X-Git-Url: http://mj.ucw.cz/gitweb/?a=blobdiff_plain;f=notation.tex;h=f2c84dd1ec0bf08c0817028aa0e55ef6d2ded9e1;hb=b66b5869a0ccfd85ada5d012fe70bfc0119bda11;hp=bbf7a534dbffe9efe73238de1c65bacfe5a87d6d;hpb=58b3a55a24e6bcab408bd048c2221397df2c744d;p=saga.git diff --git a/notation.tex b/notation.tex index bbf7a53..f2c84dd 100644 --- a/notation.tex +++ b/notation.tex @@ -10,6 +10,11 @@ \n{$\bb R$}{the set of all real numbers} \n{$\bb N$}{the set of all natural numbers, including 0} \n{${\bb N}^+$}{the set of all positive integers} +\n{$\O(g)$}{asymptotic~$O$: $f=\O(g)$ iff $\exists c>0: f(n)\le g(n)$ for all~$n\ge n_0$} +\n{$\Omega(g)$}{asymptotic~$\Omega$: $f=\Omega(g)$ iff $\exists c>0: f(n)\ge g(n)$ for all~$n\ge n_0$} +\n{$\Theta(g)$}{asymptotic~$\Theta$: $f=\Theta(g)$ iff $f=\O(g)$ and $f=\Omega(g)$} +\n{$\widetilde\O(g)$}{$f=\widetilde\O(g)$ iff $f=\O(g\cdot\log^{\O(1)} g)$} +\n{$\poly(n)$}{$f=\poly(n)$ iff $f=\O(n^c)$ for some $c$} \n{$T[u,v]$}{the path in a tree~$T$ joining vertices $u$ and $v$ \[heavy]} \n{$T[e]$}{the path in a tree~$T$ joining the endpoints of an~edge~$e$ \[heavy]} \n{$A\symdiff B$}{symetric difference of sets: $(A\setminus B) \cup (B\setminus A)$}