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Newton-Raphson Method by Micky Bullock

Newton-Raphson Method by Micky Bullock
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2013-06-14 22:24
FunctionCalculusDerivative
In collections A Level: Numerical Methods for Solving Equations
This example demonstrates the Newton-Raphson method, an iterative numerical method for finding roots of equations f(x) = 0. The construction summary shows the implementation process using commands and objects such as Point, Derivative, Segment, Text, and Textfield. Suitable for high school mathematics education and learning, particularly in calculus and numerical methods.

GeoGebra Commands & Parameters

  1. Point(xAxis) → x_0
  2. Derivative(f) → f'
  3. Segment((C1, 0), (C1, f(C1))) → D1
  4. Segment((C1, f(C1)), (C2, 0)) → E2
  5. Segment((C2, 0), (C2, f(C2))) → D2
  6. Text("x_0=", A) → F1
  7. Textfield(f) → inputBox1
  8. Segment((C3, 0), (C3, f(C3))) → D3
  9. Segment((C4, 0), (C4, f(C4))) → D4
  10. Segment((C5, 0), (C5, f(C5))) → D5
  11. Segment((C6, 0), (C6, f(C6))) → D6
  12. Segment((C7, 0), (C7, f(C7))) → D7
  13. Segment((C8, 0), (C8, f(C8))) → D8
  14. Segment((C9, 0), (C9, f(C9))) → D9
  15. Segment((C10, 0), (C10, f(C10))) → D10
  16. Segment((C11, 0), (C11, f(C11))) → D11
  17. Segment((C12, 0), (C12, f(C12))) → D12
  18. Segment((C13, 0), (C13, f(C13))) → D13
  19. Segment((C14, 0), (C14, f(C14))) → D14
  20. Segment((C15, 0), (C15, f(C15))) → D15
  21. Segment((C16, 0), (C16, f(C16))) → D16
  22. Segment((C17, 0), (C17, f(C17))) → D17
  23. Segment((C18, 0), (C18, f(C18))) → D18
  24. Segment((C19, 0), (C19, f(C19))) → D19
  25. Segment((C20, 0), (C20, f(C20))) → D20
  26. Segment((C21, 0), (C21, f(C21))) → D21
  27. Segment((C22, 0), (C22, f(C22))) → D22
  28. Segment((C23, 0), (C23, f(C23))) → D23
  29. Segment((C24, 0), (C24, f(C24))) → D24
  30. Segment((C25, 0), (C25, f(C25))) → D25
  31. Segment((C26, 0), (C26, f(C26))) → D26
  32. Segment((C27, 0), (C27, f(C27))) → D27
  33. Segment((C28, 0), (C28, f(C28))) → D28
  34. Segment((C29, 0), (C29, f(C29))) → D29
  35. Segment((C30, 0), (C30, f(C30))) → D30
  36. Segment((C31, 0), (C31, f(C31))) → D31
  37. Segment((C32, 0), (C32, f(C32))) → D32
  38. Segment((C33, 0), (C33, f(C33))) → D33
  39. Segment((C34, 0), (C34, f(C34))) → D34
  40. Segment((C35, 0), (C35, f(C35))) → D35
  41. Segment((C36, 0), (C36, f(C36))) → D36
  42. Segment((C37, 0), (C37, f(C37))) → D37
  43. Segment((C38, 0), (C38, f(C38))) → D38
  44. Segment((C39, 0), (C39, f(C39))) → D39
  45. Segment((C40, 0), (C40, f(C40))) → D40
  46. Segment((C41, 0), (C41, f(C41))) → D41
  47. Segment((C42, 0), (C42, f(C42))) → D42
  48. Segment((C43, 0), (C43, f(C43))) → D43
  49. Segment((C44, 0), (C44, f(C44))) → D44
  50. Segment((C45, 0), (C45, f(C45))) → D45
  51. Segment((C46, 0), (C46, f(C46))) → D46
  52. Segment((C47, 0), (C47, f(C47))) → D47
  53. Segment((C48, 0), (C48, f(C48))) → D48
  54. Segment((C49, 0), (C49, f(C49))) → D49
  55. Segment((C50, 0), (C50, f(C50))) → D50
  56. Segment((C51, 0), (C51, f(C51))) → D51
  57. Segment((C52, 0), (C52, f(C52))) → D52
  58. Segment((C53, 0), (C53, f(C53))) → D53
  59. Segment((C54, 0), (C54, f(C54))) → D54
  60. Segment((C55, 0), (C55, f(C55))) → D55
  61. Segment((C56, 0), (C56, f(C56))) → D56
  62. Segment((C57, 0), (C57, f(C57))) → D57
  63. Segment((C58, 0), (C58, f(C58))) → D58
  64. Segment((C59, 0), (C59, f(C59))) → D59
  65. Segment((C60, 0), (C60, f(C60))) → D60
  66. Segment((C61, 0), (C61, f(C61))) → D61
  67. Segment((C62, 0), (C62, f(C62))) → D62
  68. Segment((C63, 0), (C63, f(C63))) → D63
