二元函数可视化（第三版）

GeoGebra 命令及参数

1. Polygon((x_{max}, y_{max}), (x_{min}, y_{max}), (x_{min}, y_{min}), (x_{max}, y_{min})) → VV, j, t, c, d
2. If(b_a, Nx_a, 1) → Nx1_a
3. Polygon((x((ro; α)), y((ro; α)), z_{min}) + PTest, (x((ro; α + 180°)), y((ro; α + 180°)), z_{min}) + PTest, (x((ro; α + 180°)), y((ro; α + 180°)), z_{max}) + PTest, (x((ro; α)), y((ro; α)), z_{max}) + PTest) → poly1, k, l, m, p
4. ImplicitCurve(f(x, y) - f(x(C), y(C))) → ICurve_2
5. IntersectPath(plane0, f(x, y)) → ICurve_3
6. Point(ICurve_2) → R0
7. Length(lr2) → llr2
8. Sequence((x(Element[lr2, i]), y(Element[lr2, i]), f(x(Element[lr2, i]), y(Element[lr2, i]))), i, 1, llr2) → lllPmin01
9. If(Length[lllPmin01] ≟ 0, false, true) → bwllPmin01
10. Length(lr1) → llr1
11. Sequence((x(Element[lr1, i]), y(Element[lr1, i]), f(x(Element[lr1, i]), y(Element[lr1, i]))), i, 1, llr1) → lllPmax01
12. If(Length[lllPmax01] ≟ 0, false, true) → bwllPmax01
13. If(bwllPmax01, Max[z(lllPmax01)], 1000) → Maxz0
14. If(bwllPmax01, IndexOf[Maxz0, Sequence[z(Element[lllPmax01, i]), i, 1, Length[lllPmax01]]], 1000) → Indexmaxz0
15. If(b, true, false) → h
16. If(h, Nx, 1) → Nx1
17. Length(lr3) → llr3
18. Point(Segment[(0, 0), (6.28319, 0)]) → Af
19. Point(Segment[Px2, Px1]) → Ax
20. Point(Segment[Py2, Py1]) → Ay
21. Textfield(N_{V1}) → inputBox1
22. Textfield(x_{min}) → inputBox2
23. Textfield(x_{max}) → inputBox3
24. Textfield(y_{min}) → inputBox4
25. Textfield(y_{max}) → inputBox5
26. Textfield(f) → inputBox6
27. Textfield(z_{min}) → inputBox7
28. Textfield(z_{max}) → inputBox8
29. Point(Segment[Pz2, Pz1]) → Az
30. Textfield(ω_c) → inputBox9
31. Textfield(vt) → inputBox10
32. Sum(Sequence[If[f(x(PTest), y(PTest)) - f(x(Element[lr01, i]), y(Element[lr01, i])) > 0, 1, 0], i, 1, n]) → ext1
33. RotateText("z_{min}=" + z_{min} + "", 90°) → Text2
34. RotateText("z_{max}=" + z_{max} + "", 90°) → Text6
35. Sequence(Segment[Element[l0maxmin2, k], Element[l0maxmin2, k + 1]], k, 1, Length[l0maxmin2]) → linelmaxmin2
36. Sequence(Element[lr1, i], i, 1, llr1) → lPmax
37. Sequence(Element[lr2, i], i, 1, llr2) → lPmin
38. Sequence(Element[lr3, i], i, 1, llr3) → lPsad
39. If(bwllPmin01, Min[z(lllPmin01)], 1000) → Minz0
40. If(bwllPmin01, IndexOf[Minz0, Sequence[z(Element[lllPmin01, i]), i, 1, Length[lllPmin01]]], 1000) → Indexminz0
41. Element(lr2, Indexminz0) → P_{min0}
42. If(bwllPmin01, Element[lllPmin01, Indexminz0], (1000, 1000, 1000)) → zmin2
43. Point(Liste1) → C111a
44. Locus(C1110a, C111a) → loc
45. PolyLine(l0maxmin1) → linelmaxmin11
46. If(bwllPmax01, Element[lllPmax01, Indexmaxz0], (1000, 1000, 1000)) → zmax2
47. RemoveUndefined(Sequence[If[f(x(PTest), y(PTest)) - f(x(Element[lr01, i]), y(Element[lr01, i])) > 0, i, NaN], i, 1, n]) → lr04
