{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,16]],"date-time":"2024-03-16T13:49:33Z","timestamp":1710596973740},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"DFG","award":["373111162"],"award-info":[{"award-number":["373111162"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p> We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in Singular, which allow to make a comparison on the basis of numerous examples. We focus on a local variant, where centers are not required to be chosen globally. Moreover, we do not necessarily demand that centers are contained in the singular locus. Despite these restrictions, the techniques are connected to the computation of [Formula: see text]-adic integral whose data is given by finitely many binomials. <\/jats:p>","DOI":"10.1142\/s0218196723500108","type":"journal-article","created":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T03:45:07Z","timestamp":1666928707000},"page":"161-195","source":"Crossref","is-referenced-by-count":1,"title":["Algorithmic local monomialization of a binomial: A comparison of different approaches"],"prefix":"10.1142","volume":"33","author":[{"given":"Sabrina Alexandra","family":"Gaube","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Carl von Ossietzky Universit\u00e4t Oldenburg, 26111 Oldenburg, Germany"}]},{"given":"Bernd","family":"Schober","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Carl von Ossietzky Universit\u00e4t Oldenburg, 26111 Oldenburg, Germany"}]}],"member":"219","published-online":{"date-parts":[[2022,12,9]]},"reference":[{"issue":"4","key":"S0218196723500108BIB001","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1007\/s13398-019-00672-x","volume":"113","author":"Cossart V.","year":"2019","journal-title":"Rev. R. Acad. Cienc. Exactas F\u00eds. Nat. Ser. A Mat. RACSAM"},{"issue":"2","key":"S0218196723500108BIB002","doi-asserted-by":"crossref","first-page":"217","DOI":"10.4171\/PRIMS\/56-2-1","volume":"56","author":"Cossart V.","year":"2020","journal-title":"Publ. Res. Inst. Math. Sci."},{"issue":"330","key":"S0218196723500108BIB004","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1090\/mcom\/3624","volume":"90","author":"Fr\u00fchbis-Kr\u00fcger A.","year":"2021","journal-title":"Math. Comp."},{"key":"S0218196723500108BIB006","series-title":"Lecture Notes in Mathematics","volume-title":"Desingularization of Excellent Surfaces","volume":"1101","author":"Hironaka H.","year":"1984"},{"issue":"12","key":"S0218196723500108BIB007","doi-asserted-by":"crossref","first-page":"4737","DOI":"10.1090\/S0002-9947-03-03247-1","volume":"355","author":"Hu Y.","year":"2003","journal-title":"Trans. Amer. Math. Soc."},{"issue":"2","key":"S0218196723500108BIB008","first-page":"535","volume":"58","author":"Li L.","year":"2009","journal-title":"Michigan Math. J."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196723500108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T07:34:27Z","timestamp":1675668867000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196723500108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,9]]},"references-count":6,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1142\/S0218196723500108"],"URL":"https:\/\/doi.org\/10.1142\/s0218196723500108","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,9]]}}}