  69. Segment((C64, 0), (C64, f(C64))) → D64
  70. Segment((C65, 0), (C65, f(C65))) → D65
  71. Segment((C66, 0), (C66, f(C66))) → D66
  72. Segment((C67, 0), (C67, f(C67))) → D67
  73. Segment((C68, 0), (C68, f(C68))) → D68
  74. Segment((C69, 0), (C69, f(C69))) → D69
  75. Segment((C70, 0), (C70, f(C70))) → D70
  76. Segment((C71, 0), (C71, f(C71))) → D71
  77. Segment((C72, 0), (C72, f(C72))) → D72
  78. Segment((C73, 0), (C73, f(C73))) → D73
  79. Segment((C74, 0), (C74, f(C74))) → D74
  80. Segment((C75, 0), (C75, f(C75))) → D75
  81. Segment((C76, 0), (C76, f(C76))) → D76
  82. Segment((C77, 0), (C77, f(C77))) → D77
  83. Segment((C78, 0), (C78, f(C78))) → D78
  84. Segment((C79, 0), (C79, f(C79))) → D79
  85. Segment((C80, 0), (C80, f(C80))) → D80
  86. Segment((C81, 0), (C81, f(C81))) → D81
  87. Segment((C82, 0), (C82, f(C82))) → D82
  88. Segment((C83, 0), (C83, f(C83))) → D83
  89. Segment((C84, 0), (C84, f(C84))) → D84
  90. Segment((C85, 0), (C85, f(C85))) → D85
  91. Segment((C86, 0), (C86, f(C86))) → D86
  92. Segment((C87, 0), (C87, f(C87))) → D87
  93. Segment((C88, 0), (C88, f(C88))) → D88
  94. Segment((C89, 0), (C89, f(C89))) → D89
  95. Segment((C90, 0), (C90, f(C90))) → D90
  96. Segment((C91, 0), (C91, f(C91))) → D91
  97. Segment((C92, 0), (C92, f(C92))) → D92
  98. Segment((C93, 0), (C93, f(C93))) → D93
  99. Segment((C94, 0), (C94, f(C94))) → D94
  100. Segment((C95, 0), (C95, f(C95))) → D95
  101. Segment((C96, 0), (C96, f(C96))) → D96
  102. Segment((C97, 0), (C97, f(C97))) → D97
  103. Segment((C98, 0), (C98, f(C98))) → D98
  104. Segment((C99, 0), (C99, f(C99))) → D99
  105. Segment((C100, 0), (C100, f(C100))) → D100
  106. Segment((C2, f(C2)), (C3, 0)) → E3
  107. Segment((C3, f(C3)), (C4, 0)) → E4
  108. Segment((C4, f(C4)), (C5, 0)) → E5
  109. Segment((C5, f(C5)), (C6, 0)) → E6
  110. Segment((C6, f(C6)), (C7, 0)) → E7
  111. Segment((C7, f(C7)), (C8, 0)) → E8
  112. Segment((C8, f(C8)), (C9, 0)) → E9
  113. Segment((C9, f(C9)), (C10, 0)) → E10
  114. Segment((C10, f(C10)), (C11, 0)) → E11
  115. Segment((C11, f(C11)), (C12, 0)) → E12
  116. Segment((C12, f(C12)), (C13, 0)) → E13
  117. Segment((C13, f(C13)), (C14, 0)) → E14
  118. Segment((C14, f(C14)), (C15, 0)) → E15
  119. Segment((C15, f(C15)), (C16, 0)) → E16
  120. Segment((C16, f(C16)), (C17, 0)) → E17
  121. Segment((C17, f(C17)), (C18, 0)) → E18
  122. Segment((C18, f(C18)), (C19, 0)) → E19
  123. Segment((C19, f(C19)), (C20, 0)) → E20
  124. Segment((C20, f(C20)), (C21, 0)) → E21
  125. Segment((C21, f(C21)), (C22, 0)) → E22
  126. Segment((C22, f(C22)), (C23, 0)) → E23
  127. Segment((C23, f(C23)), (C24, 0)) → E24
  128. Segment((C24, f(C24)), (C25, 0)) → E25
  129. Segment((C25, f(C25)), (C26, 0)) → E26
  130. Segment((C26, f(C26)), (C27, 0)) → E27
  131. Segment((C27, f(C27)), (C28, 0)) → E28
  132. Segment((C28, f(C28)), (C29, 0)) → E29
  133. Segment((C29, f(C29)), (C30, 0)) → E30
  134. Segment((C30, f(C30)), (C31, 0)) → E31
  135. Segment((C31, f(C31)), (C32, 0)) → E32
  136. Segment((C32, f(C32)), (C33, 0)) → E33
  137. Segment((C33, f(C33)), (C34, 0)) → E34
  138. Segment((C34, f(C34)), (C35, 0)) → E35
  139. Segment((C35, f(C35)), (C36, 0)) → E36
  140. Segment((C36, f(C36)), (C37, 0)) → E37
  141. Segment((C37, f(C37)), (C38, 0)) → E38
  142. Segment((C38, f(C38)), (C39, 0)) → E39
  143. Segment((C39, f(C39)), (C40, 0)) → E40
  144. Segment((C40, f(C40)), (C41, 0)) → E41
  145. Segment((C41, f(C41)), (C42, 0)) → E42
  146. Segment((C42, f(C42)), (C43, 0)) → E43
  147. Segment((C43, f(C43)), (C44, 0)) → E44
  148. Segment((C44, f(C44)), (C45, 0)) → E45
