1、Regarding the issue of conservatism 2、lie group mapping

[zhengnx0906]

When I test the following code：
x = Interval(-4,4)
f = Function("x", "cos(x)*cos(x)+sin(x)*sin(x)")
y = f.eval(x)
print(y)
I have obtained the following results：
([-2, 2])
So, for the sake of convenience in calculation, did we not consider the relationship between internal variables？

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I continued to test ContractorNetwork:
a = Interval(-4,4)
y = Interval(-6,6)
x = Interval(-6,6)
z = Interval(0,36)
cn = ContractorNetwork() # Creating a Contractor Network
ctc_add = CtcFunction(Function("x", "a", "cos(a)-x")) #x=cos(a)
ctc_add2 = CtcFunction(Function("y", "a", "sin(a)-y")) #y=sin(a)
ctc_add3 = CtcFunction(Function("x", "y", "z", "x * x+y * y-z")) #z=x^2+y^2
cn.add(ctc_add, [x, a]) # Adding the C+ contractor to the network,
cn.add(ctc_add2, [y, a]) # Adding the C+ contractor to the network
cn.add(ctc_add3, [x, y, z]) # Adding the C+ contractor to the network
cn.contract()
print(x)
print(z)
Obtained similar results：
[-1, 1]
[-2, 2]

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Now I am reproducing the following literature. There are still many questions about the mapping of three-dimensional Lie groups and Lie algebras. Can you provide me with some help？
Set inversion and box contraction on Lie groups using interval analysis Nicolas Merlinge
https://doi.org/10.1016/j.automatica.2024.111688