Initial commit

1 files changed, 97 insertions, 0 deletions

diff --git a/macros.tex b/macros.tex
new file mode 100755
index 0000000..fe65124
--- /dev/null
+++ b/macros.tex
@@ -0,0 +1,97 @@
+\definecolor{darkgreen}{rgb}{0,.5,0}
+
+\renewcommand{\t}{\mathsf T}
+\newcommand{\conv}{*}
+\newcommand{\adj}[1]{#1^*}
+\newcommand{\bigo}[1]{\mathcal O(#1)}
+\newcommand{\commut}[2]{[#1, #2]}
+\newcommand{\correlation}[1]{\left< #1 \right>}
+\newcommand{\dimensionless}[1]{\mathrm{#1}}
+\newcommand{\dsurf}{\mathrm d \sigma}
+\newcommand{\dummy}{{\,\cdot\,}}
+% \newcommand{\dummy}{\mathord{\color{black!33}\bullet}}%
+\newcommand{\eip}[2]{\left\langle\left\langle{#1,#2}\right\rangle\right\rangle}
+\newcommand{\enorm}[1]{|||#1|||}
+\newcommand{\expect}[0]{\mathbf{E}}
+\newcommand{\var}[0]{\mathbf{V}}
+\newcommand{\filtration}[0]{\mathcal}
+\newcommand{\grad}[0]{\nabla}
+\newcommand{\hermitef}[1]{\mathbf #1}
+\newcommand{\hermite}[1]{\mathbf{#1}}
+\newcommand{\iip}[2]{(\!(#1, #2)\!)}
+\newcommand{\inter}{\, \cap \,}
+\newcommand{\kron}[2]{\delta_{#1,#2}}
+\newcommand{\laplacian}{\Delta}
+\newcommand{\littleo}[1]{o(#1)}
+\newcommand{\lploc}[2]{L_{loc}^{#1}\left(#2\right)}
+\newcommand{\mat}[1]{\boldsymbol{\mathbf #1}}
+\newcommand{\nat}[0]{\mathbf{N}}
+\newcommand{\op}[0]{\mathcal}
+\newcommand{\operator}[0]{\mathcal}
+\newcommand{\orth}[1]{#1^\perp}
+\newcommand{\poly}[1]{\mathbf{P}_{#1}}
+\newcommand{\proba}[0]{\mathbf{P}}
+% \newcommand{\proj}[2]{\pi\left(#1,#2\right)}
+\newcommand{\proj}[2]{\Pi_d #1}
+\newcommand{\real}[0]{\mathbf{R}}
+\newcommand{\red}[1]{\textcolor{darkred}{#1}}
+\newcommand{\schwartz}[1]{S (#1)}
+\newcommand{\seq}[4]{{\left\{#1_{#2}\right\}}_{#2=#3}^{#4}}
+\newcommand{\smooth}[1]{C^\infty(#1)}
+\newcommand{\test}[1]{C^\infty_c (#1)}
+\newcommand{\torus}[0]{\mathbf{T}}
+\newcommand{\vect}[1]{\boldsymbol{\mathbf #1}}
+\renewcommand{\det}[1]{\left| #1 \right|}
+\renewcommand{\d}[0]{\mathrm{d}}
+% \renewcommand{\alert}[1]{\textcolor{darkgreen}{#1}}
+
+% Cahn-Hilliard
+\newcommand{\energyA}[0]{\frac{1}{\varepsilon}}
+\newcommand{\energyB}[0]{\varepsilon}
+
+\DeclareMathOperator{\trace}{tr}
+\DeclareMathOperator{\e}{e}
+\DeclareMathOperator{\support}{supp}
+\DeclareMathOperator{\sign}{sign}
+\DeclareMathOperator{\id}{id}
+\DeclareMathOperator{\Span}{span}
+\DeclareMathOperator{\gateau}{Grad}
+\DeclareMathOperator*{\argmin}{arg\,min}
+\DeclareMathOperator*{\argmax}{arg\,max}
+
+\DeclareDocumentCommand\abs{s m} {\IfBooleanTF{#1}{|#2|}{\left|#2\right|}}
+\DeclareDocumentCommand\cont{o m o} {C\IfNoValueF{#1}{^{#1}}(#2\IfNoValueF{#3}{;#3})}
+\DeclareDocumentCommand\contc{o m o} {C_c\IfNoValueF{#1}{^{#1}}(#2\IfNoValueF{#3}{;#3})}
+\DeclareDocumentCommand\sobolev{m m o} {H^{#1}(#2 \IfNoValueF{#3}{,#3})}
+\DeclareDocumentCommand\lp{m m o} {L^{#1}\left(#2 \IfNoValueF{#3}{,#3}\right)}
+\DeclareDocumentCommand\norm{s m o} {\IfBooleanTF{#1}{\|#2\|}{\left\|#2\right\|}\IfNoValueF{#3}{_{#3}}}
+\DeclareDocumentCommand\seminorm{s m o} {\IfBooleanTF{#1}{\|#2\|}{\left\|#2\right\|}\IfNoValueF{#3}{_{#3}}}
+\DeclareDocumentCommand\ip{m m o o} {\left\langle{#1,#2}\right\rangle\IfNoValueF{#3}{_{#3 \IfNoValueF{#4}{,#4}}}}
+\DeclareDocumentCommand\dup{m m o} {\left\langle{#1,#2}\right\rangle\IfNoValueF{#3}{_{#3', #3}}}
+\DeclareDocumentCommand\gaussian{O{0} O{I}} {g_{#1, #2}}
+
+% Derivative
+\makeatletter
+\DeclareDocumentCommand \derivative{s m o m}{%
+    \def\@der{\IfBooleanTF{#1}{\mathrm{d}}{\partial}}
+    \def\@default{%
+        \mathchoice{%
+                \frac{%
+                    \@der\ifnum\pdfstrcmp{#2}{1}=0\else^{#2}\fi {\IfNoValueTF{#3}{}{#3}}
+                }{%
+                    \@for\@token:={#4}\do{\@der \@token}
+                }
+            } {%
+                \@for\@token:={#4}\do{\@der_\@token} \IfNoValueTF{#3}{}{#3}
+            } {} {}
+    }
+    \IfBooleanTF{#1}{\IfNoValueTF{#3}{\@default}{%
+                #3%
+                \ifnum\pdfstrcmp{#2}{1}=0'\else%
+                \ifnum\pdfstrcmp{#2}{2}=0''\else%
+                \ifnum\pdfstrcmp{#2}{3}=0'''\else%
+                \ifnum\pdfstrcmp{#2}{4}=0^{(iv)}\else^{(#2)}\fi\fi\fi\fi
+            }
+        }{\@default}
+}
+\makeatother