  149. Segment((C45, f(C45)), (C46, 0)) → E46
  150. Segment((C46, f(C46)), (C47, 0)) → E47
  151. Segment((C47, f(C47)), (C48, 0)) → E48
  152. Segment((C48, f(C48)), (C49, 0)) → E49
  153. Segment((C49, f(C49)), (C50, 0)) → E50
  154. Segment((C50, f(C50)), (C51, 0)) → E51
  155. Segment((C51, f(C51)), (C52, 0)) → E52
  156. Segment((C52, f(C52)), (C53, 0)) → E53
  157. Segment((C53, f(C53)), (C54, 0)) → E54
  158. Segment((C54, f(C54)), (C55, 0)) → E55
  159. Segment((C55, f(C55)), (C56, 0)) → E56
  160. Segment((C56, f(C56)), (C57, 0)) → E57
  161. Segment((C57, f(C57)), (C58, 0)) → E58
  162. Segment((C58, f(C58)), (C59, 0)) → E59
  163. Segment((C59, f(C59)), (C60, 0)) → E60
  164. Segment((C60, f(C60)), (C61, 0)) → E61
  165. Segment((C61, f(C61)), (C62, 0)) → E62
  166. Segment((C62, f(C62)), (C63, 0)) → E63
  167. Segment((C63, f(C63)), (C64, 0)) → E64
  168. Segment((C64, f(C64)), (C65, 0)) → E65
  169. Segment((C65, f(C65)), (C66, 0)) → E66
  170. Segment((C66, f(C66)), (C67, 0)) → E67
  171. Segment((C67, f(C67)), (C68, 0)) → E68
  172. Segment((C68, f(C68)), (C69, 0)) → E69
  173. Segment((C69, f(C69)), (C70, 0)) → E70
  174. Segment((C70, f(C70)), (C71, 0)) → E71
  175. Segment((C71, f(C71)), (C72, 0)) → E72
  176. Segment((C72, f(C72)), (C73, 0)) → E73
  177. Segment((C73, f(C73)), (C74, 0)) → E74
  178. Segment((C74, f(C74)), (C75, 0)) → E75
  179. Segment((C75, f(C75)), (C76, 0)) → E76
  180. Segment((C76, f(C76)), (C77, 0)) → E77
  181. Segment((C77, f(C77)), (C78, 0)) → E78
  182. Segment((C78, f(C78)), (C79, 0)) → E79
  183. Segment((C79, f(C79)), (C80, 0)) → E80
  184. Segment((C80, f(C80)), (C81, 0)) → E81
  185. Segment((C81, f(C81)), (C82, 0)) → E82
  186. Segment((C82, f(C82)), (C83, 0)) → E83
  187. Segment((C83, f(C83)), (C84, 0)) → E84
  188. Segment((C84, f(C84)), (C85, 0)) → E85
  189. Segment((C85, f(C85)), (C86, 0)) → E86
  190. Segment((C86, f(C86)), (C87, 0)) → E87
  191. Segment((C87, f(C87)), (C88, 0)) → E88
  192. Segment((C88, f(C88)), (C89, 0)) → E89
  193. Segment((C89, f(C89)), (C90, 0)) → E90
  194. Segment((C90, f(C90)), (C91, 0)) → E91
  195. Segment((C91, f(C91)), (C92, 0)) → E92
  196. Segment((C92, f(C92)), (C93, 0)) → E93
  197. Segment((C93, f(C93)), (C94, 0)) → E94
  198. Segment((C94, f(C94)), (C95, 0)) → E95
  199. Segment((C95, f(C95)), (C96, 0)) → E96
  200. Segment((C96, f(C96)), (C97, 0)) → E97
  201. Segment((C97, f(C97)), (C98, 0)) → E98
  202. Segment((C98, f(C98)), (C99, 0)) → E99
  203. Segment((C99, f(C99)), (C100, 0)) → E100
  204. Text("x_" * B11 + "_" * A11 * "=", (x(A), y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → F11
  205. Text("x_" * B12 + "_" * A12 * "=", (x(A), y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → F12
  206. Text("x_" * B13 + "_" * A13 * "=", (x(A), y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → F13
  207. Text("x_" * B14 + "_" * A14 * "=", (x(A), y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → F14
  208. Text("x_" * B15 + "_" * A15 * "=", (x(A), y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → F15
  209. Text("x_" * B16 + "_" * A16 * "=", (x(A), y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → F16
  210. Text("x_" * B17 + "_" * A17 * "=", (x(A), y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → F17
  211. Text("x_" * B18 + "_" * A18 * "=", (x(A), y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → F18
  212. Text("x_" * B19 + "_" * A19 * "=", (x(A), y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → F19
  213. Text("x_" * B20 + "_" * A20 * "=", (x(A), y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → F20
