利用根的和与积构造新的三次方程

GeoGebra 命令及参数

1. Expand(g) → r
2. Coefficients(r) → l1
3. Denominator(m) → v
4. Denominator(l) → u
5. Denominator(k) → o
6. Denominator(j) → n
7. LCM({n, o, u, v}) → w
8. Root(f) → α, β, γ
9. FractionText(e) → text2
10. Expand(s) → h
11. Expand(t) → f_1
12. Simplify((y - q) / p) → g_1
13. Simplify(y - q) → h_1
14. If(b < 0, "" + b, "+" + b) → condb
15. If(c < 0, "" + c, "+" + c) → condc
16. If(d < 0, "" + d, "+" + d) → condd
17. If(b < 0, "-", "+") → fracb
18. If(c < 0, "-", "+") → fracc
19. Expand((y - q)^(3)) → p_1
20. Expand((y - q)^(2)) → q_1
21. Simplify(a / pcubed) → r_1
22. Simplify(absb / psquared) → s_1
23. Simplify(absc / p) → t_1
24. FractionText(r_1(0), false) → text9
25. FractionText(s_1(0), false) → text10
26. FractionText(t_1(0), false) → text11
27. Denominator(a / pcubed) → a_1
28. Denominator(b / psquared) → b_1
29. Denominator(c / p) → c_1
30. LCM({a_1, b_1, c_1}) → lcm
31. Coefficients(f_1) → l2
32. Expand((a * ((y - q) / p)^(3)) + (b * ((y - q) / p)^(2)) + (c * (y - q) / p) + d) → f_2
33. Expand((w * ((a * ((y - q) / p)^(3)) + (b * ((y - q) / p)^(2)) + (c * (y - q) / p) + d))) → g_2
34. If(q < 0, "" + q, "+" + q) → text12