Changes between Version 42 and Version 44 of Ticket #17601


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Timestamp:
09/22/15 14:15:28 (4 years ago)
Author:
dkrenn
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  • Ticket #17601

    • Property Dependencies changed from #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
  • Ticket #17601 – Description

    v42 v44  
    1 We intend to implement asymptotic expressions in Sage. We would like to do computations with simple expressions such as
     1We intend to implement asymptotic expansions in SageMath. We would like to do computations with simple expansions such as
    22
    33n^2^ + n^3/2^ + O(n^1/2^),
    44
    5 but also with expressions such as
     5but also with expansions such as
    66
    772^n^ * n + O(n*log(n))
    88
    9 or even multivariate expressions such as
     9or even multivariate expansions such as
    1010
    11113*k/n + O(k^2^ / n^2^) with |k| <= n^(1/2)^.
    1212
    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 O-constants shall also be supported.
     13Of course, O(n) - O(n) = O(n) must hold and we want to perform various arithmetic operations with these asymptotic expansions. Eventually, specified O-constants shall also be supported.
    1414
    1515-------
     
    2525    * #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.
    2626    * #18930: Factory for user-friendly generation of growth groups
    27     * #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 big-Oh 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 expression.
    29     * #17716 (!AsymptoticRing and !AsymptoticExpression): 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 big-Oh 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.
    3030
    3131* 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)
    3433        * #18223: cartesian products with orders
    3534        * #18586: passing on parameters and extra_category for cartesian products
     35    * #19028: More growth group implementations: exponential growth groups.
    3636
    37 * Extending the functionality of the !AsymptoticRing and !AsymptoticExpression
    38     * #19068: Implement Division for asymptotic Expressions.
    39     * #19094: Implement higher-order operations like `exp` and `log` for asymptotic expressions.
     37* Extending the functionality of the !AsymptoticRing and !AsymptoticExpansion
    4038    * #19048: `AsymptoticRing.an_element()`
    4139        * #19047: `QQ.some_elements()`
     40    * #19068: Implement Division for asymptotic expansions.
    4241    * #19073: categorial constructions, pushout and coercions (extended) for asymptotic ring and growth groups
    4342        * #18182: pushout construction and finding common parents for/including cartesian products
    4443        * #19079: !ConstructionFunctor: remove `__str__`
     44    * #19094: Implement higher-order operations like `exp` and `log` for asymptotic expansions.
    4545    * #19083: !AsymptoticRing: cleanup, some improvements, documentation.
    4646
     
    5050        * growth groups with asymptotic at a non-infinity point
    5151    * other
    52         * Deal with comparison for asymptotic expressions.
     52        * Deal with comparison for asymptotic expansions.
    5353        * Check and improve the performance of computations in the !AsymptoticRing.
    5454        * Implementation of more types of asymptotic terms (little-oh terms, omega-terms, variations of big-Oh terms ...)