  214. Text("x_" * B21 + "_" * A21 * "=", (x(A), y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → F21
  215. Text("x_" * B22 + "_" * A22 * "=", (x(A), y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → F22
  216. Text("x_" * B23 + "_" * A23 * "=", (x(A), y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → F23
  217. Text("x_" * B24 + "_" * A24 * "=", (x(A), y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → F24
  218. Text("x_" * B25 + "_" * A25 * "=", (x(A), y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → F25
  219. Text("x_" * B26 + "_" * A26 * "=", (x(A), y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → F26
  220. Text(C11, (x(A) + 0.4 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → G11
  221. Text(C12, (x(A) + 0.4 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → G12
  222. Text(C13, (x(A) + 0.4 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → G13
  223. Text(C14, (x(A) + 0.4 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → G14
  224. Text(C15, (x(A) + 0.4 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → G15
  225. Text(C16, (x(A) + 0.4 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → G16
  226. Text(C17, (x(A) + 0.4 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → G17
  227. Text(C18, (x(A) + 0.4 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → G18
  228. Text(C19, (x(A) + 0.4 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → G19
  229. Text(C20, (x(A) + 0.4 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → G20
  230. Text(C21, (x(A) + 0.4 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → G21
  231. Text(C22, (x(A) + 0.4 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → G22
  232. Text(C23, (x(A) + 0.4 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → G23
  233. Text(C24, (x(A) + 0.4 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → G24
  234. Text(C25, (x(A) + 0.4 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → G25
  235. Text(C26, (x(A) + 0.4 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → G26
  236. Text("x_" * A10 * "=", (x(A), y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → F10
  237. Text("x_" * A2 * "=", (x(A), y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → F2
  238. Text("x_" * A3 * "=", (x(A), y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → F3
  239. Text("x_" * A4 * "=", (x(A), y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → F4
  240. Text("x_" * A5 * "=", (x(A), y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → F5
  241. Text("x_" * A6 * "=", (x(A), y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → F6
  242. Text("x_" * A7 * "=", (x(A), y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → F7
  243. Text("x_" * A8 * "=", (x(A), y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → F8
  244. Text("x_" * A9 * "=", (x(A), y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → F9
  245. Text(C10, (x(A) + 0.4 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → G10
  246. Text(C2, (x(A) + 0.4 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → G2
  247. Text(C3, (x(A) + 0.4 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → G3
  248. Text(C4, (x(A) + 0.4 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → G4
  249. Text(C5, (x(A) + 0.4 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → G5
  250. Text(C6, (x(A) + 0.4 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → G6
  251. Text(C7, (x(A) + 0.4 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → G7
  252. Text(C8, (x(A) + 0.4 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → G8
  253. Text(C9, (x(A) + 0.4 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → G9
