Changes between Version 23 and Version 24 of Ticket #17601
 Timestamp:
 08/18/15 17:35:40 (4 years ago)
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Ticket #17601 – Description
v23 v24 11 11 3*k/n + O(k^2^ / n^2^) with k <= n^(1/2)^. 12 12 13 Of course, O(n)  O(n) = O(n) must hold .13 Of course, O(n)  O(n) = O(n) must hold and we want to perform various arithmetic operations with these asymptotic expressions. Eventually, specified Oconstants shall also be supported. 14 14 15 Eventually, specified Oconstants shall also be supported. 16 17 The current plan is to implement the following classes (plus derivatives for more concrete situations). For simplicity, the corresponding parents are not listed here. 18 19 20 !AsymptoticGrowthElement:: hold _one_ term, e.g. n^2^ or k/n or n*log(n). This can compare, multiply etc., but has **no** coefficient. Here, only the order of magnitude shall be managed. 21 22 !AsymptoticTerm:: 23 24 holds one !AsymptoticGrowthElement, plus information on the coefficient or that it is an Oterm etc. 25 26 !AsymptoticExpression:: 27 28 represents the sum of several !AsymptoticTerms. 29 30 The idea is to override !AsymptoticGrowthElement to obtain specific behaviour (as mentioned in our wishlist) because it seems unlikely to be able to handle everything in one class. 31 For starters, there will be an !GrowthGroupPowerElement. 32 33 !AsymptoticTerm is expected to be more general; it might be necessary to override it for the case of specified Oconstants. 34 35 !AsymptoticExpression, however, can be general enough to deal with all cases; here, the sum, the product, the exponential function, etc. are implemented in a generic setting. 36 15 See #17716 for more examples. 37 16  38 17 … … 41 20 42 21 * Implementing a minimal working example 43 * #17600 (!AsymptoticGrowthElement): elements which handle the asymptotic growth. Concretely: !MonomialGrowthElement, implementation for powers.22 * #17600 (!AsymptoticGrowthElement): elements which handle the asymptotic growth. Such an element holds, e.g. n^2^ or k/n or n*log(n). This can compare, multiply etc., but has **no** coefficient; the order of magnitude is managed here. Concretely for this ticket: !MonomialGrowthElement, implementation for powers. 44 23 * #18930: Factory for userfriendly generation of growth groups 45 * #17715 (!AsymptoticTerm): "building blocks" for asymptotic expressions, they contain the growth and additional information on the type of the term. For starters, there will be bigOh terms and exact terms.24 * #17715 (!AsymptoticTerm): a summand for asymptotic expressions. They contain the growth and additional information on the type of the summand. For starters, there will be bigOh terms (e.g. `O(n)` and exact terms (e.g. `3*n^2`). 46 25 * #17693 (!MutablePoset): data structure for storing asymptotic terms within an asymptotic expression. 47 26 * #17716 (!AsymptoticRing and !AsymptoticExpression): sum of asymptotic terms. … … 55 34 * Improve the performance of computations in the !AsymptoticRing. 56 35 * #19048: `AsymptoticRing.an_element()` 36 * #19047: `QQ.some_elements()` 57 37 58 38 * Extending the functionality of growth groups … … 71 51 * #18182: pushout construction and finding common parents for/including cartesian products 72 52 * #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130) 73 * #19047: `QQ.some_elements()`