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From a formal language perspective, we prove that the set of solutions to a system of equations forms an EDT0L language, with respect to a natural normal form. Looking at growth, we show that the growth series of the language of solutions is rational. Furthermore, considering the set of solutions as a set of tuples of group elements, we show that it has rational relative growth series with respect to any finite generating set. <\/jats:p>","DOI":"10.1142\/s0218196722500205","type":"journal-article","created":{"date-parts":[[2022,2,17]],"date-time":"2022-02-17T06:17:15Z","timestamp":1645078635000},"page":"411-442","source":"Crossref","is-referenced-by-count":7,"title":["Equations in virtually abelian groups: Languages and growth"],"prefix":"10.1142","volume":"32","author":[{"given":"Alex","family":"Evetts","sequence":"first","affiliation":[{"name":"Heilbronn Institute for Mathematical Research and Department of Mathematics, The University of Manchester, Manchester, M13 9PL, UK"}]},{"given":"Alex","family":"Levine","sequence":"additional","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK"}]}],"member":"219","published-online":{"date-parts":[[2022,2,16]]},"reference":[{"key":"S0218196722500205BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(77)90308-4"},{"key":"S0218196722500205BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01394026"},{"key":"S0218196722500205BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2020.12.003"},{"key":"S0218196722500205BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72023-8"},{"key":"S0218196722500205BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196716500363"},{"key":"S0218196722500205BIB006","series-title":"LIPIcs. 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