  254. Text(C1, (x(A) + 0.4 * zoomX, y(A))) → G1
  255. Text(C27, (x(A) + 2.1 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → G27
  256. Text("x_" * B27 + "_" * A27 * "=", (x(A) + 1.7 * zoomX, y(A) - (B2 * 10 + A2) * 0.15 * zoomY)) → F27
  257. Text("x_" * B28 + "_" * A28 * "=", (x(A) + 1.7 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → F28
  258. Text("x_" * B29 + "_" * A29 * "=", (x(A) + 1.7 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → F29
  259. Text("x_" * B30 + "_" * A30 * "=", (x(A) + 1.7 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → F30
  260. Text("x_" * B31 + "_" * A31 * "=", (x(A) + 1.7 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → F31
  261. Text("x_" * B32 + "_" * A32 * "=", (x(A) + 1.7 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → F32
  262. Text("x_" * B33 + "_" * A33 * "=", (x(A) + 1.7 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → F33
  263. Text("x_" * B34 + "_" * A34 * "=", (x(A) + 1.7 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → F34
  264. Text("x_" * B35 + "_" * A35 * "=", (x(A) + 1.7 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → F35
  265. Text("x_" * B36 + "_" * A36 * "=", (x(A) + 1.7 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → F36
  266. Text("x_" * B37 + "_" * A37 * "=", (x(A) + 1.7 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → F37
  267. Text("x_" * B38 + "_" * A38 * "=", (x(A) + 1.7 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → F38
  268. Text("x_" * B39 + "_" * A39 * "=", (x(A) + 1.7 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → F39
  269. Text("x_" * B40 + "_" * A40 * "=", (x(A) + 1.7 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → F40
  270. Text("x_" * B41 + "_" * A41 * "=", (x(A) + 1.7 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → F41
  271. Text("x_" * B42 + "_" * A42 * "=", (x(A) + 1.7 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → F42
  272. Text("x_" * B43 + "_" * A43 * "=", (x(A) + 1.7 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → F43
  273. Text("x_" * B44 + "_" * A44 * "=", (x(A) + 1.7 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → F44
  274. Text("x_" * B45 + "_" * A45 * "=", (x(A) + 1.7 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → F45
  275. Text("x_" * B46 + "_" * A46 * "=", (x(A) + 1.7 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → F46
  276. Text("x_" * B47 + "_" * A47 * "=", (x(A) + 1.7 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → F47
  277. Text("x_" * B48 + "_" * A48 * "=", (x(A) + 1.7 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → F48
  278. Text("x_" * B49 + "_" * A49 * "=", (x(A) + 1.7 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → F49
  279. Text("x_" * B50 + "_" * A50 * "=", (x(A) + 1.7 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → F50
  280. Text("x_" * B51 + "_" * A51 * "=", (x(A) + 1.7 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → F51
  281. Text("x_" * B52 + "_" * A52 * "=", (x(A) + 1.7 * zoomX, y(A) - (B27 * 10 + A27) * 0.15 * zoomY)) → F52
  282. Text("x_" * B53 + "_" * A53 * "=", (x(A) + 1.7 * zoomX, y(A) - (B28 * 10 + A28) * 0.15 * zoomY)) → F53
  283. Text("x_" * B54 + "_" * A54 * "=", (x(A) + 1.7 * zoomX, y(A) - (B29 * 10 + A29) * 0.15 * zoomY)) → F54
  284. Text("x_" * B55 + "_" * A55 * "=", (x(A) + 1.7 * zoomX, y(A) - (B30 * 10 + A30) * 0.15 * zoomY)) → F55
  285. Text("x_" * B56 + "_" * A56 * "=", (x(A) + 1.7 * zoomX, y(A) - (B31 * 10 + A31) * 0.15 * zoomY)) → F56
  286. Text("x_" * B57 + "_" * A57 * "=", (x(A) + 1.7 * zoomX, y(A) - (B32 * 10 + A32) * 0.15 * zoomY)) → F57
