algebraically

English

Etymology

From algebraic +‎ -ally, or alternatively algebraical +‎ -ly.

Pronunciation

• (US) IPA^(key): /ˌæl.d͡ʒɪˈbɹeɪ.ɪk.li/, /ˌæl.d͡ʒɪˈbɹeɪ.ɪ.kə.li/

• Audio (Southern England):

  (file)

Adverb

algebraically (comparative more algebraically, superlative most algebraically)

1. Using algebra; in terms of algebra.
   • 1981, John M. Ziman, Puzzles, Problems and Enigmas: Occasional Pieces on the Human Aspects of Science, Cambridge University Press, →ISBN, page 51:

     In principle, we should not then have made any approximation at all; it is a rule of pure mathematics, hallowed by centuries of usage, and justified by the mysteries known to undergraduates as 'epsilontics', that a convergent series is as good as a simple finite algebraic expression for a solution — which is just as well, because almost every expression that appears in any formula in physics, such as a cosine, or a logarithm, is itself only definable algebraically as the sum of an infinite series.

   • 2000, Alain M. Robert, A Course in p-adic Analysis, Springer, page 127:

     It turns out that the algebraic closure ${𝐐}_p^{\mathrm{a}}$ is not complete, so we shall consider its completion ${𝐂}_p$: This field turns out to be algebraically closed and is a natural domain for the study of "analytic functions."

Derived terms

• algebraically closed
• algebraically independent
• nonalgebraically

Related terms

• algebraicize

Translations

using algebra

• Catalan: algèbricament (ca), algebraicament (ca)
• Dutch: algebraïsch (nl)
• French: algébriquement (fr)
• Galician: alxebricamente
• Italian: algebricamente (it)
• Polish: algebraicznie (pl)
• Portuguese: algebricamente
• Spanish: algebraicamente