UserManual | (ÆüËܸì)
This module provides functions which solve roots of equation and congruence.
Input of function f is the following:
f := a_0 + a_1 * x + ... + a_n * x**n => f = [a_0, a_1, ... ,a_n]
n is a rational integer, p is a prime number.
Return the solution a*x + b = 0, where f=[b,a].
Return the solution a*x = b (mod n), where c=[a,b].
Return the roots of a * x**2 + b * x + c = 0, where f=[c,b,a].
If the same values are returned, then the values are multiple roots.
Return the solutions of a*x**2 + b*x + c = 0 mod p, where f=[c,b,a].
If the same values are returned, then the values are multiple roots.
Return the roots of a * x**3 + b * x**2 + c * x + d = 0, where f=[d,c,b,a].
If the same values are returned, then the values are multiple roots.
Return the solutions of a * x**3 + b * x**2 + c * x + d = 0 mod p, where f=[d,c,b,a].
If the same values are returned, then the values are multiple roots.
Return a approximation root of f, where coeffcients of f is the real number.
Initial inputs as a initial number of Newton, Repeat inputs as the number of steps.
Default of Initial is 1, Repeat is 100.
Remark : There is a case which this method returns False output. For example, f(x) = x**2 + 1
Return the approximation roots, where coefficients of f is the complex number.
Repeat is the number of this method's steps, NewtonInitial is a Initial number of Newton Method which use in this method.
If this method returns Error in Newton Method, Then please change the NewtonInitial's value.
Default of NewtonInitial is 1, Repeat is 200.
Remark : If f has multiple root, maybe return Error.