vasu wrote :
Hi all
Suppose I have an positive integer parameter 't', and a polynomial
Delta(t) , which is a polynomial in 't' with coefficients being
integers. Assume we also know that Delta(t) > 0.
There is another polynomial with integer coefficients , say F(t).
Consider an expression
[x(t)]^3 = F(t) + i * sqrt ( D(t) )
( i being the square root of -1)
Given a concrete value for t, I could always find the cube-roots. But
is there a method in Sage, which gives me x(t) as a function of t.
In case the question is ill-posed, I'd also be happy if there are
methods which give approximations to the cube roots in terms of t
You get an algebraic expression with Z^(1/3)
[and don't forget Z^(1/3)*exp(2*i*pi/3) and Z^(1/3)*exp(-2*i*pi/3).
Or look at a polar form r = sqrt(F(t)^2+D(t)) and
a=atan2(sqrt(D(t),F(t)) [=atan(y,x) in z=x+i*y]
So r^(1/3) [a positive real] * exp(i*a/3) is an other method to get this
radix.
(...expression...).n() gives the numerical approximation of the expression.
I'm not sure I help you a lot...
F.
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