\def\ep{{\varepsilon}} \def\th{{\theta}}   % ~ < > `
% \mathring{K} mette il pallino su K
\def\ui{{\mathbf i}} \def\ZZ{{\mathbb Z}} \def\la{{\lambda}}
\def\f#1#2{\frac{#1}{#2}}                           %%%\def\rank{\hbox{rank}}
\def\exp#1{e^{#1}}
\def\cb#1#2{  {\footnotesize \big( \!\!\bi{c} #1 \\ #2 \ei \!\!\big) } }
\def\ba#1{\left[\begin{array}{#1}}  \def\ea{\end{array}\right]}
\def\then{{\Rightarrow}} \def\fa{{\forall}}
\def\al{{\alpha}} \def\be{{\beta}} \def\de{{\delta}} \def\si{{\sigma}}
\def\na{{\nabla}} \def\De{{\Delta}} \def\vs{{\varsigma}}

\def\vphi{{\varphi}} \def\Ga{{\Gamma}} \def\Om{{\Omega}}
\def\ga{{\gamma}} \def\om{{\omega}}
\def\W{{\omega}} \def\E{{\lambda}}
\def\La{{\Lambda}} \def\la{{\lambda}}

\def\um{\frac{1}{2}}
\def\bi#1{\begin{array}{#1}}  \def\ei{\end{array}}
\def\beq{\begin{equation}} \def\eeq{\end{equation}}
\def\o{\overline}
\def\rII{\sqrt{2}}  \def\rIII{\sqrt{3}} \def\rV{\sqrt{5}}
\def\f#1#2{\frac{#1}{#2}}

\def\R#1{\sqrt{#1}} \def\sq{{\square}}

% puntini in salita (dots going up):
\def\addots{\mathinner{\mkern1mu\raise1pt\vbox{\kern7pt\hbox{.}}%
\mkern2mu
    \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}}

\def\tg{\hbox{\,tg\,}} \def\tr{\hbox{\,tr\,}}
\def\DP{\partial} \def\and{\hbox{and}}  \def\pd{\hbox{p.d.}}
\def\Span{\hbox{\,Span\,}}                     %%%\def\sign{\hbox{\,sign\,}}
\def\deg{\hbox{\,deg\,}}
\def\diag{\hbox{\,diag\,}} \def\supp{\hbox{\,supp\,}} \def\cas{\hbox{\,cas\,}}
\def\diam{\hbox{\,diam\,}} \def\sp#1{s({#1})} \def\sd{\hbox{\,sd\,}}
\def\es{{\emptyset}} \def\mod{\hbox{\,mod\,}}

\def\v{{\mathbf v}} \def\y{{\mathbf y}} \def\x{{\mathbf x}}
\def\z{{\mathbf z}} \def\b{{\mathbf b}} \def\e{{\mathbf e}}
\def\a{{\mathbf a}} \def\r{{\mathbf r}} \def\q{{\mathbf q}}
\def\s{{\mathbf s}} \def\vf{{\mathbf f}} \def\g{{\mathbf g}}
\def\w{{\mathbf w}} \def\u{{\mathbf u}}  \def\p{{\mathbf p}}
\def\c{{\mathbf c}} \def\d{{\mathbf d}} \def\h{{\mathbf h}}
\def\n{{\mathbf n}} \def\vo{{\mathbf o}}

\def\vn{{\mathbf 0}}  \def\ui{{\mathbf i}}

\def\A{{\mathcal A}} \def\L{{\mathcal L}} \def\M{{\mathcal M}}
\def\K{{\mathcal K}} \def\G{{\mathcal G}} \def\C{{\mathcal C}}
\def\S{{\mathcal S}} \def\D{{\mathcal D}} \def\I{{\mathcal I}}
\def\N{{\mathcal N}} \def\V{{\mathcal V}} \def\F{{\mathcal F}}
\def\Rc{{\mathcal R}} \def\W{{\mathcal W}} \def\H{{\mathcal H}}

\def\hh{{\mathbb h}} \def\KK{{\mathbb K}} \def\NN{{\mathbb N}}
\def\ZZ{{\mathbb Z}} \def\PP{{\mathbb P}} \def\VV{{\mathbb V}} \def\QQ{{\mathbb Q}}
\def\CC{{\mathbb C}} \def\CCn{{\CC^n}} \def\CCnn{{\CC^{n\times n}}}
\def\RR{{\mathbb R}} \def\RRn{{\RR^n}} \def\RRnn{{\RR^{n\times n}}} 