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CotangentSchubert :: fugacity

fugacity -- compute the fugacity of puzzles



To each puzzle is associated an element of the base field (cohomology/K-theory of a point), its so-called fugacity, in such a way that the sum of fugacities of puzzles with prescribed boundaries a, b, c, is equal to the coefficient of the expansion of the product of classes indexed by the strings a and b into the class class indexed by the string c. Here the classes are motivic Segre classes sClass if Generic=>true, Schubert classes schubertClass if Generic=>false. The options Ktheory, Equivariant, Generic are inherited from the puzzle by default, but they can be overridden.

fugacityTally processes a list of puzzles, and returns a hash table where to each string appearing at the bottom of a puzzle is associated the sum of fugacities of the corresponding puzzles.

fugacityVextor similarly processes a list of puzzles, and returns the result as a vector where each entry is the sum of fugacities of puzzles with a given bottom string. The ordering of strings is the same as the list returned by setupCotangent.

For the programmer

The object fugacity is a function closure.