Might mean (unverified): Mathematical study of polynomial equations.
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We found 2 dictionaries that define the word algebraic analysis:

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  1. Algebraic analysis: Wikipedia, the Free Encyclopedia
  2. algebraic analysis: Wiktionary

Definitions from Wiktionary (algebraic analysis)

noun:  Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems.
noun:  (algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).

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