Arrow diagrams on spherical curves and computations

On the Algebra of Arrow Diagrams

A descent method for explicit computations on curves

‎It is shown that the knowledge of a surjective morphism $Xto Y$ of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve ‎with period lattice $(1,tau)$‎, ‎the period matrix for the Jacobian of a family of genus-$2$ curves‎ ‎complementing the classi...

Semantics of Simple Arrow Diagrams

Arrows illustrate a large variety of semantics in diagrams. An automated interpretation of arrows would be highly desirable in pen-based interfaces. This paper formalizes the structural patterns of arrows, and identifies three structural properties that contribute to the interpretation of arrows: (1) the assignment of components to three slots, (2) the semantic types of the components, and (3) ...

Structure and Semantics of Arrow Diagrams

Arrows are major components of diagrams, where they are typically used to facilitate the communication of spatial and temporal knowledge. An automated interpretation of arrow diagrams would be highly desirable in pen-based interfaces. This paper develops a method for deducing possible interpretations of arrow diagrams, which is composed of a uni-directional arrow symbol and one or more componen...

Arrow Diagrams and Lie Bialgebras - Program

SetAttributes@Diag, OrderlessD; Place@8ar<, 8i_, j_<D := 8Diag@ar@i, jDD, Diag@ar@j, iDD<; Place@8ar, objs__<, 8i_, rest__<D := Flatten@Table@ Outer@Join, Place@8ar<, 8i, 8rest<@@kDD<D, Place@8objs<, Delete@8rest<, kDD D, 8k, Length@8rest<D< DD; Place@8R6T<, 8i_, j_, k_<D := Permutations@8i, j, k<D . 8i1_, j1_, k1_< ¦ Diag@R6T@i1, j1, k1DD; Place@8R6T, objs__<, 8i_, rest__<D := Flatten@Table@ ...