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SUMMARY:Two signature-based variants of Buchberger's algorithm over princi
pal ideal domains
DTSTART;VALUE=DATE-TIME:20210330T083000Z
DTEND;VALUE=DATE-TIME:20210330T093000Z
DTSTAMP;VALUE=DATE-TIME:20210508T044440Z
UID:indico-event-6607@indico.math.cnrs.fr
DESCRIPTION:Since their introduction for algorithm F5 in 2002\, signature
Gröbner\nbases have brought large improvements to the performances of Gr
öbner\nbases algorithms for polynomial systems over fields. Furthermore\,
they\ncontain additional data which can be used\, for example\, to comput
e the\nmodule of syzygies of an ideal or to compute coefficients in terms
of\nthe input generators.\n\nIn this talk\, we present two variants of Buc
hberger's algorithm\ncomputing signature Gröbner bases over principal ide
al domains. The\nfirst one is adapted from Kandri-Rody and Kapur's algorit
hm (1988)\,\nwhereas the second one uses the ideas developed in the algori
thms by Pan\n(1989) and Lichtblau (2012). The fact that the algorithms hav
e a\nstructure similar to Buchberger's allows to examine more powerful\nsi
gnature criteria than in previous signature-based algorithms over\nrings\,
and we will explain how the differences in constructions between\nthe two
algorithms lead to different criteria being applicable.\n\n(Joint work wi
th Maria Francis)\n\nhttps://indico.math.cnrs.fr/event/6607/
LOCATION:https://bbb.unilim.fr/b/vac-m6r-7dv
URL:https://indico.math.cnrs.fr/event/6607/
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