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Base X Machine for Polynomial Addition

Base X Machine for Polynomial Addition
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2020-04-14 00:20
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This example demonstrates polynomial addition in a Base X machine. Key mathematical concepts include polynomials, base conversion, and addition operations. Using GeoGebra commands such as Join, Polygon, and IndexOf, the process of polynomial addition is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Join({x31N, x32N}) → rx3N
  2. Join({x31P, x32P}) → rx3P
  3. Join({x11N, x12N}) → rx1N
  4. Join({x11P, x12P}) → rx1P
  5. Join({x21N, x22N}) → rx2N
  6. Join({x21P, x22P}) → rx2P
  7. Polygon(I_3, J_3, K_3, L_3) → X31, a14, a16, a32, a29
  8. Polygon(L_3, M_3, N_3, K_3) → X21, a1, a27, a28, a3
  9. Polygon(M_3, P_3, O_3, N_3) → X11, a5, a25, a26, a7
  10. Polygon(P_3, Q_3, R_3, O_3) → X01, a9, a17, a24, a10
  11. Polygon(S_3, V_3, U_3, T_3) → X32, a23, a20, a21, a22
  12. Polygon(V_3, W_3, Z_3, U_3) → X22, a11, a19, a18, a12
  13. Polygon(W_3, B_4, A_4, Z_3) → X12, a13, a4, a2, a15
  14. Polygon(B_4, C_4, D_4, A_4) → X02, a31, a6, a8, a30
  15. Polygon(I_3, L_3, U_3, T_3) → Rx3, r11, r10, r9, r7
  16. Polygon(L_3, M_3, Z_3, U_3) → Rx2, r5, r4, r2, r3
  17. Polygon(M_3, P_3, A_4, Z_3) → Rx1, r6, r1, r14, r12
  18. Polygon(P_3, Q_3, D_4, A_4) → Rx0, r16, r15, r13, r8
  19. IndexOf(false, FP) → tmpI
  20. IndexOf(false, FN1) → NDtmpI
  21. First(x31P) → TAtmpI
  22. If(NDtmpI ≟ NDtmpI, true, false) → NDH
  23. If(Length[x31P] - Length[x31N] ≟ Element[Coef1, IndexOf["x^3", Order1]], true, false) → Bx31
  24. If(Length[x21P] - Length[x21N] ≟ Element[Coef1, IndexOf["x^2", Order1]], true, false) → Bx21
  25. If(Length[x11P] - Length[x11N] ≟ Element[Coef1, IndexOf["x", Order1]], true, false) → Bx11
  26. If(Length[x01P] - Length[x01N] ≟ Element[Coef1, IndexOf["", Order1]], true, false) → Bx01
  27. Shuffle({1, 2, 3, 4}) → OrderS, {2, 1, 3, 4}
  28. Random(-5, 5) → L23Co01
  29. Random(-5, 5) → L23Co02
  30. Random(-5, 5) → L23Co32
  31. Random(-5, 5) → L23Co31
  32. Random(-5, 5) → L23Co22
  33. Random(-5, 5) → L23Co21
  34. Random(-5, 5) → L23Co12
  35. Random(-5, 5) → L23Co11
  36. If(Length[x32P] - Length[x32N] ≟ Element[Coef2, IndexOf["x^3", Order2]], true, false) → Bx32
  37. If(Length[x22P] - Length[x22N] ≟ Element[Coef2, IndexOf["x^2", Order2]], true, false) → Bx22
  38. If(Length[x12P] - Length[x12N] ≟ Element[Coef2, IndexOf["x", Order2]], true, false) → Bx12
  39. If(Length[x02P] - Length[x02N] ≟ Element[Coef2, IndexOf["", Order2]], true, false) → Bx02
  40. Join({x01N, x02N}) → rx0N
  41. Join({x01P, x02P}) → rx0P
  42. If(TAPP ≟ true ∧ TANN ≟ true, true, false) → TAPN
  43. First(rx0P) → tmpP
  44. First(rx0N) → tmpN
  45. If(Element[tmpP, 1] ≟ Element[tmpP, 1], true, false) → tP
  46. If(Element[tmpN, 1] ≟ Element[tmpN, 1], true, false) → tN
  47. Textfield(Br3) → Ir3
  48. Textfield(Br2) → Ir2
  49. Textfield(Br1) → Ir1
  50. Textfield(Br0) → Ir0
  51. Random(0, 5) → L1Co01
  52. Random(0, 5) → L1Co02
  53. Random(0, 5) → L1Co11
  54. Random(0, 5) → L1Co12
  55. Random(0, 5) → L1Co21
  56. Random(0, 5) → L1Co22
  57. Random(0, 5) → L1Co31
  58. Random(0, 5) → L1Co32
  59. Random(1, 2) → SignL1
  60. Polygon(A, B, C, D) → Background, a, b, c, d
  61. IndexOf(false, FP) → PDtmpI
  62. If(PDtmpI ≟ PDtmpI, true, false) → PDH
  63. If(SelectedIndex[Level] ≟ 3 ∧ Stage ≟ 1, true, false) → BL3
  64. If(SelectedIndex[Level] ≟ 2 ∧ Stage ≟ 1, true, false) → BL2
  65. If(SelectedIndex[Level] ≟ 1 ∧ Stage ≟ 1, true, false) → BL1
  66. If(SelectedIndex[Level] ≟ 3, true, false) → BL3N
  67. If(SelectedIndex[Level] ≟ 2, true, false) → BL2N
  68. If(SelectedIndex[Level] ≟ 1, true, false) → BL1N
  69. If(x12P ≠ {}, true, false) → TAPH
  70. If(x12N ≠ {}, true, false) → TANH