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Comp."],"abstract":"<p>\n                    The Coleman integral is a\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -adic line integral that plays a key role in computing several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman integration on curves, using the algorithms of the second author [Math. Comp. 85 (2016), pp.\u00a0961\u2013981] and [Finite Fields Appl. 45 (2019), pp.\u00a0301\u2013322] to compute the action of Frobenius on\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -adic cohomology. We present a collection of examples computed with our implementation. This includes integrals on a genus 55 curve, where other methods do not currently seem practical.\n                  <\/p>","DOI":"10.1090\/mcom\/3542","type":"journal-article","created":{"date-parts":[[2020,3,25]],"date-time":"2020-03-25T12:10:17Z","timestamp":1585138217000},"page":"2965-2984","source":"Crossref","is-referenced-by-count":14,"title":["Explicit Coleman integration for curves"],"prefix":"10.1090","volume":"89","author":[{"given":"Jennifer","family":"Balakrishnan","sequence":"first","affiliation":[]},{"given":"Jan","family":"Tuitman","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2020,5,22]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"41","DOI":"10.2140\/obs.2013.1.41","article-title":"Iterated Coleman integration for hyperelliptic curves","author":"Balakrishnan, Jennifer S.","year":"2013","ISBN":"https:\/\/id.crossref.org\/isbn\/9781935107019"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1112\/S1461157015000029","article-title":"Coleman integration for even-degree models of hyperelliptic curves","volume":"18","author":"Balakrishnan, Jennifer S.","year":"2015","journal-title":"LMS J. 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