43717413740625*^9, 3.43717415459375*^9}, { 3.4371743195*^9, 3.437174348125*^9}, 3.437174600609375*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"e1", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"3", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"4", " ", SuperscriptBox["y", "2"]}]}], "==", "48"}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"3", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"4", " ", SuperscriptBox["y", "2"]}]}], "\[Equal]", "48"}], "}"}]], "Output", CellChangeTimes->{3.437174191453125*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}]], "Input", CellChangeTimes->{3.43717410884375*^9}], Cell[BoxData[ RowBox[{"3", " ", SuperscriptBox["x", "2"]}]], "Output", CellChangeTimes->{3.437174110625*^9, 3.43717419496875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]], "Input"], Cell[BoxData["48"], "Output", CellChangeTimes->{3.437174208484375*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DivideBy", "[", RowBox[{ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}], ",", RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.43717422875*^9, 3.43717424834375*^9}}], Cell[BoxData[ FractionBox[ SuperscriptBox["x", "2"], "16"]], "Output", CellChangeTimes->{3.437174250890625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["e1"], "Input", CellChangeTimes->{{3.437174257125*^9, 3.437174258328125*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["x", "2"], "16"], "+", RowBox[{"4", " ", SuperscriptBox["y", "2"]}]}], "\[Equal]", "48"}], "}"}]], "Output", CellChangeTimes->{3.437174258828125*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DivideBy", "[", RowBox[{ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "2"}], "]"}], "]"}], ",", RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{3.437174279828125*^9}], Cell[BoxData[ FractionBox[ SuperscriptBox["y", "2"], "12"]], "Output", CellChangeTimes->{3.437174281921875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["e1"], "Input", CellChangeTimes->{{3.437174285625*^9, 3.437174285875*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["x", "2"], "16"], "+", FractionBox[ SuperscriptBox["y", "2"], "12"]}], "\[Equal]", "48"}], "}"}]], "Output", CellChangeTimes->{3.437174286515625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}], "=", "1"}]], "Input"], Cell[BoxData["1"], "Output", CellChangeTimes->{3.437174303421875*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["e1"], "Input", CellChangeTimes->{{3.437174305015625*^9, 3.437174306*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["x", "2"], "16"], "+", FractionBox[ SuperscriptBox["y", "2"], "12"]}], "\[Equal]", "1"}], "}"}]], "Output", CellChangeTimes->{3.437174306484375*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"t", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"e0", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "i"}], "]"}], "]"}], "\[Equal]", RowBox[{"e1", "[", RowBox[{"[", RowBox[{"1", ",", "1", ",", "i"}], "]"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "2"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.43717452653125*^9, 3.4371745675*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ FractionBox[ SuperscriptBox["x", "2"], SuperscriptBox["a", "2"]], "\[Equal]", FractionBox[ SuperscriptBox["x", "2"], "16"]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox[ SuperscriptBox["y", "2"], SuperscriptBox["b", "2"]], "\[Equal]", FractionBox[ SuperscriptBox["y", "2"], "12"]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.43717455159375*^9, 3.43717457225*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Flatten", "[", "t", "]"}]], "Input", CellChangeTimes->{{3.437174575171875*^9, 3.437174587109375*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["x", "2"], SuperscriptBox["a", "2"]], "\[Equal]", FractionBox[ SuperscriptBox["x", "2"], "16"]}], ",", RowBox[{ FractionBox[ SuperscriptBox["y", "2"], SuperscriptBox["b", "2"]], "\[Equal]", FractionBox[ SuperscriptBox["y", "2"], "12"]}]}], "}"}]], "Output", CellChangeTimes->{3.437174588390625*^9}] }, Open ]] }, WindowSize->{537, 535}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, Magnification->1.5, FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (April 28, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[568, 21, 467, 8, 71, "Input"], Cell[CellGroupData[{ Cell[1060, 33, 1737, 53, 241, "Input"], Cell[2800, 88, 392, 11, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3229, 104, 1072, 27, 179, "Input"], Cell[4304, 133, 764, 26, 80, "Output"] }, Open ]], Cell[5083, 162, 228, 3, 56, "Input"], Cell[CellGroupData[{ Cell[5336, 169, 232, 8, 48, "Input"], Cell[5571, 179, 251, 8, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5859, 192, 153, 4, 43, "Input"], Cell[6015, 198, 134, 3, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6186, 206, 102, 3, 43, "Input"], Cell[6291, 211, 71, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6399, 217, 317, 9, 43, "Input"], Cell[6719, 228, 115, 3, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6871, 236, 91, 1, 43, "Input"], Cell[6965, 239, 250, 8, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7252, 252, 298, 9, 43, "Input"], Cell[7553, 263, 115, 3, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7705, 271, 88, 1, 43, "Input"], Cell[7796, 274, 249, 8, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8082, 287, 127, 4, 43, "Input"], Cell[8212, 293, 70, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8319, 299, 88, 1, 43, "Input"], Cell[8410, 302, 248, 8, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8695, 315, 484, 14, 125, "Input"], Cell[9182, 331, 512, 17, 67, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9731, 353, 126, 2, 43, "Input"], Cell[9860, 357, 433, 15, 67, "Output"] }, Open ]] } ] *) (* End of internal cache information *)