{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:15:45Z","timestamp":1776849345269,"version":"3.51.2"},"reference-count":25,"publisher":"American Mathematical Society (AMS)","issue":"316","license":[{"start":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T00:00:00Z","timestamp":1559174400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100005736","name":"Universit\u00c3\u00a9 Paris Diderot","doi-asserted-by":"publisher","award":["57212102"],"award-info":[{"award-number":["57212102"]}],"id":[{"id":"10.13039\/501100005736","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006537","name":"Campus France","doi-asserted-by":"publisher","award":["57212102"],"award-info":[{"award-number":["57212102"]}],"id":[{"id":"10.13039\/501100006537","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001655","name":"Deutscher Akademischer Austauschdienst","doi-asserted-by":"publisher","award":["57212102"],"award-info":[{"award-number":["57212102"]}],"id":[{"id":"10.13039\/501100001655","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"y Superscript m Baseline equals f left-parenthesis x right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>y<\/mml:mi>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>f<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">y^m=f(x)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . It relies on rigorous numerical integration of differentials between Weierstrass points, which is done using Gauss method if the curve is hyperelliptic (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m equals 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m=2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) or the Double-Exponential method. The algorithm is implemented and makes it possible to reach thousands of digits accuracy even on large genus curves.\n                  <\/p>","DOI":"10.1090\/mcom\/3351","type":"journal-article","created":{"date-parts":[[2017,12,27]],"date-time":"2017-12-27T09:20:03Z","timestamp":1514366403000},"page":"847-888","source":"Crossref","is-referenced-by-count":15,"title":["Computing period matrices and the Abel-Jacobi map of superelliptic curves"],"prefix":"10.1090","volume":"88","author":[{"given":"Pascal","family":"Molin","sequence":"first","affiliation":[]},{"given":"Christian","family":"Neurohr","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2018,5,30]]},"reference":[{"key":"1","series-title":"National Bureau of Standards Applied Mathematics Series, No. 55","volume-title":"Handbook of mathematical functions with formulas, graphs, and mathematical tables","author":"Abramowitz, Milton","year":"1964"},{"key":"2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1112\/S146115701600019X","article-title":"A database of genus-2 curves over the rational numbers","volume":"19","author":"Booker, Andrew R.","year":"2016","journal-title":"LMS J. 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