Opened 5 years ago

Closed 5 years ago

#20044 closed enhancement (fixed)

calculate asymptotic expansions to some asymptotic expansions exponents directly

Reported by: dkrenn Owned by:
Priority: major Milestone: sage-7.1
Component: asymptotic expansions Keywords:
Cc: behackl, cheuberg Merged in:
Authors: Daniel Krenn Reviewers: Clemens Heuberger
Report Upstream: N/A Work issues:
Branch: 29bffe0 (Commits) Commit: 29bffe011e7e034e4807714e6a4a4918b439449f
Dependencies: #20043 Stopgaps:



sage: (1+1/n^2)^n

and related be calculated directly.

Change History (6)

comment:1 Changed 5 years ago by dkrenn

  • Branch set to u/dkrenn/asy/pow-var

comment:2 Changed 5 years ago by git

  • Commit set to c6ca928f170c82030dae101ef400f3df95410a8d

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

98591d6Trac #20044: NoConvergenceError
69c090cTrac #20044: extend __pow_number__ and test for convergence
7ed3541Trac #20044: add shortcuts for exponents 0 and 1 in __pow__
3f7a661Trac #20044: use new extension in __pow__
c6ca928Merge branch 'u/dkrenn/asy/one-times-zero' of git:// into t/20044/asy/pow-var

comment:3 Changed 5 years ago by dkrenn

  • Dependencies set to #20043
  • Status changed from new to needs_review

comment:4 Changed 5 years ago by cheuberg

  • Branch changed from u/dkrenn/asy/pow-var to u/cheuberg/asy/pow-var

comment:5 Changed 5 years ago by cheuberg

  • Commit changed from c6ca928f170c82030dae101ef400f3df95410a8d to 29bffe011e7e034e4807714e6a4a4918b439449f
  • Reviewers set to Clemens Heuberger
  • Status changed from needs_review to positive_review

Proving mathematical correctness is not completely trivial: if one rewrites it as exp( exponent*log(1+x)), this is no problem. And expanding these exponential function and logarithms leads to some monomials in x and exponent. The error is O((exponent + exponent^K)*x^K) if K is the number of exact summands in the binomial series. Both of these error terms actually occur in the binomial expansion, so everything is fine.

Added a minor commit (one comma removed); the rest is fine.

New commits:

29bffe0Trac #20044: punctuation

comment:6 Changed 5 years ago by vbraun

  • Branch changed from u/cheuberg/asy/pow-var to 29bffe011e7e034e4807714e6a4a4918b439449f
  • Resolution set to fixed
  • Status changed from positive_review to closed
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