Changes between Version 42 and Version 44 of Ticket #17601
 Timestamp:
 09/22/15 14:15:28 (5 years ago)
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Ticket #17601

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Dependencies
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#17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110
to#17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269

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Ticket #17601 – Description
v42 v44 1 We intend to implement asymptotic exp ressions in Sage. We would like to do computations with simple expressions such as1 We intend to implement asymptotic expansions in SageMath. We would like to do computations with simple expansions such as 2 2 3 3 n^2^ + n^3/2^ + O(n^1/2^), 4 4 5 but also with exp ressions such as5 but also with expansions such as 6 6 7 7 2^n^ * n + O(n*log(n)) 8 8 9 or even multivariate exp ressions such as9 or even multivariate expansions such as 10 10 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 and we want to perform various arithmetic operations with these asymptotic exp ressions. Eventually, specified Oconstants shall also be supported.13 Of course, O(n)  O(n) = O(n) must hold and we want to perform various arithmetic operations with these asymptotic expansions. Eventually, specified Oconstants shall also be supported. 14 14 15 15  … … 25 25 * #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. 26 26 * #18930: Factory for userfriendly generation of growth groups 27 * #17715 (!AsymptoticTerm): a summand for asymptotic exp ressions. 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`).28 * #17693 (!MutablePoset): data structure for storing asymptotic terms within an asymptotic exp ression.29 * #17716 (!AsymptoticRing and !AsymptoticExp ression): sum of asymptotic terms.27 * #17715 (!AsymptoticTerm): a summand for asymptotic expansions. 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`). 28 * #17693 (!MutablePoset): data structure for storing asymptotic terms within an asymptotic expansions. 29 * #17716 (!AsymptoticRing and !AsymptoticExpansion): sum of asymptotic terms. 30 30 31 31 * Extending the functionality of growth groups 32 * #19028: More growth group implementations: exponential growth groups. 33 * #18587: cartesian products for growth groups (allowing the construction of more complicated univariate as well as multivariate asymptotic expressions) 32 * #18587: cartesian products for growth groups (allowing the construction of more complicated univariate as well as multivariate asymptotic expansions) 34 33 * #18223: cartesian products with orders 35 34 * #18586: passing on parameters and extra_category for cartesian products 35 * #19028: More growth group implementations: exponential growth groups. 36 36 37 * Extending the functionality of the !AsymptoticRing and !AsymptoticExpression 38 * #19068: Implement Division for asymptotic Expressions. 39 * #19094: Implement higherorder operations like `exp` and `log` for asymptotic expressions. 37 * Extending the functionality of the !AsymptoticRing and !AsymptoticExpansion 40 38 * #19048: `AsymptoticRing.an_element()` 41 39 * #19047: `QQ.some_elements()` 40 * #19068: Implement Division for asymptotic expansions. 42 41 * #19073: categorial constructions, pushout and coercions (extended) for asymptotic ring and growth groups 43 42 * #18182: pushout construction and finding common parents for/including cartesian products 44 43 * #19079: !ConstructionFunctor: remove `__str__` 44 * #19094: Implement higherorder operations like `exp` and `log` for asymptotic expansions. 45 45 * #19083: !AsymptoticRing: cleanup, some improvements, documentation. 46 46 … … 50 50 * growth groups with asymptotic at a noninfinity point 51 51 * other 52 * Deal with comparison for asymptotic exp ressions.52 * Deal with comparison for asymptotic expansions. 53 53 * Check and improve the performance of computations in the !AsymptoticRing. 54 54 * Implementation of more types of asymptotic terms (littleoh terms, omegaterms, variations of bigOh terms ...)