Please help me find a simple (geometric?) problem
For an example for some research I'm working on, I need to think of a problem - it can be anything, but a simple (possibly geometric) problem would be ideal - where the problem can be formulated as a number of inputs, say I_1, ..., I_n, and we are interested in several properties of the problem (outputs O_1, ..., O_m) that can be calculated from the inputs in some way.
*edit*
The important thing is that we need to have at least two outputs, say X1 and X2, and the set of inputs determining X1, say J1, and the set of inputs determining X2, say J2, have the property that J1 != J2, J1 not subset J2, and J2 not subset J1. They can intersect, but I'd like each to contain elements not in the other.
I have a few ideas, but none of them are fantastic. If there's an easily understood geometric problem that captures this behaviour nicely, that would be truly awesome :D.
Thanks, all!
A small example: polynomials over a field F, say f = a_n x^n + a_{n-1}x^{n-1} + ... + a_1 x + a_0
Inputs: a_0, ..., a_n
Output 1: derivative of f, depends on a_1, ..., a_n
Output 2: y-intercept of f, depends on a_0
(I would ideally like something more interesting than this, where there's at least one more output and some of the input dependency sets intersect.)
*edit*
The important thing is that we need to have at least two outputs, say X1 and X2, and the set of inputs determining X1, say J1, and the set of inputs determining X2, say J2, have the property that J1 != J2, J1 not subset J2, and J2 not subset J1. They can intersect, but I'd like each to contain elements not in the other.
I have a few ideas, but none of them are fantastic. If there's an easily understood geometric problem that captures this behaviour nicely, that would be truly awesome :D.
Thanks, all!
A small example: polynomials over a field F, say f = a_n x^n + a_{n-1}x^{n-1} + ... + a_1 x + a_0
Inputs: a_0, ..., a_n
Output 1: derivative of f, depends on a_1, ..., a_n
Output 2: y-intercept of f, depends on a_0
(I would ideally like something more interesting than this, where there's at least one more output and some of the input dependency sets intersect.)