Polar Representation Ambiquity
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% create the definition symbol
\def\bydef{\stackrel{\Delta}{=}}
%\def\circconv{\otimes}
\def\circconv{\circledast}
\newcommand{\qed}{\mbox{ } \Box}
\newcommand{\infint}{\int_{-\infty}^{\infty}}
% z transform
\newcommand{\ztp}{ ~~ \mathop{\mathcal{Z}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\iztp}{ ~~ \mathop{\mathcal{Z}^{-1}}\limits_{\longleftrightarrow} ~~ }
% fourier transform pair
\newcommand{\ftp}{ ~~ \mathop{\mathcal{F}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\iftp}{ ~~ \mathop{\mathcal{F}^{-1}}\limits_{\longleftrightarrow} ~~ }
% laplace transform
\newcommand{\ltp}{ ~~ \mathop{\mathcal{L}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\iltp}{ ~~ \mathop{\mathcal{L}^{-1}}\limits_{\longleftrightarrow} ~~ }
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\newcommand{\iftrans}[1]{ \mathcal{F}^{-1} \left\{#1\right\} }
\newcommand{\ztrans}[1]{ \mathcal{Z} \left\{#1\right\} }
\newcommand{\iztrans}[1]{ \mathcal{Z}^{-1} \left\{#1\right\} }
\newcommand{\ltrans}[1]{ \mathcal{L} \left\{#1\right\} }
\newcommand{\iltrans}[1]{ \mathcal{L}^{-1} \left\{#1\right\} }
% coordinate vector relative to a basis (linear algebra)
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% change of coordinate matrix (linear algebra)
\newcommand{\cocm}[2]{ \mathop{P}\limits_{#2 \leftarrow #1} }
% Transformed vector set
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% sum transformed vector set
\newcommand{\tsetcsum}[4]{{#1}_1#2(\vec{#3}_1) + {#1}_2#2(\vec{#3}_2) + \cdots + {#1}_{#4}#2(\vec{#3}_{#4})}
\newcommand{\tsetcsumall}[4]{#2\lr{{#1}_1\vec{#3}_1 + {#1}_2\vec{#3}_2 + \cdots + {#1}_{#4}\vec{#3}_{#4}}}
\newcommand{\cvecsum}[3]{{#1}_1\vec{#2}_1 + {#1}_2\vec{#2}_2 + \cdots + {#1}_{#3}\vec{#2}_{#3}}
% function def
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% vector set
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% absolute value
\newcommand{\abs}[1]{\left| #1 \right|}
% vector norm
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% trans
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% evaluate integral
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% slist
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% vectors
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% real
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% imaginary
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\newcommand{\Q}{\mathbb{Q}}
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\newcommand{\I}{\mathbb{I}}
\newcommand{\Th}[1]{\mathop\mathrm{Th(#1)}}
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%Category Names:
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<!-- For the set of reals and integers -->
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Puts them in standard font face and creates an index entry.
arg: The term being defined.
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<!-- For bold terms to be index, but defined elsewhere
Puts them in bold face and creates an index entry.
arg: The term being defined. -->
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<!-- For set names.
Puts them in italics. In math mode, yields decent spacing.
arg: The name of the set. -->
\newcommand{\set}[1]{\textit{#1}}
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