48. Zip(Vector[b, a], a, Sequence[Element[lr01, Element[lr04, i]], i, 1, Length[lr04]], b, Sequence[Element[lr02, Element[lr04, i]], i, 1, Length[lr04]]) → lr06
49. Sequence((x(Element[lr01, i]), y(Element[lr01, i]), f(x(Element[lr01, i]), y(Element[lr01, i]))), i, 1, n) → lr013
50. Sequence((x(Element[lr02, i]), y(Element[lr02, i]), f(x(Element[lr02, i]), y(Element[lr02, i]))), i, 1, n) → lr023
51. Zip(Vector[b, a], a, Sequence[Element[lr013, Element[lr04, i]], i, 1, Length[lr04]], b, Sequence[Element[lr023, Element[lr04, i]], i, 1, Length[lr04]]) → lr063
52. Zip(Vector[a, b], a, Sequence[Element[lr01, Element[lr05, i]], i, 1, Length[lr05]], b, Sequence[Element[lr02, Element[lr05, i]], i, 1, Length[lr05]]) → lr07
53. Zip(Vector[a, b], a, Sequence[Element[lr013, Element[lr05, i]], i, 1, Length[lr05]], b, Sequence[Element[lr023, Element[lr05, i]], i, 1, Length[lr05]]) → lr073
54. Textfield(zoom_{3D}) → InputBox1
55. Element(lr1, rmax - 1) → Pzmax
56. Element(lr2, rmin - 1) → Pzmin
57. Element(lr3, rsad - 1) → Pzsad
58. Text("( x , y , z )") → TextR01
59. Join({{TextR01}, lllPmax01}) → llPmax01
60. Element(lr1, Indexmaxz0) → P_{max0}
61. Sequence((x(Element[lr3, i]), y(Element[lr3, i]), f(x(Element[lr3, i]), y(Element[lr3, i]))), i, 1, llr3) → lllPsp
62. Join({{TextR01}, lllPmin01}) → llPmin01
63. Join({{TextR01}, lllPsp}) → llPsad01
64. Element(lllPsp, rsad - 1) → Pzsad_{3D}
65. Element(lllPmax01, rmax - 1) → Pzmax_{3D}
66. Element(lllPmin01, rmin - 1) → Pzmin_{3D}
67. Textfield(A) → InputBox2
68. RemoveUndefined(Sequence[If[f(x(PTest), y(PTest)) - f(x(Element[lr01, i]), y(Element[lr01, i])) > 0, i, (-i)], i, 1, n]) → lr04c
69. Append(lr04c, Element[lr04c, 1]) → lr04cc
70. Sum(Sequence[If[(Element[lr04cc, i] * Element[lr04cc, i + 1]) < 0, 1, 0], i, 1, n + 1]) → lr04ccc
71. Line(A, RoR) → i
72. ImplicitCurve(f(x, y) - zi) → list3
73. ImplicitCurve(f(x, y) - zii) → list4
74. Vector(R0, R41) → w_11
75. Vector(R0, R0 + R11) → u_11
76. Textfield(ω0_c) → InputBox3
77. Textfield(r_a) → InputBox5
78. Point(c) → G
79. Point(j) → H
80. Point(w_11, 1) → I
81. Vector(F, I_{3D}) → v
82. If(ext1 ≟ n, 1, If[ext1 ≟ 0, 2, If[lr04ccc > 2 ∧ lr04ccc ≤ 4, 3, 4]]) → roo
83. Textfield(n_c) → InputBox6
84. Textfield(a_c) → InputBox7
85. Textfield(r_{lc}) → InputBox8
86. Textfield(vt) → InputBox9
87. PolyLine(Bl) → Bly
88. PolyLine(Gr) → Gry
89. PolyLine(Ro) → Roy
90. Textfield(Nx) → Resolution
91. Textfield(r) → InputBox11
92. Textfield(v_{m4}) → InputBox4
93. Textfield(Nz) → InputBox10
94. Textfield(n) → InputBox12
95. Textfield(rr) → InputBox13
96. Textfield(r_{ext}) → InputBox14
97. Textfield(v_{zi}) → InputBox15
98. Textfield(d_1) → InputBox16
99. Textfield(f_1) → InputBox17
100. Textfield(v_{m3}) → InputBox18