  287. Text("x_" * B58 + "_" * A58 * "=", (x(A) + 1.7 * zoomX, y(A) - (B33 * 10 + A33) * 0.15 * zoomY)) → F58
  288. Text("x_" * B59 + "_" * A59 * "=", (x(A) + 1.7 * zoomX, y(A) - (B34 * 10 + A34) * 0.15 * zoomY)) → F59
  289. Text("x_" * B60 + "_" * A60 * "=", (x(A) + 1.7 * zoomX, y(A) - (B35 * 10 + A35) * 0.15 * zoomY)) → F60
  290. Text("x_" * B61 + "_" * A61 * "=", (x(A) + 1.7 * zoomX, y(A) - (B36 * 10 + A36) * 0.15 * zoomY)) → F61
  291. Text("x_" * B62 + "_" * A62 * "=", (x(A) + 1.7 * zoomX, y(A) - (B37 * 10 + A37) * 0.15 * zoomY)) → F62
  292. Text("x_" * B63 + "_" * A63 * "=", (x(A) + 1.7 * zoomX, y(A) - (B38 * 10 + A38) * 0.15 * zoomY)) → F63
  293. Text("x_" * B64 + "_" * A64 * "=", (x(A) + 1.7 * zoomX, y(A) - (B39 * 10 + A39) * 0.15 * zoomY)) → F64
  294. Text("x_" * B65 + "_" * A65 * "=", (x(A) + 1.7 * zoomX, y(A) - (B40 * 10 + A40) * 0.15 * zoomY)) → F65
  295. Text("x_" * B66 + "_" * A66 * "=", (x(A) + 1.7 * zoomX, y(A) - (B41 * 10 + A41) * 0.15 * zoomY)) → F66
  296. Text("x_" * B67 + "_" * A67 * "=", (x(A) + 1.7 * zoomX, y(A) - (B42 * 10 + A42) * 0.15 * zoomY)) → F67
  297. Text("x_" * B68 + "_" * A68 * "=", (x(A) + 1.7 * zoomX, y(A) - (B43 * 10 + A43) * 0.15 * zoomY)) → F68
  298. Text("x_" * B69 + "_" * A69 * "=", (x(A) + 1.7 * zoomX, y(A) - (B44 * 10 + A44) * 0.15 * zoomY)) → F69
  299. Text("x_" * B70 + "_" * A70 * "=", (x(A) + 1.7 * zoomX, y(A) - (B45 * 10 + A45) * 0.15 * zoomY)) → F70
  300. Text("x_" * B71 + "_" * A71 * "=", (x(A) + 1.7 * zoomX, y(A) - (B46 * 10 + A46) * 0.15 * zoomY)) → F71
  301. Text("x_" * B72 + "_" * A72 * "=", (x(A) + 1.7 * zoomX, y(A) - (B47 * 10 + A47) * 0.15 * zoomY)) → F72
  302. Text("x_" * B73 + "_" * A73 * "=", (x(A) + 1.7 * zoomX, y(A) - (B48 * 10 + A48) * 0.15 * zoomY)) → F73
  303. Text("x_" * B74 + "_" * A74 * "=", (x(A) + 1.7 * zoomX, y(A) - (B49 * 10 + A49) * 0.15 * zoomY)) → F74
  304. Text("x_" * B75 + "_" * A75 * "=", (x(A) + 1.7 * zoomX, y(A) - (B50 * 10 + A50) * 0.15 * zoomY)) → F75
  305. Text("x_" * B76 + "_" * A76 * "=", (x(A) + 1.7 * zoomX, y(A) - (B51 * 10 + A51) * 0.15 * zoomY)) → F76
  306. Text("x_" * B77 + "_" * A77 * "=", (x(A) + 1.7 * zoomX, y(A) - (B52 * 10 + A52) * 0.15 * zoomY)) → F77
  307. Text("x_" * B78 + "_" * A78 * "=", (x(A) + 1.7 * zoomX, y(A) - (B53 * 10 + A53) * 0.15 * zoomY)) → F78
  308. Text("x_" * B79 + "_" * A79 * "=", (x(A) + 1.7 * zoomX, y(A) - (B54 * 10 + A54) * 0.15 * zoomY)) → F79
  309. Text("x_" * B80 + "_" * A80 * "=", (x(A) + 1.7 * zoomX, y(A) - (B55 * 10 + A55) * 0.15 * zoomY)) → F80
  310. Text("x_" * B81 + "_" * A81 * "=", (x(A) + 1.7 * zoomX, y(A) - (B56 * 10 + A56) * 0.15 * zoomY)) → F81
  311. Text("x_" * B82 + "_" * A82 * "=", (x(A) + 1.7 * zoomX, y(A) - (B57 * 10 + A57) * 0.15 * zoomY)) → F82
  312. Text("x_" * B83 + "_" * A83 * "=", (x(A) + 1.7 * zoomX, y(A) - (B58 * 10 + A58) * 0.15 * zoomY)) → F83
  313. Text("x_" * B84 + "_" * A84 * "=", (x(A) + 1.7 * zoomX, y(A) - (B59 * 10 + A59) * 0.15 * zoomY)) → F84
  314. Text("x_" * B85 + "_" * A85 * "=", (x(A) + 1.7 * zoomX, y(A) - (B60 * 10 + A60) * 0.15 * zoomY)) → F85
  315. Text("x_" * B86 + "_" * A86 * "=", (x(A) + 1.7 * zoomX, y(A) - (B61 * 10 + A61) * 0.15 * zoomY)) → F86
  316. Text("x_" * B87 + "_" * A87 * "=", (x(A) + 1.7 * zoomX, y(A) - (B62 * 10 + A62) * 0.15 * zoomY)) → F87
  317. Text("x_" * B88 + "_" * A88 * "=", (x(A) + 1.7 * zoomX, y(A) - (B63 * 10 + A63) * 0.15 * zoomY)) → F88
  318. Text("x_" * B89 + "_" * A89 * "=", (x(A) + 1.7 * zoomX, y(A) - (B64 * 10 + A64) * 0.15 * zoomY)) → F89
  319. Text("x_" * B90 + "_" * A90 * "=", (x(A) + 1.7 * zoomX, y(A) - (B65 * 10 + A65) * 0.15 * zoomY)) → F90
