Studies of Euler diagrams/transformations
These are pairs of functions in the same clan (NP equivalence class), so they can be expressed in terms of each other.
The clan numbers refer to the rational ordering. (Which will at some point be replaced by a better one.)
The transformation from one to the other is a signed permutation, which means that arguments are negated and permuted.
It can be just a set of negated places or just a permutation. (These cases are marked with N, P or NP respecitively.)
clan 84: dakota and tinora (NP)
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This Euler diagram has no symmetry. Therefore the transformation of one into the other is unique.
The transformation from right to left is , the inverse of the one shown above.
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clan 157: dagoro and darimi (NP)
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Dagoro is a gap variant of tinora (shown above on the right). These two functions do not have the same set of (relevant) arguments. But that is not a problem. The transformation from left to right is . It means the following:
The transformation from right to left is , the inverse of the one shown above.
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clan 109: tamino and niliko (NP)
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The diagrams in this EC are mirror symmetric.
That means that there are two transformations between each pair of functions. |
clan 203: dukeli and netuno (NP)
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Each function can be represented by two mirror symmetric Euler diagrams. Here both are shown for netuno. The transformation from the chosen diagram of dukeli to the one of netuno below is . Its inverse is . This whole NP equivalence class with 192 functions (represented by 384 diagrams) can be found in dukeli NP.
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clan 349: nagini and medusa (P)
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These diagrams have the symmetry of a rectangle, which can be flipped in four ways. The arguments are only permuted, but not negated. So only the colors change, but not the direction of the spikes. |
clan 15: potero and makoto (NP)
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Each function can be represented by two mirror symmetric Euler diagrams. Here both are shown for makoto. The transformation from the chosen diagram of potero to the one of makoto below is . Its inverse is . |
potero and potula (N)
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These two diagrams differ only in the orientation of border A. The self-inverse transformation between them is . |
potula and basori (P)
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The transformation between the two diagrams is
, which is self-inverse.
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clan 19: dobare and dobipi (N)
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Euler diagrams in this EC have 3-fold dihedral symmetry.
(This is obfuscated by the conventional representation on the right.) |
barita filtrates (P)
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bloatless alternatives (N)
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