From d843c9d2d5c25ecc10760b1fc834348b1290921b Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 17 Aug 2021 19:10:01 +0200 Subject: Lots of work. --- real-im-to-analytic.nb | 175 +++++++++++++++++++++++++++++++++---------------- 1 file changed, 119 insertions(+), 56 deletions(-) (limited to 'real-im-to-analytic.nb') diff --git a/real-im-to-analytic.nb b/real-im-to-analytic.nb index 66f14ea..0953065 100644 --- a/real-im-to-analytic.nb +++ b/real-im-to-analytic.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 654811, 11396] -NotebookOptionsPosition[ 649326, 11294] -NotebookOutlinePosition[ 649721, 11310] -CellTagsIndexPosition[ 649678, 11307] +NotebookDataLength[ 657165, 11461] +NotebookOptionsPosition[ 651267, 11353] +NotebookOutlinePosition[ 651664, 11369] +CellTagsIndexPosition[ 651621, 11366] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -58,6 +58,65 @@ Cell[BoxData[ 3.827497233522489*^9}, {3.827497395954739*^9, 3.827497449960273*^9}}, CellLabel->"In[80]:=",ExpressionUUID->"5912efbc-7c4d-43fd-ac08-c167efb03ead"], +Cell[BoxData[ + RowBox[{"Integrate", "[", + RowBox[{"2", + FractionBox[ + SuperscriptBox["\[Theta]", "2"], "\[Pi]"]}]}]], "Input", + CellChangeTimes->{{3.837590409295301*^9, 3.837590410328467*^9}, { + 3.837590461265456*^9, + 3.8375904670199213`*^9}},ExpressionUUID->"d15b0160-d7de-4111-9269-\ +455ff8bf1a23"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FullSimplify", "[", + RowBox[{ + RowBox[{ + RowBox[{"{", + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"z", " ", + RowBox[{"Exp", "[", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"\[Pi]", "/", + RowBox[{"(", + RowBox[{"2", " ", "\[CapitalDelta]"}], ")"}]}]}], "]"}]}], ")"}], + RowBox[{"-", "\[CapitalDelta]"}]], ",", + SuperscriptBox["z", + RowBox[{"-", "\[CapitalDelta]"}]]}], "}"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[CapitalDelta]", "->", + RowBox[{"RandomReal", "[", "]"}]}], ",", + RowBox[{"z", "->", + RowBox[{"RandomReal", "[", "]"}]}]}], "}"}]}], ",", + RowBox[{"Assumptions", "->", + RowBox[{"{", + RowBox[{ + RowBox[{"z", ">", "0"}], ",", + RowBox[{"\[CapitalDelta]", ">", "0"}]}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.837590554460486*^9, 3.837590648157104*^9}, { + 3.8375906921504383`*^9, 3.8375906995980263`*^9}}, + CellLabel->"In[24]:=",ExpressionUUID->"70da4643-cc9f-4644-8e02-03ec3a220ba1"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"0.18593136134882174`", "\[VeryThinSpace]", "+", + RowBox[{"1.7766410373245114`", " ", "\[ImaginaryI]"}]}], ",", + "1.7863437089873107`"}], "}"}]], "Output", + CellChangeTimes->{{3.837590699774778*^9, 3.837590709576022*^9}}, + CellLabel->"Out[24]=",ExpressionUUID->"45ef3551-900b-4c09-b954-3793de4853bd"] +}, Open ]], + +Cell[BoxData["("], "Input", + CellChangeTimes->{ + 3.8375907653764353`*^9},ExpressionUUID->"42793f9e-e7c9-4ac7-acff-\ +2369705ca99f"], + Cell[CellGroupData[{ Cell[BoxData[ @@ -11292,9 +11351,9 @@ f/tbvY1ly5b9x4B+6d++8hZ/+9f/B97XJbuV/0z0739d6//91/r3b/G3//IO 96.],ExpressionUUID->"4f4f4f2f-5f1f-4c17-a075-89617859470a"] }, Open ]] }, -WindowSize->{1437, 792}, -WindowMargins->{{1.5, Automatic}, {1.5, Automatic}}, -FrontEndVersion->"12.1 for Linux ARM (32-bit) (August 18, 2020)", +WindowSize->{1915.5, 528.}, +WindowMargins->{{2.25, Automatic}, {2.25, Automatic}}, +FrontEndVersion->"12.3 for Linux x86 (64-bit) (May 11, 2021)", StyleDefinitions->"Default.nb", ExpressionUUID->"d4a88797-94bb-45a7-a506-b83a92696b1d" ] @@ -11309,98 +11368,102 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[558, 20, 375, 9, 29, "Input",ExpressionUUID->"eff314f5-6828-4938-9917-55be27ef319a"], -Cell[936, 31, 426, 11, 45, "Input",ExpressionUUID->"1079e99d-46c1-4027-999c-bfea3c9cc555"], -Cell[1365, 44, 709, 14, 29, "Input",ExpressionUUID->"5912efbc-7c4d-43fd-ac08-c167efb03ead"], +Cell[558, 20, 375, 9, 22, "Input",ExpressionUUID->"eff314f5-6828-4938-9917-55be27ef319a"], +Cell[936, 31, 426, 11, 37, "Input",ExpressionUUID->"1079e99d-46c1-4027-999c-bfea3c9cc555"], +Cell[1365, 44, 709, 14, 22, "Input",ExpressionUUID->"5912efbc-7c4d-43fd-ac08-c167efb03ead"], +Cell[2077, 60, 311, 8, 38, "Input",ExpressionUUID->"d15b0160-d7de-4111-9269-455ff8bf1a23"], Cell[CellGroupData[{ -Cell[2099, 62, 1569, 40, 52, "Input",ExpressionUUID->"faa37334-6b38-47c0-b3f2-b15a9b638888"], -Cell[3671, 104, 1276, 23, 59, "Message",ExpressionUUID->"b9e452cd-3f14-4277-8346-3613b7d1059b"], -Cell[4950, 129, 1471, 40, 65, "Output",ExpressionUUID->"48a7929b-fdf0-4637-91b6-9ba73fae2113"] +Cell[2413, 72, 1095, 30, 24, "Input",ExpressionUUID->"70da4643-cc9f-4644-8e02-03ec3a220ba1"], +Cell[3511, 104, 358, 7, 25, "Output",ExpressionUUID->"45ef3551-900b-4c09-b954-3793de4853bd"] }, Open ]], -Cell[6436, 172, 456, 14, 29, "Input",ExpressionUUID->"d4cb242d-0fd9-44bf-9a2d-ea9e14e8d4f8"], +Cell[3884, 114, 131, 3, 22, "Input",ExpressionUUID->"42793f9e-e7c9-4ac7-acff-2369705ca99f"], Cell[CellGroupData[{ -Cell[6917, 190, 341, 8, 29, "Input",ExpressionUUID->"43e99def-5276-4d44-be42-b93c0fcddd80"], -Cell[7261, 200, 284, 5, 33, "Output",ExpressionUUID->"0b28767a-50e2-4d5a-bf80-15f97217705e"] +Cell[4040, 121, 1569, 40, 42, "Input",ExpressionUUID->"faa37334-6b38-47c0-b3f2-b15a9b638888"], +Cell[5612, 163, 1276, 23, 48, "Message",ExpressionUUID->"b9e452cd-3f14-4277-8346-3613b7d1059b"], +Cell[6891, 188, 1471, 40, 53, "Output",ExpressionUUID->"48a7929b-fdf0-4637-91b6-9ba73fae2113"] }, Open ]], +Cell[8377, 231, 456, 14, 22, "Input",ExpressionUUID->"d4cb242d-0fd9-44bf-9a2d-ea9e14e8d4f8"], Cell[CellGroupData[{ -Cell[7582, 210, 1089, 27, 