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at_lat_ea/ (libat_lat_ea.a) is a library for computation in atomic lattice ordered effect algebras. Each such algebra is a union of blocks (atomic MV-effect algebras). Each block is specified by the list of atoms (atom_id(s)) and by the list of orders of these atoms. If all orders are 1, it provides computation in orthomodular lattices. *MV_Block* is a class that contains `number of atoms`, the list of atom_ids, the list of corresponding orders. Example: MV_Block b{3, {1,2,3}, {2, 3, 5}}; - b represents atomic MV-effect algebra with atoms `1`, `2`, `3` with orders 2, 3, 5, respectively, i.e., `1`(2), `2`(3), `3`(5). *Lattice_EA* is a class that specify a list (std::vector) of MV_Block(s) Examples: Lattice_EA l{b}; - l is a atomic lattice effect algebra consisting of a single block Lattice_EA l2{{2, {1,2}, {3, 4}}, {3, {2,3,4}, {4, 1, 1}}; - l2 contains two blocks, one with two atoms `1`(3), `2`(4) and other with `2`(4), `3`(1), `4`(1). *Lattice_EA_ops* is a class that take Lattice_EA specification and provides basic operations on it. Examples of usage are in lattice_ea_tests.cpp file. Example: Lattice_EA_ops lo{l2}; get_size() - provides number of elements in lo. Each element is specified in Lattice_EA class as a pair (b, e), where b is block index (from 0) and e is index of an element in block b. In Lattice_EA_ops each element is specified just by an index (int). Operations provided: *Before accessing any operation generate_ops() method must be called.* order(e1, e2) - returns 1 if e1 <= e2, otherwise it returns 0 inf(e1, e2) - returns infimum of e1 and e2, if infimum does not exists it returns -1 - e1 ^ e2 sup(e1, e2) - returns supremum of e1 and e2, if supremum does not exists it returns -1 - e1 v e2 oplus(e1, e2) - return e1 + e2, if it does not exists, returns -1 orthosupplement(e) - returns e' impl(e1, e2) - returns e1' + (e1 ^ e2)
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Atomic lattice effect algebras computation
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