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Copy file name to clipboardExpand all lines: docs/src/developerguide.md
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@@ -77,11 +77,11 @@ in a final step.
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All terms of all sequences have the same type. Currently this is the
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type fmpz as provided by the Nemo library.
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Sequences supports the use of notation using unicode characters, especially the
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traditional notation used in number theory. For example we define
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IntegerSequences supports the use of notation using unicode characters, especially the traditional notation used in number theory. For example we define
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```
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τ(n) = Nemo.sigma(n, 0)
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μ(n) = Nemo.moebiusmu(n)
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V006171(n) = EulerTransform(τ)(n)
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```
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We also support new notations like the proposal from Knuth, Graham and
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Patashnik in Concrete Mathematics:
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For example ``⊥(n, ϕ(n))`` indicates if there is just one group of order ``n``.
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But this is not only a concise mathematical formula, this is also valid Julia
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code (defined in Sequences). The predicate gives rise to the sequence of cyclic
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numbers, A003277 in the OEIS.
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code (defined in IntegerSequences). The predicate gives rise to the sequence of cyclic numbers, A003277 in the OEIS.
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Similarly possible definitions of some sequences (not necessarily efficient ones
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in the computational sense) are
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In the OEIS, on the other hand, a sequence is an enumeration, a set with an index function where the first index (called offset o) is specified. With this we arrive at this picture:
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``a_o, b_{o+1}, c_{o+2}, d_{o+3}, ...``
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``a_o, a_{o+1}, a_{o+2}, a_{o+3}, ...``
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In this view a list (representing the initial segment of the sequence)
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takes the place of the iteration.
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``[ a_{o}, b_{o+1}, c_{o+2}, ..., z_{o+n-1} ]``
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``[ a_{o}, a_{o+1}, a_{o+2}, ..., a_{o+n-1} ]``
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In contrast in our setup the concept of offset and indexing does not occur at all but is transferred to the interpretation: only the application decides about indexing and offset. In practice our setup avoiding the use of an offset turns out
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