  320. Text("x_" * B91 + "_" * A91 * "=", (x(A) + 1.7 * zoomX, y(A) - (B66 * 10 + A66) * 0.15 * zoomY)) → F91
  321. Text("x_" * B92 + "_" * A92 * "=", (x(A) + 1.7 * zoomX, y(A) - (B67 * 10 + A67) * 0.15 * zoomY)) → F92
  322. Text("x_" * B93 + "_" * A93 * "=", (x(A) + 1.7 * zoomX, y(A) - (B68 * 10 + A68) * 0.15 * zoomY)) → F93
  323. Text("x_" * B94 + "_" * A94 * "=", (x(A) + 1.7 * zoomX, y(A) - (B69 * 10 + A69) * 0.15 * zoomY)) → F94
  324. Text("x_" * B95 + "_" * A95 * "=", (x(A) + 1.7 * zoomX, y(A) - (B70 * 10 + A70) * 0.15 * zoomY)) → F95
  325. Text("x_" * B96 + "_" * A96 * "=", (x(A) + 1.7 * zoomX, y(A) - (B71 * 10 + A71) * 0.15 * zoomY)) → F96
  326. Text("x_" * B97 + "_" * A97 * "=", (x(A) + 1.7 * zoomX, y(A) - (B72 * 10 + A72) * 0.15 * zoomY)) → F97
  327. Text("x_" * B98 + "_" * A98 * "=", (x(A) + 1.7 * zoomX, y(A) - (B73 * 10 + A73) * 0.15 * zoomY)) → F98
  328. Text("x_" * B99 + "_" * A99 * "=", (x(A) + 1.7 * zoomX, y(A) - (B74 * 10 + A74) * 0.15 * zoomY)) → F99
  329. Text("x_" * B100 + "_" * A100 * "=", (x(A) + 1.7 * zoomX, y(A) - (B75 * 10 + A75) * 0.15 * zoomY)) → F100
  330. Text(C28, (x(A) + 2.1 * zoomX, y(A) - (B3 * 10 + A3) * 0.15 * zoomY)) → G28
  331. Text(C29, (x(A) + 2.1 * zoomX, y(A) - (B4 * 10 + A4) * 0.15 * zoomY)) → G29
  332. Text(C30, (x(A) + 2.1 * zoomX, y(A) - (B5 * 10 + A5) * 0.15 * zoomY)) → G30
  333. Text(C31, (x(A) + 2.1 * zoomX, y(A) - (B6 * 10 + A6) * 0.15 * zoomY)) → G31
  334. Text(C32, (x(A) + 2.1 * zoomX, y(A) - (B7 * 10 + A7) * 0.15 * zoomY)) → G32
  335. Text(C33, (x(A) + 2.1 * zoomX, y(A) - (B8 * 10 + A8) * 0.15 * zoomY)) → G33
  336. Text(C34, (x(A) + 2.1 * zoomX, y(A) - (B9 * 10 + A9) * 0.15 * zoomY)) → G34
  337. Text(C35, (x(A) + 2.1 * zoomX, y(A) - (B10 * 10 + A10) * 0.15 * zoomY)) → G35
  338. Text(C36, (x(A) + 2.1 * zoomX, y(A) - (B11 * 10 + A11) * 0.15 * zoomY)) → G36
  339. Text(C37, (x(A) + 2.1 * zoomX, y(A) - (B12 * 10 + A12) * 0.15 * zoomY)) → G37
  340. Text(C38, (x(A) + 2.1 * zoomX, y(A) - (B13 * 10 + A13) * 0.15 * zoomY)) → G38
  341. Text(C39, (x(A) + 2.1 * zoomX, y(A) - (B14 * 10 + A14) * 0.15 * zoomY)) → G39
  342. Text(C40, (x(A) + 2.1 * zoomX, y(A) - (B15 * 10 + A15) * 0.15 * zoomY)) → G40
  343. Text(C41, (x(A) + 2.1 * zoomX, y(A) - (B16 * 10 + A16) * 0.15 * zoomY)) → G41
  344. Text(C42, (x(A) + 2.1 * zoomX, y(A) - (B17 * 10 + A17) * 0.15 * zoomY)) → G42
  345. Text(C43, (x(A) + 2.1 * zoomX, y(A) - (B18 * 10 + A18) * 0.15 * zoomY)) → G43
  346. Text(C44, (x(A) + 2.1 * zoomX, y(A) - (B19 * 10 + A19) * 0.15 * zoomY)) → G44
  347. Text(C45, (x(A) + 2.1 * zoomX, y(A) - (B20 * 10 + A20) * 0.15 * zoomY)) → G45
  348. Text(C46, (x(A) + 2.1 * zoomX, y(A) - (B21 * 10 + A21) * 0.15 * zoomY)) → G46
  349. Text(C47, (x(A) + 2.1 * zoomX, y(A) - (B22 * 10 + A22) * 0.15 * zoomY)) → G47
  350. Text(C48, (x(A) + 2.1 * zoomX, y(A) - (B23 * 10 + A23) * 0.15 * zoomY)) → G48
  351. Text(C49, (x(A) + 2.1 * zoomX, y(A) - (B24 * 10 + A24) * 0.15 * zoomY)) → G49
  352. Text(C50, (x(A) + 2.1 * zoomX, y(A) - (B25 * 10 + A25) * 0.15 * zoomY)) → G50
  353. Text(C51, (x(A) + 2.1 * zoomX, y(A) - (B26 * 10 + A26) * 0.15 * zoomY)) → G51
  354. Text(C52, (x(A) + 2.1 * zoomX, y(A) - (B27 * 10 + A27) * 0.15 * zoomY)) → G52
  355. Text(C53, (x(A) + 2.1 * zoomX, y(A) - (B28 * 10 + A28) * 0.15 * zoomY)) → G53
  356. Text(C54, (x(A) + 2.1 * zoomX, y(A) - (B29 * 10 + A29) * 0.15 * zoomY)) → G54
  357. Text(C55, (x(A) + 2.1 * zoomX, y(A) - (B30 * 10 + A30) * 0.15 * zoomY)) → G55
  358. Text(C56, (x(A) + 2.1 * zoomX, y(A) - (B31 * 10 + A31) * 0.15 * zoomY)) → G56
  359. Text(C57, (x(A) + 2.1 * zoomX, y(A) - (B32 * 10 + A32) * 0.15 * zoomY)) → G57