29, "Input",ExpressionUUID->"bd6e10a4-ed6f-4e36-8380-8d8ce28cde7c"], -Cell[8674, 239, 776, 20, 62, "Output",ExpressionUUID->"23d0454f-f2d9-4fb3-bdc7-4ffb1b74e6aa"] +Cell[8858, 249, 341, 8, 22, "Input",ExpressionUUID->"43e99def-5276-4d44-be42-b93c0fcddd80"], +Cell[9202, 259, 284, 5, 25, "Output",ExpressionUUID->"0b28767a-50e2-4d5a-bf80-15f97217705e"] }, Open ]], Cell[CellGroupData[{ -Cell[9487, 264, 1187, 28, 29, "Input",ExpressionUUID->"56fcdd5c-2d7b-42f3-95fa-0d2a1c3bedb9"], -Cell[10677, 294, 852, 21, 62, "Output",ExpressionUUID->"071f206f-c384-43a2-82f3-232f48980db8"] +Cell[9523, 269, 1089, 27, 24, "Input",ExpressionUUID->"bd6e10a4-ed6f-4e36-8380-8d8ce28cde7c"], +Cell[10615, 298, 776, 20, 51, "Output",ExpressionUUID->"23d0454f-f2d9-4fb3-bdc7-4ffb1b74e6aa"] }, Open ]], Cell[CellGroupData[{ -Cell[11566, 320, 1187, 28, 29, "Input",ExpressionUUID->"a757608f-16b2-4602-9ded-d15035d5dfdd"], -Cell[12756, 350, 574, 11, 48, "Output",ExpressionUUID->"4ef1c684-f7f6-4ea1-9629-76aadd2710e5"] +Cell[11428, 323, 1187, 28, 24, "Input",ExpressionUUID->"56fcdd5c-2d7b-42f3-95fa-0d2a1c3bedb9"], +Cell[12618, 353, 852, 21, 51, "Output",ExpressionUUID->"071f206f-c384-43a2-82f3-232f48980db8"] }, Open ]], Cell[CellGroupData[{ -Cell[13367, 366, 1186, 28, 29, "Input",ExpressionUUID->"3a1a179e-70d2-47be-8e40-72cc070ade83"], -Cell[14556, 396, 572, 11, 48, "Output",ExpressionUUID->"53419b6f-c170-48c5-81af-042ab186b9ce"] +Cell[13507, 379, 1187, 28, 41, "Input",ExpressionUUID->"a757608f-16b2-4602-9ded-d15035d5dfdd"], +Cell[14697, 409, 574, 11, 40, "Output",ExpressionUUID->"4ef1c684-f7f6-4ea1-9629-76aadd2710e5"] }, Open ]], Cell[CellGroupData[{ -Cell[15165, 412, 1184, 28, 29, "Input",ExpressionUUID->"6ffbb49f-260f-4e66-a0f8-656af593e15f"], -Cell[16352, 442, 478, 8, 33, "Output",ExpressionUUID->"72beeeb2-8b86-472d-b55b-1ef065f3dd89"] +Cell[15308, 425, 1186, 28, 41, "Input",ExpressionUUID->"3a1a179e-70d2-47be-8e40-72cc070ade83"], +Cell[16497, 455, 572, 11, 40, "Output",ExpressionUUID->"53419b6f-c170-48c5-81af-042ab186b9ce"] }, Open ]], Cell[CellGroupData[{ -Cell[16867, 455, 1238, 29, 29, "Input",ExpressionUUID->"cd460901-4cd5-41ad-a9d0-de867c141243"], -Cell[18108, 486, 500, 8, 33, "Output",ExpressionUUID->"c7c03aec-9000-4255-8a2e-4f044b92e998"] +Cell[17106, 471, 1184, 28, 41, "Input",ExpressionUUID->"6ffbb49f-260f-4e66-a0f8-656af593e15f"], +Cell[18293, 501, 478, 8, 25, "Output",ExpressionUUID->"72beeeb2-8b86-472d-b55b-1ef065f3dd89"] }, Open ]], Cell[CellGroupData[{ -Cell[18645, 499, 1238, 29, 29, "Input",ExpressionUUID->"1c5c11e7-2da7-43f2-856a-cf557fec4282"], -Cell[19886, 530, 554, 9, 33, "Output",ExpressionUUID->"2437c0ac-fbd5-4a7d-ba1c-9de115755a14"] +Cell[18808, 514, 1238, 29, 41, "Input",ExpressionUUID->"cd460901-4cd5-41ad-a9d0-de867c141243"], +Cell[20049, 