# smackcrane

 1d awarded Nice Answer Mar 10 awarded Popular Question Feb 25 awarded Popular Question Jun 12 awarded Yearling Jun 12 awarded Yearling Jun 9 awarded Yearling May 16 accepted Extracting numbers from LaTeX code in Perl May 15 comment Extracting numbers from LaTeX code in Perl@perreal I'm running through the second dimension of the array in the outer loop, so that should be the length of that dimension. Perhaps that's not idiomatic, it's been a while since I've used Perl. May 15 asked Extracting numbers from LaTeX code in Perl Feb 2 awarded Nice Question Dec 24 answered prove $\lceil{x}\rceil=-\lfloor-x\rfloor$ Dec 15 answered Different equivalence relations of the set $\{a,b\}$ Dec 14 answered Expectation of a uniform point chosen out of a triangle with vertices $(0,0), (1,0), (0,2)$ Dec 12 answered There exist an infinite subset $S\subseteq\mathbb{R}^3$ such that any three vectors in $S$ are linearly independent. Dec 10 answered Calculating the dimension of a vector space in 2 different ways Dec 2 accepted Show that $\mathbb{Z}[\theta]$ (where $\theta = (1 + \sqrt{19}i)/2$) is a principal ideal domain. Nov 30 answered Show that $\mathbb{Z}[\theta]$ (where $\theta = (1 + \sqrt{19}i)/2$) is a principal ideal domain. Nov 30 revised Show that $\mathbb{Z}[\theta]$ (where $\theta = (1 + \sqrt{19}i)/2$) is a principal ideal domain.problem partly solved Nov 29 comment Calculating the Odds of Victory in RiskI agree! I wrote a Risk simulation a few years ago, and I believe this was the method I used to calculate winning probabilities in battles. Nov 29 comment Show that $\mathbb{Z}[\theta]$ (where $\theta = (1 + \sqrt{19}i)/2$) is a principal ideal domain.$\pm \theta$ is certainly good enough: as you probably saw, the point of saying $N(2a/b - \theta - m) < 1$ is simply that $N(b)N(2a/b - \theta - m) = N(2a - \theta b - mb) < N(b)$ contradicts $b$'s minimality.