User alexandre passos - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T17:00:44Z http://mathoverflow.net/feeds/user/7899 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/35567/zero-knowledge-proof-of-positivity/35574#35574 Answer by Alexandre Passos for Zero-knowledge proof of positivity Alexandre Passos 2010-08-14T11:37:41Z 2010-08-14T11:37:41Z <p>I don't understand why a positive x implies 0 &lt; x mod (p-1) &lt; (p-1)/2. Doesn't (for example) x = p-2 violate this property without necessarily being negative?</p> http://mathoverflow.net/questions/33432/projective-transformation-between-polygons/33450#33450 Answer by Alexandre Passos for Projective transformation between polygons. Alexandre Passos 2010-07-26T22:25:07Z 2010-07-26T22:25:07Z <p>A hacky way would be, enumerate the points of the two polygons (with adjacent points adjacent in the enumerations), as in $P_1 = [p_{1,1}, p_{1,2}, \ldots, p_{1,n}]$ and $P_2 = [p_{2,1}, \ldots, P_{2,n}]$, build N systems of linear equations, in the form $\forall i, \mathbf{T} p_{1,i} = p_{2,i+j}$ (indexed by $j$). There will be only N such systems, and if any one of them can be satistied (that is, it there is a $\mathbf{T}$ that takes all points $p_{1,i}$ into $p_{2,i+j}$ for some $j$) you have an answer.</p>