  360. Text(C58, (x(A) + 2.1 * zoomX, y(A) - (B33 * 10 + A33) * 0.15 * zoomY)) → G58
  361. Text(C59, (x(A) + 2.1 * zoomX, y(A) - (B34 * 10 + A34) * 0.15 * zoomY)) → G59
  362. Text(C60, (x(A) + 2.1 * zoomX, y(A) - (B35 * 10 + A35) * 0.15 * zoomY)) → G60
  363. Text(C61, (x(A) + 2.1 * zoomX, y(A) - (B36 * 10 + A36) * 0.15 * zoomY)) → G61
  364. Text(C62, (x(A) + 2.1 * zoomX, y(A) - (B37 * 10 + A37) * 0.15 * zoomY)) → G62
  365. Text(C63, (x(A) + 2.1 * zoomX, y(A) - (B38 * 10 + A38) * 0.15 * zoomY)) → G63
  366. Text(C64, (x(A) + 2.1 * zoomX, y(A) - (B39 * 10 + A39) * 0.15 * zoomY)) → G64
  367. Text(C65, (x(A) + 2.1 * zoomX, y(A) - (B40 * 10 + A40) * 0.15 * zoomY)) → G65
  368. Text(C66, (x(A) + 2.1 * zoomX, y(A) - (B41 * 10 + A41) * 0.15 * zoomY)) → G66
  369. Text(C67, (x(A) + 2.1 * zoomX, y(A) - (B42 * 10 + A42) * 0.15 * zoomY)) → G67
  370. Text(C68, (x(A) + 2.1 * zoomX, y(A) - (B43 * 10 + A43) * 0.15 * zoomY)) → G68
  371. Text(C69, (x(A) + 2.1 * zoomX, y(A) - (B44 * 10 + A44) * 0.15 * zoomY)) → G69
  372. Text(C70, (x(A) + 2.1 * zoomX, y(A) - (B45 * 10 + A45) * 0.15 * zoomY)) → G70
  373. Text(C71, (x(A) + 2.1 * zoomX, y(A) - (B46 * 10 + A46) * 0.15 * zoomY)) → G71
  374. Text(C72, (x(A) + 2.1 * zoomX, y(A) - (B47 * 10 + A47) * 0.15 * zoomY)) → G72
  375. Text(C73, (x(A) + 2.1 * zoomX, y(A) - (B48 * 10 + A48) * 0.15 * zoomY)) → G73
  376. Text(C74, (x(A) + 2.1 * zoomX, y(A) - (B49 * 10 + A49) * 0.15 * zoomY)) → G74
  377. Text(C75, (x(A) + 2.1 * zoomX, y(A) - (B50 * 10 + A50) * 0.15 * zoomY)) → G75
  378. Text(C76, (x(A) + 2.1 * zoomX, y(A) - (B51 * 10 + A51) * 0.15 * zoomY)) → G76
  379. Text(C77, (x(A) + 2.1 * zoomX, y(A) - (B52 * 10 + A52) * 0.15 * zoomY)) → G77
  380. Text(C78, (x(A) + 2.1 * zoomX, y(A) - (B53 * 10 + A53) * 0.15 * zoomY)) → G78
  381. Text(C79, (x(A) + 2.1 * zoomX, y(A) - (B54 * 10 + A54) * 0.15 * zoomY)) → G79
  382. Text(C80, (x(A) + 2.1 * zoomX, y(A) - (B55 * 10 + A55) * 0.15 * zoomY)) → G80
  383. Text(C81, (x(A) + 2.1 * zoomX, y(A) - (B56 * 10 + A56) * 0.15 * zoomY)) → G81
  384. Text(C82, (x(A) + 2.1 * zoomX, y(A) - (B57 * 10 + A57) * 0.15 * zoomY)) → G82
  385. Text(C83, (x(A) + 2.1 * zoomX, y(A) - (B58 * 10 + A58) * 0.15 * zoomY)) → G83
  386. Text(C84, (x(A) + 2.1 * zoomX, y(A) - (B59 * 10 + A59) * 0.15 * zoomY)) → G84
  387. Text(C85, (x(A) + 2.1 * zoomX, y(A) - (B60 * 10 + A60) * 0.15 * zoomY)) → G85
  388. Text(C86, (x(A) + 2.1 * zoomX, y(A) - (B61 * 10 + A61) * 0.15 * zoomY)) → G86
  389. Text(C87, (x(A) + 2.1 * zoomX, y(A) - (B62 * 10 + A62) * 0.15 * zoomY)) → G87
  390. Text(C88, (x(A) + 2.1 * zoomX, y(A) - (B63 * 10 + A63) * 0.15 * zoomY)) → G88
  391. Text(C89, (x(A) + 2.1 * zoomX, y(A) - (B64 * 10 + A64) * 0.15 * zoomY)) → G89
  392. Text(C90, (x(A) + 2.1 * zoomX, y(A) - (B65 * 10 + A65) * 0.15 * zoomY)) → G90
  393. Text(C91, (x(A) + 2.1 * zoomX, y(A) - (B66 * 10 + A66) * 0.15 * zoomY)) → G91
  394. Text(C92, (x(A) + 2.1 * zoomX, y(A) - (B67 * 10 + A67) * 0.15 * zoomY)) → G92
  395. Text(C93, (x(A) + 2.1 * zoomX, y(A) - (B68 * 10 + A68) * 0.15 * zoomY)) → G93
  396. Text(C94, (x(A) + 2.1 * zoomX, y(A) - (B69 * 10 + A69) * 0.15 * zoomY)) → G94
  397. Text(C95, (x(A) + 2.1 * zoomX, y(A) - (B70 * 10 + A70) * 0.15 * zoomY)) → G95
  398. Text(C96, (x(A) + 2.1 * zoomX, y(A) - (B71 * 10 + A71) * 0.15 * zoomY)) → G96
  399. Text(C97, (x(A) + 2.1 * zoomX, y(A) - (B72 * 10 + A72) * 0.15 * zoomY)) → G97
  400. Text(C98, (x(A) + 2.1 * zoomX, y(A) - (B73 * 10 + A73) * 0.15 * zoomY)) → G98
  401. Text(C99, (x(A) + 2.1 * zoomX, y(A) - (B74 * 10 + A74) * 0.15 * zoomY)) → G99
  402. Text(C100, (x(A) + 2.1 * zoomX, y(A) - (B75 * 10 + A75) * 0.15 * zoomY)) → G100