临界点作为几何中位数及其性质利用Hessian矩阵

GeoGebra 命令及参数

1. Polygon({((-π), ((-π)) / 2), ((-π), π / 2), (π, π / 2), (π, ((-π)) / 2)}) → q
2. PointIn(q) → aP1
3. PointIn(q) → aP2
4. PointIn(q) → aP3
5. PointIn(q) → aP4
6. PointIn(q) → aP5
7. PointIn(q) → aP6
8. PointIn(q) → aP7
9. PointIn(q) → aP8
10. PointIn(q) → P9
11. PointIn(q) → aP10
12. First({P1, P2, P3, P4, P5, P6, P7, P8, P9, P10}, n) → lP
13. PointIn(q) → A_2
14. Sum(Zip[sqrt((x(a) - ((R * cos(x)) * cos(y)))^(2) + (y(a) - ((R * sin(x)) * cos(y)))^(2) + (z(a) - (R * sin(y)))^(2)), a, lP]) → f
15. Sequence(If[D(i) > 0, If[f_{xx}(i) > 0, "local minimum", "local maximum"], If[(D(i) * f_{xx}(i)) ≟ 0, "?", "saddle point"]], i, 1, Length[l1]) → l4
16. Zip((x(a), y(a)), a, l1) → l5
17. TableText(Append["i", 1…Length[l1]], Append["critical points", l5], Append["f_{x}", lfx], Append["f_{y}", lfy], Append["f_{xx}", f_{xx}], Append["Det", D], Append["", l4], "v") → text1
18. Function((q_f * f(u, v)) + b_0, u, (-π), π, v, ((-π)) / 2, π / 2) → f0
19. Length(lsad) → läsad
20. Length(lmax) → lämax
21. Length(lmin) → lämin
22. Zip(Segment[A, p], p, lP) → seg
23. Sum(seg) → sum_seg
24. Flatten(Sequence[Sequence[((-π) + ((2 * π / na) * i), ((-π)) / 2 + (π / na * j)), j, 1, na - 1], i, 1, na - 1]) → ltest_2
25. Zip((R; x(a); y(a)), a, ltest_2) → ltest_3
26. TableText(Append["i", Sequence[Length[lmax]]], Append["P_{Max }\;(φ,θ)", lmax], Append["(f'x,f'y)", lZf'xymax], "v") → textmax
27. TableText(Append["i", Sequence[Length[(lmin * x)]]], Append["P_{Max }\;(φ,θ)", lmin], Append["(f'x,f'y)", lZf'xymin], "v") → textmin
28. TableText(Append["i", Sequence[Length[(lsad * x)]]], Append["P_{Max }\;(φ,θ)", lsad], Append["(f'x,f'y)", lZf'xysad], "v") → textsad
29. Textfield(R) → InputBox1
30. Textfield(n) → InputBox2
31. Textfield(lP0) → InputBox3