MathPlotAI Logo MathPlotAI

Graphical and Numerical CAS Solution of a System with Implicit Functions (1)

Graphical and Numerical CAS Solution of a System with Implicit Functions (1)
Loading the math board and drawing, please wait…
2017-02-06 15:48
FunctionCoordinate GeometryGraphing
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve Solution of Systems of nonlinear Equations
This example demonstrates solving a system of two equations with implicit functions using graphical and numerical methods with CAS. Key mathematical concepts include implicit functions, intersections, and functions. GeoGebra commands used include ImplicitCurve, Intersect, PolyLine, etc. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. ImplicitCurve(f1(x, y)) → a
  2. Intersect(Circle[D, r_a], OrthogonalLine[D, Segment[D, ClosestPoint[a, D]]], 2) → Z2_a
  3. Intersect(Circle[D, r_a], OrthogonalLine[D, Segment[D, ClosestPoint[a, D]]], 1) → Z1_a
  4. PolyLine(Zip[ClosestPoint[a, B], B, Z1_a + ((Z2_a - Z1_a) / n_a * Sequence[i, i, 0, n_a])]) → polZa
  5. ImplicitCurve(f2(x, y)) → b
  6. Intersect(Circle[D, r_b], OrthogonalLine[D, Segment[D, ClosestPoint[b, D]]], 1) → Z1_b
  7. Intersect(Circle[D, r_b], OrthogonalLine[D, Segment[D, ClosestPoint[b, D]]], 2) → Z2_b
  8. PolyLine(Zip[ClosestPoint[b, B], B, Z1_b + ((Z2_b - Z1_b) / n_b * Sequence[i, i, 0, n_b])]) → polZb
  9. Element({Intersect[polZa, polZb]}, 1) → PZ
  10. Textfield(Nn) → InputBox4
  11. Textfield(e) → InputBox5
  12. Textfield(x_{min}) → InputBox6
  13. Textfield(x_{max}) → InputBox7
  14. Textfield(y_{min}) → InputBox8
  15. Textfield(y_{max}) → InputBox9
  16. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, g1_s, g2_s, g3_s, s4_s
  17. Length(lr1) → llr1
  18. Length(lf2) → llf2
  19. Textfield(r) → InputBox16
  20. Element(lr1, i_{manual}) → C_t
  21. Length(lf1) → llf1
  22. Textfield(n_a) → InputBox21
  23. Textfield(n_b) → InputBox22
  24. Textfield(r_a) → InputBox23
  25. Textfield(q) → InputBox24
  26. PolyLine(Z1_a + ((Z2_a - Z1_a) / n_a * Sequence[i, i, 0, n_a])) → poly2_aa
  27. PolyLine(Z1_b + ((Z2_b - Z1_b) / n_b * Sequence[i, i, 0, n_b])) → poly2_bb
  28. Point(poly2_aa, e1) → R_a
  29. Point(poly2_bb, e2) → R_b
  30. ClosestPoint(a, R_a) → R'_a
  31. ClosestPoint(b, R_b) → R'_b
  32. Length(R'_a - R'_b) → dmaxmins2
  33. If(Defined[PZ], If[fza2 < fzb2, (f1za2, f2za2), (f1zb2, f2zb2)], (NaN, NaN)) → errorz2
  34. If(Defined[PZ], If[fza2 < fzb2, R'_a, R'_b], (NaN, NaN)) → Pz2
  35. If(ca, PZ, Pz2) → PZ0
  36. If(ca, f11, x(errorz2)) → f110
  37. If(ca, f22, y(errorz2)) → f220
  38. Element(listxyres1, f) → B_t
  39. Textfield(r_b) → InputBox13
  40. Element(roots0, f) → A
  41. Textfield(f1) → InputBox1
  42. Textfield(f2) → InputBox3
  43. Corner(1) → Corner1
  44. Corner(2) → Corner2
  45. Corner(3) → Corner3
  46. ImplicitCurve(f01(x, y)) → c
  47. Textfield(α) → InputBox11
  48. TableText({Join[{{"N"}, Sequence[i, i, 1, llr1]}], Join[{{""}, Sequence["→", i, 1, i_{manual}]}], Join[{{"x:"}, x(lr1)}], Join[{{"y:"}, y(lr1)}], Join[{{"f1* 10^-6"}, lf1}], Join[{{"f2* 10^-6"}, lf2}]}, "vr") → text8
  49. Textfield(i_{manual}) → Eingabefeld1
  50. Textfield(f) → Eingabefeld2
  51. Length(lr2) → llr2
  52. If(Length[listxyres1] ≟ 0 ∨ (i > m1), E, Element[listxyres1, i]) → B
  53. TableText({Join[{{"N"}, Sequence[i, i, 1, Length[roots0]]}], Join[{{""}, Sequence["→", i, 1, f]}], Join[{{" x:"}, x(roots0)}], Join[{{" y:"}, y(roots0)}], Join[{{"f1*10^-6"}, lf1_{Pr}2}], Join[{{"f2* 10^-6"}, lf2_{Pr}2}]}, "vr") → Text2
  54. Textfield(v_i) → InputBox2
  55. Textfield(t) → InputBox10