I've noticed a lot of cases in which this rule seems to apply, provided of course that the polynomial equations are linearly independent (there wasn't enough space to specify this in the title). And I can't think of any situation where it doesn't work. Is it always true?
2026-04-29 17:19:24.1777483164
Does a system of $k$ polynomial equations in $n$ variables always represent an $(n-k)$-dimensional manifold embedded in an $n$-dimensional space?
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