Ancillary files for "Graded transcendental functions: an application to four-point amplitudes with one off-shell leg"

<p>We provide ancillary files to "Graded transcendental functions: an application to four-point amplitudes with one off-shell leg".</p> <p>All attached files are in Mathematica format. See also appendix C of the manuscript for details on the ancillary files.&nbsp;</p> <ul> <li><strong>Families.zip:&nbsp;</strong><br>For each integral family, we provide in a single file <em>familyname.m</em> the list of propagators, a canonical basis and the corresponding differential&nbsp;equations, and a regularised boundary vector at the point (x, y) = (0, 0).&nbsp;<br>Files contain a list of Mathematica replacement rules in the format {prop["familyname"]-&gt; {...}, basis["familyname"]-&gt; {...}, boundaries["familyname"]-&gt; {....}, DE["familyname"]-&gt; {...}}.&nbsp;</li> <li><strong>BoundariesDemo.zip</strong>: An executable notebook implementing the fixing of boundary&nbsp;constants using the method for a two-loop example.</li> <li><strong>TridentFunctions.zip</strong>: For each relevant canonical integral and kinematic crossing listed in <em>basis_labels.m</em>, we provide a map to the trident functions in the form of a sparse rational array of size 13812 &times; 1282 in <em>mapping_positions.m</em> and <em>mapping_values.m</em>. We also provide the UT Laurent expansions of the trident functions in terms of 42258 iterated integrals and transcendental constants in <em>sb_labels.m</em>, again as a sparse array in <em>expansion_positions.m</em> and <em>expansion_values.m</em>.</li> <li><strong>FormFactor.zip</strong>: We provide the three-loop finite remainders R(3) and E(3) of the N = 4&nbsp;sYM form factor in terms of Chen iterated integrals and MPLs.</li> <li><strong>Hjet.zip</strong>: The three independent helicity coefficients for the decay of a H boson to three partons at three loops are given in terms of iterated integrals and in a manifestly real MPL representation. In particular, we provide the part of the finite remainders containing new letters, with rational coefficients evaluated at x = 3/13, y = 11/17.&nbsp;</li> </ul>