545, 500, 8, 25, "Output",ExpressionUUID->"c7c03aec-9000-4255-8a2e-4f044b92e998"] }, Open ]], Cell[CellGroupData[{ -Cell[20477, 544, 1925, 46, 51, "Input",ExpressionUUID->"bff34808-e357-4250-b00c-4dcfdfd93f24"], -Cell[22405, 592, 152, 3, 33, "Output",ExpressionUUID->"cae0f81f-6c2a-413b-bd58-cf04551377d7"] +Cell[20586, 558, 1238, 29, 41, "Input",ExpressionUUID->"1c5c11e7-2da7-43f2-856a-cf557fec4282"], +Cell[21827, 589, 554, 9, 25, "Output",ExpressionUUID->"2437c0ac-fbd5-4a7d-ba1c-9de115755a14"] }, Open ]], Cell[CellGroupData[{ -Cell[22594, 600, 490, 14, 29, "Input",ExpressionUUID->"830295c2-5fa1-456d-a4d8-c1b20ce3c872"], -Cell[23087, 616, 925, 29, 62, "Output",ExpressionUUID->"100ed52b-af07-479d-bbeb-1496ce7ea929"] +Cell[22418, 603, 1925, 46, 93, "Input",ExpressionUUID->"bff34808-e357-4250-b00c-4dcfdfd93f24"], +Cell[24346, 651, 152, 3, 25, "Output",ExpressionUUID->"cae0f81f-6c2a-413b-bd58-cf04551377d7"] }, Open ]], Cell[CellGroupData[{ -Cell[24049, 650, 490, 14, 29, "Input",ExpressionUUID->"486631aa-c262-4bcf-b82f-3f9a094c4d92"], -Cell[24542, 666, 879, 27, 62, "Output",ExpressionUUID->"134c2909-13c9-4920-aa73-566d68dec7d6"] +Cell[24535, 659, 490, 14, 24, "Input",ExpressionUUID->"830295c2-5fa1-456d-a4d8-c1b20ce3c872"], +Cell[25028, 675, 925, 29, 51, "Output",ExpressionUUID->"100ed52b-af07-479d-bbeb-1496ce7ea929"] }, Open ]], Cell[CellGroupData[{ -Cell[25458, 698, 519, 15, 29, "Input",ExpressionUUID->"4024f218-a338-419b-bc21-2a4fc77880ec"], -Cell[25980, 715, 13099, 235, 237, "Output",ExpressionUUID->"073b32d3-f41e-4cfd-b366-20d745660272"] +Cell[25990, 709, 490, 14, 24, "Input",ExpressionUUID->"486631aa-c262-4bcf-b82f-3f9a094c4d92"], +Cell[26483, 725, 879, 27, 51, "Output",ExpressionUUID->"134c2909-13c9-4920-aa73-566d68dec7d6"] }, Open ]], Cell[CellGroupData[{ -Cell[39116, 955, 704, 20, 29, "Input",ExpressionUUID->"380239cf-c27d-418f-a09d-304242e1a51d"], -Cell[39823, 977, 929, 29, 62, "Output",ExpressionUUID->"a863aff4-d24d-411b-8577-211c8cd934b0"] +Cell[27399, 757, 519, 15, 22, "Input",ExpressionUUID->"4024f218-a338-419b-bc21-2a4fc77880ec"], +Cell[27921, 774, 13099, 235, 178, "Output",ExpressionUUID->"073b32d3-f41e-4cfd-b366-20d745660272"] }, Open ]], Cell[CellGroupData[{ -Cell[40789, 1011, 466, 12, 29, "Input",ExpressionUUID->"399a0086-c1d6-482f-b673-37f2aa2193f0"], -Cell[41258, 1025, 721, 21, 66, "Output",ExpressionUUID->"0159d837-58c4-45d4-8d86-3d3c622e8fc6"] +Cell[41057, 1014, 704, 20, 24, "Input",ExpressionUUID->"380239cf-c27d-418f-a09d-304242e1a51d"], +Cell[41764, 1036, 929, 29, 51, "Output",ExpressionUUID->"a863aff4-d24d-411b-8577-211c8cd934b0"] }, Open ]], Cell[CellGroupData[{ -Cell[42016, 1051, 481, 13, 29, "Input",ExpressionUUID->"39fdbc07-65be-4716-9a42-f8c6ff3fa620"], -Cell[42500, 1066, 204, 3, 