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I have an implicitly defined system (say $x^2 + y^2 + z^2 - 1 = 0$). I want to find an expression that will describe the points satisfying the earlier equation when projected onto a lower dimension. For example, consider the sphere discussed earlier. When the points on it are projected onto x-y plane, they can be described as $x^2+y^2-1 \leq 0$.

Is there a general method to get the latter expression (irrespective of the number of variables)?

Many Thanks!

Jean Marie
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Curious Iitian
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    Your issue can be cast into the more general context of shadows (or more exactly shadow's boundaries) issued from a light point source, which implies finding the tangent cone of light, here in the case where the light source is at infinity on the $z$ axis.. – Jean Marie Aug 23 '19 at 06:45
  • Can you suggest some beginner's reading on this topic? – Curious Iitian Aug 26 '19 at 05:26

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