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Author: shiroeExecutions: 158
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Although the form of the equation after the Chirn House transformation may vary depending on the book or website,
here we will use the form X^3 + 3PX + 2Q = 0.
For the cube roots of a complex number, we use De Moivre’s theorem.
The program outputs approximate solutions x0, x1, and x2.
To verify the calculations and check the accuracy, the approximate solutions are substituted into the original cubic equation, and the results are displayed.
If the values are close to 0, it means a good approximation has been obtained.
here we will use the form X^3 + 3PX + 2Q = 0.
For the cube roots of a complex number, we use De Moivre’s theorem.
The program outputs approximate solutions x0, x1, and x2.
To verify the calculations and check the accuracy, the approximate solutions are substituted into the original cubic equation, and the results are displayed.
If the values are close to 0, it means a good approximation has been obtained.
| a | |
| b | |
| c | |
| d | |
| t | Chirn House Transformation |
| P | |
| Q | |
| u | Variable Conversion |
| v | Variable Conversion |
| x0 | Solution ① |
| x1 | Solution ② |
| x2 | Solution ③ |
| y0 | Verification: Value of f(x0) |
| y1 | Verification: Value of f(x1) |
| y2 | Verification: Value of f(x2) |
Approximate real numbers are not always output as real numbers.
Complex numbers (non-real numbers with a non-zero imaginary part) whose real and imaginary parts are close to the true values are also treated as approximate values here.
The results are derived from operations involving approximations of pi, double roots, inverse trigonometric functions, and trigonometric functions.
Display setting: 50 digits. The number of digits can be changed. Complex number calculation mode.
Complex numbers (non-real numbers with a non-zero imaginary part) whose real and imaginary parts are close to the true values are also treated as approximate values here.
The results are derived from operations involving approximations of pi, double roots, inverse trigonometric functions, and trigonometric functions.
Display setting: 50 digits. The number of digits can be changed. Complex number calculation mode.
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It is the formula for solving cubic equations.
It outputs intermediate results such as the Churnhouse variable and variable transformations.