Mathematica code

\(\DeclareMathOperator{\RE}{Re} \DeclareMathOperator{\IM}{Im} \DeclareMathOperator{\ess}{ess} \DeclareMathOperator{\intr}{int} \DeclareMathOperator{\dist}{dist} \DeclareMathOperator{\dom}{dom} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\span}{span} \DeclareMathOperator{\null}{null} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\col}{col} \DeclareMathOperator{\row}{row} \DeclareMathOperator{\proj}{proj} \DeclareMathOperator\re{\mathrm {Re~}} \DeclareMathOperator\im{\mathrm {Im~}} \newcommand\dd{\mathrm d} \newcommand{\eps}{\varepsilon} \newcommand{\To}{\longrightarrow} \newcommand{\hilbert}{\mathcal{H}} \newcommand{\s}{\mathcal{S}_2} \newcommand{\A}{\mathcal{A}} \newcommand\h{\mathcal{H}} \newcommand{\J}{\mathcal{J}} \newcommand{\M}{\mathcal{M}} \newcommand{\F}{\mathbb{F}} \newcommand{\N}{\mathcal{N}} \newcommand{\T}{\mathbb{T}} \newcommand{\W}{\mathcal{W}} \newcommand{\X}{\mathcal{X}} \newcommand{\D}{\mathbb{D}} \newcommand{\C}{\mathbb{C}} \newcommand{\BOP}{\mathbf{B}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\BH}{\mathbf{B}(\mathcal{H})} \newcommand{\KH}{\mathcal{K}(\mathcal{H})} \newcommand{\pick}{\mathcal{P}_2} \newcommand{\schur}{\mathcal{S}_2} \newcommand{\R}{\mathbb{R}} \newcommand{\Complex}{\mathbb{C}} \newcommand{\Field}{\mathbb{F}} \newcommand{\RPlus}{\Real^{+}} \newcommand{\Polar}{\mathcal{P}_{\s}} \newcommand{\Poly}{\mathcal{P}(E)} \newcommand{\EssD}{\mathcal{D}} \newcommand{\Lop}{\mathcal{L}} \newcommand{\cc}[1]{\overline{#1}} \newcommand{\abs}[1]{\left\vert#1\right\vert} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\seq}[1]{\left\lt#1\right>} \newcommand{\norm}[1]{\left\Vert#1\right\Vert} \newcommand{\essnorm}[1]{\norm{#1}_{\ess}} \newcommand{\tr}{\operatorname{tr}} \newcommand{\ran}[1]{\operatorname{ran}#1} \newcommand{\nt}{\stackrel{\mathrm {nt}}{\to}} \newcommand{\pnt}{\xrightarrow{pnt}} \newcommand{\ip}[2]{\left\langle #1, #2 \right\rangle} \newcommand{\ad}{^\ast} \newcommand{\inv}{^{-1}} \newcommand{\adinv}{^{\ast -1}} \newcommand{\invad}{^{-1 \ast}} \newcommand\Pick{\mathcal P} \newcommand\Ha{\mathbb{H}} \newcommand{\HH}{\Ha\times\Ha} \newcommand\Htau{\mathbb{H}(\tau)} \newcommand{\vp}{\varphi} \newcommand{\ph}{\varphi} \newcommand\al{\alpha} \newcommand\ga{\gamma} \newcommand\de{\delta} \newcommand\ep{\varepsilon} \newcommand\la{\lambda} \newcommand\up{\upsilon} \newcommand\si{\sigma} \newcommand\beq{\begin{equation}} \newcommand\ds{\displaystyle} \newcommand\eeq{\end{equation}} \newcommand\df{\stackrel{\rm def}{=}} \newcommand\ii{\mathrm i} \newcommand{\vectwo}[2] { \begin{pmatrix} #1 \\ #2 \end{pmatrix} } \newcommand{\vecthree}[3] { \begin{pmatrix} #1 \\ #2 \\ #3 \end{pmatrix} } \newcommand\blue{\color{blue}} \newcommand\black{\color{black}} \newcommand\red{\color{red}} \newcommand\nn{\nonumber} \newcommand\bbm{\begin{bmatrix}} \newcommand\ebm{\end{bmatrix}} \newcommand\bpm{\begin{pmatrix}} \newcommand\epm{\end{pmatrix}} \numberwithin{equation}{section} \newcommand\nin{\noindent} \newcommand{\nCr}[2]{\,_{#1}C_{#2}} \newcommand{\vec}[1]{{\bf #1}} \newcommand{\ps}{\displaystyle \sum_{n=0}^\infty a_n x^n} \newcommand{\psg}{\displaystyle \sum_{n=0}^\infty b_n x^n} \newcommand{\hz}{\,\mathrm{Hz}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Section 2 Mathematica code

The notebooks below contain code that produces the examples from the manuscript, as well as notebooks to produce the examples above. (right-click and "save as").

examples.nb contains computations that produce the examples covered in the manuscript, as well as interesting extensions.
risps_from_graphs.nb contains a method for producing new RISPs from the Nevanlinna representation for analytic self-maps of the upper half plane in several variables. See Agler, Tully-Doyle, Young , Pascoe, and Bickel, Pascoe, Sola for more on Nevanlinna representations and RIFs.
qalpha_test.nb contains code to work with the polynomial qa.