33, "Output",ExpressionUUID->"0580e8c0-d6d9-4faf-9964-63d3d79dd649"] +Cell[42730, 1070, 466, 12, 24, "Input",ExpressionUUID->"399a0086-c1d6-482f-b673-37f2aa2193f0"], +Cell[43199, 1084, 721, 21, 55, "Output",ExpressionUUID->"0159d837-58c4-45d4-8d86-3d3c622e8fc6"] }, Open ]], Cell[CellGroupData[{ -Cell[42741, 1074, 291, 5, 29, "Input",ExpressionUUID->"8ad49bde-2970-4105-94cf-47a96e4e700f"], -Cell[43035, 1081, 427, 10, 62, "Output",ExpressionUUID->"7aecbe9d-a492-4834-a509-7e4245e2eab3"] +Cell[43957, 1110, 481, 13, 22, "Input",ExpressionUUID->"39fdbc07-65be-4716-9a42-f8c6ff3fa620"], +Cell[44441, 1125, 204, 3, 25, "Output",ExpressionUUID->"0580e8c0-d6d9-4faf-9964-63d3d79dd649"] }, Open ]], Cell[CellGroupData[{ -Cell[43499, 1096, 808, 17, 29, "Input",ExpressionUUID->"bf73fae8-8163-4a94-a4b8-bc840ec85d39"], -Cell[44310, 1115, 8430, 158, 244, "Output",ExpressionUUID->"412ed524-900d-4555-a68d-a308ff953229"] +Cell[44682, 1133, 291, 5, 22, "Input",ExpressionUUID->"8ad49bde-2970-4105-94cf-47a96e4e700f"], +Cell[44976, 1140, 427, 10, 51, "Output",ExpressionUUID->"7aecbe9d-a492-4834-a509-7e4245e2eab3"] }, Open ]], Cell[CellGroupData[{ -Cell[52777, 1278, 204, 3, 29, "Input",ExpressionUUID->"fea5f784-f8f9-4f32-a638-3b000e454486"], -Cell[52984, 1283, 209, 3, 33, "Output",ExpressionUUID->"e918a310-9674-4cea-9d35-2b98c7dd7a6e"] +Cell[45440, 1155, 808, 17, 22, "Input",ExpressionUUID->"bf73fae8-8163-4a94-a4b8-bc840ec85d39"], +Cell[46251, 1174, 8430, 158, 183, "Output",ExpressionUUID->"412ed524-900d-4555-a68d-a308ff953229"] }, Open ]], Cell[CellGroupData[{ -Cell[53230, 1291, 204, 3, 29, "Input",ExpressionUUID->"f14f52dc-41c4-475b-9b03-a8046f40e2dd"], -Cell[53437, 1296, 149, 2, 33, "Output",ExpressionUUID->"5f42a503-4f2a-45bd-9321-a8e2650ca35d"] +Cell[54718, 1337, 204, 3, 22, "Input",ExpressionUUID->"fea5f784-f8f9-4f32-a638-3b000e454486"], +Cell[54925, 1342, 209, 3, 25, "Output",ExpressionUUID->"e918a310-9674-4cea-9d35-2b98c7dd7a6e"] }, Open ]], Cell[CellGroupData[{ -Cell[53623, 1303, 1099, 23, 29, "Input",ExpressionUUID->"37e11c89-2a80-41dd-b7a6-61cbdedd0290"], -Cell[54725, 1328, 594585, 9963, 377, 322902, 5508, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"4f4f4f2f-5f1f-4c17-a075-89617859470a"] +Cell[55171, 1350, 204, 3, 22, "Input",ExpressionUUID->"f14f52dc-41c4-475b-9b03-a8046f40e2dd"], +Cell[55378, 1355, 149, 2, 25, "Output",ExpressionUUID->"5f42a503-4f2a-45bd-9321-a8e2650ca35d"] +}, Open ]], +Cell[CellGroupData[{ +Cell[55564, 1362, 1099, 23, 24, "Input",ExpressionUUID->"37e11c89-2a80-41dd-b7a6-61cbdedd0290"], +Cell[56666, 1387, 594585, 9963, 374, 322902, 5508, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"4f4f4f2f-5f1f-4c17-a075-89617859470a"] }, Open ]] } ] *) -(* End of internal cache information *) - -- cgit v1.2.3-54-g00ecf