[Python] Numpy Slicing problem: Possible way to reduce array size while retaining the...

I want to finding a general formula or algorithm to determine all possible values of `step` that satisfy the three conditions (boundary, equal spacing, and symmetry) when slicing an array with the same properties.

Let says I have an initial_array = np.linspace(-10, 10, 11)

[-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10]
​

I want to slice the array such that the reduced_array retains 3 condition:

1. Boundary condition. The minimum and maximum elements should remain unchanged.
2. Equal spacing property. Spacing between each elements should be constant.
3. Symmetry property. The whole array should have an symmetry around zero, whether or not the zero is included in the array.

One way to slice the initial_array is to set reduced_array=initial_array[::2], which get us

[-10, -6, -2, 2, 6, 10]
​

For initial_array = np.linspace(-10, 10, 11),

[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
​

I can slice it by setting reduced_array=initial_array[::2],

[-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10]
​

or reduced_array=initial_array[::4]

[-10, -6, -2, 2, 6, 10]
​

Right now, I am trying to find out, for an arbitrary size of array

#initial condition
max = 200
min = -max
size= 314
initial_array = np.linspace(min,max,size)

step= ? #unknown, to be solved
reduced_array = initial_array[::step]


Some pattern I observed is that for size of 11,21 and 31, value of step is the factor of 10,20 and 30 etc.

Clearly, step<=floor(size/2). Ultimately, I want to locate the reduced_array which does not include 0. One application for me is to create a high resolution linspace for calculation. Then, when doing visualization, I slice it down to a much smaller size for plotting. One example of wanting to exclude 0 from the reduced array is when 0 is a singularity point that cannot be visualized.

How many and how can I slice the array while keeping all 3 proposed conditions? Is there a way to formulate the problem mathematically?

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