拉格朗日乘数法示例2

GeoGebra 命令及参数

1. LeftSide(Cu_g) → g
2. Simplify(Derivative[g, x, 1]) → gx'
3. Simplify(Derivative[g, y, 1]) → gy'
4. Simplify(Derivative[f, x, 1]) → fx'
5. Simplify(Derivative[f, y, 1]) → fy'
6. Point(Cu_g) → B
7. UnitVector(Vector[B, Dg]) → u_g
8. UnitVector(Vector[B, Df]) → u_f
9. Angle(u_g, u_f) → α
10. LaTeX(f, true) → text8a
11. LaTeX(Cu_g, true) → text8b
12. Textfield(Cu0_x) → InputBox1
13. Textfield(Cu0_y) → InputBox2
14. Textfield(f) → InputBox3
15. Textfield(Cu_g) → InputBox4
16. Zip((x(a), y(a), f(a)), a, Sequence[Point[Cu_g, t / n], t, 0, n]) → lg_1
17. Textfield(n) → InputBox5
18. Zip("(" + (LaTeX[ScientificText[x(a), 2]]) + "," + (LaTeX[ScientificText[y(a), 2]]) + ")", a, l1xy'_f) → l1xy'_fa
19. CurveCartesian((sqrt(3) * cos(t)), (sqrt(3) * sin(t)), f((sqrt(3) * cos(t)), (sqrt(3) * sin(t))), t, (-π), π) → q1
20. Surface((sqrt(3) * cos(t)), (sqrt(3) * sin(t)), u, t, (-π), π, u, -2.1, 2.1) → g1
21. RotateText(text15, 90°) → text20
22. Zip(Text["(" + (SurdText[x(a)]) + "," + (SurdText[y(a)]) + ")", (0, 0), true, true], a, l1) → l1surd
23. Zip(Text["(" + (SurdText[x(a)]) + "," + (SurdText[y(a)]) + ")", (0, 0), true, true], a, l2) → l2surd
24. Sequence(If[lα1(i) ≟ 180°, 1, lα1(i) ≟ 0°, 2, 3], i, 1, Length[l1]) → l1_α
25. Sequence(If[lα2(i) ≟ 180°, 1, lα2(i) ≟ 0°, 2, 3], i, 1, Length[l2]) → l2_α
26. RemoveUndefined(Sequence[If[l1_α(i) ≟ 1, l1(i), NaN], i, 1, Length[l1]]) → l1min
27. RemoveUndefined(Sequence[If[l1_α(i) ≟ 2, l1(i), NaN], i, 1, Length[l1]]) → l1max
28. RemoveUndefined(Sequence[If[l1_α(i) ≟ 3, l1(i), NaN], i, 1, Length[l1]]) → l1loc1
29. RemoveUndefined(Sequence[If[l1_α(i) ≟ 1, l1f(i), NaN], i, 1, Length[l1f]]) → l1min_{3D}
30. RemoveUndefined(Sequence[If[l1_α(i) ≟ 2, l1f(i), NaN], i, 1, Length[l1f]]) → l1max_{3D}
31. RemoveUndefined(Sequence[If[l2_α(i) ≟ 2, l2(i), NaN], i, 1, Length[l2]]) → l2max
32. RemoveUndefined(Sequence[If[l2_α(i) ≟ 2, l2f(i), NaN], i, 1, Length[l2f]]) → l2max_{3D}
33. RemoveUndefined(Sequence[If[l2_α(i) ≟ 1, l2(i), NaN], i, 1, Length[l2]]) → l2min
34. RemoveUndefined(Sequence[If[l2_α(i) ≟ 1, l2f(i), NaN], i, 1, Length[l2f]]) → l2min_{3D}
35. Text("∇f", Point[u_f, 1]) → text25
36. Text("∇g", Point[u_g, 1]) → text25g
37. TableText(Append["N", 1…Length[l1]], Append["\fgcolor{red}{Cp}", l1surd], Append["\fgcolor{blue}{f}(\fgcolor{red}{C_p })", l1fa], Append["(\dot{f_x},\dot{f_y})", l1xy'_fa], Append["(\dot{g_x},\dot{g_y})", l1xy'_ga], Append["λ_x", lλ1ax], Append["λ_y", lλ1ay], Append["\widehat{\dot{g}\dot{f}} ", lα1], "c|_") → tTab1
38. TableText(Append["N", 1…Length[l2]], Append["\fgcolor{red}{Cp}", l2surd], Append["\fgcolor{blue}{f}(\fgcolor{red}{C_p })", l2fa], Append["(\dot{f_x},\dot{f_y})", l2xy'_fa], Append["(\dot{g_x},\dot{g_y})", l2xy'_ga], Append["λ_x", lλ2ax], Append["λ_y", lλ2ay], Append["\widehat{\dot{g}\dot{f}} ", lα2], "c|_") → tTab2
39. Segment(B, C) → f_1
40. RemoveUndefined(Zip[Vector[c, c + UnitVector[a]], a, l1xy'_f, c, l1]) → lvec1_f
41. RemoveUndefined(Zip[Vector[c, c + UnitVector[a]], a, l1xy'_g, c, l1]) → lvec1_g
42. RemoveUndefined(Zip[Vector[c, c + UnitVector[a]], a, l2xy'_f, c, l2]) → lvec2_f
43. RemoveUndefined(Zip[Vector[c, c + UnitVector[a]], a, l2xy'_g, c, l2]) → lvec2_g
44. Zip(Segment[a, b], a, l1, b, l1f) → l1seg
45. Sequence(Text[i, l1(i) + (0.2, 0.1)], i, 1, lä1) → l1txt
46. Sequence(Text[i, l2(i) + (0.2, 0.1)], i, 1, lä2) → l2txt
47. Zip(Segment[a, b], a, l2, b, l2f) → l2seg