Changes between Version 17 and Version 18 of Ticket #17601


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Timestamp:
06/18/15 11:51:14 (4 years ago)
Author:
behackl
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  • Ticket #17601

    • Property Keywords gsoc15 added
  • Ticket #17601 – Description

    v17 v18  
    1616
    1717The 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  !AsymptoticGrowthElement::
    20   hold _one_ term, e.g. n^2^ or k/n or n*log(n). This can compare, multiply etc.,
    21   but has **no** coefficient. Here, only the order of magnitude shall be managed.
    2218
    23  !AsymptoticTerm::
     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::
    2423
    2524  holds one !AsymptoticGrowthElement, plus information on the coefficient or that it is an O-term etc.
    2625
    27  !AsymptoticExpression::
     26 !AsymptoticExpression:: 
    2827
    2928  represents the sum of several !AsymptoticTerms.
    30 
    3129
    3230The 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.
     
    3735!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.
    3836
    39 Related Tickets:
    40     #17600 (!AsmyptoticGrowthElement): elements which handle the asymptotic growth.
    41     #17715 (!AsymptoticTerm): "building blocks" for asymptotic expressions, growth + additional information (OTerm, !ExactTerm, ...).
    42     #17716 (!AsymptoticExpression): sum of multiple asymptotic terms.
    43     #17693 (!MutablePoset): data structure for storing asymptotic terms within an asymptotic expression.
    44     #18587: cartesian products of growth groups
     37-------
    4538
    46 Other Dependencies:
    47     #18182: pushout construction and finding common parents for/including cartesian products
    48     #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)
    49     #18223: cartesian products with orders
    50     #18586: passing on parameters and extra_category
     39**Roadmap**:
     40
     41
     42* Implementing a minimal working example
     43    * #17600 (!AsymptoticGrowthElement): elements which handle the asymptotic growth. Concretely: !MonomialGrowthElement, implementation for powers.
     44    * #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 big-Oh terms and exact terms.
     45    * #17693 (!MutablePoset): data structure for storing asymptotic terms within an asymptotic expression.
     46    * #17716 (!AsymptoticExpression): sum of asymptotic terms.
     47
     48* Extending the functionality of !AsymptoticExpression
     49    * Implement Division for asymptotic Expressions
     50    * Implement higher-order operations like `exp` and `log` for asymptotic expressions.
     51    * Improve the user interface: extend the conversion from the symbolic ring such that more than just monomials can be converted.
     52    * Implement comparison for asymptotic expressions.
     53
     54* Extending the functionality of growth groups
     55    * More growth group implementations: logarithmic and exponential growth groups.
     56    * #18587: cartesian products for growth groups (allowing the construction of more complicated univariate as well as multivariate asymptotic expressions)
     57        * #18223: cartesian products with orders
     58        * #18586: passing on parameters and extra_category for cartesian products
     59        * implement dependencies like |k| <= n^1/2^ for different growth group variables.
     60
     61* Further plans
     62    * growth groups with asymptotic at a non-infinity point
     63    * Implementation of more types of asymptotic terms (little-oh terms, omega-terms, variations of big-Oh terms ...)
     64
     65
     66* Additional Dependencies:
     67    * #18182: pushout construction and finding common parents for/including cartesian products
     68    * #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)