Opened 4 years ago
Closed 4 years ago
#20044 closed enhancement (fixed)
calculate asymptotic expansions to some asymptotic expansions exponents directly
Reported by:  dkrenn  Owned by:  

Priority:  major  Milestone:  sage7.1 
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: 
Description
Make
sage: (1+1/n^2)^n
and related be calculated directly.
Change History (6)
comment:1 Changed 4 years ago by
 Branch set to u/dkrenn/asy/powvar
comment:2 Changed 4 years ago by
 Commit set to c6ca928f170c82030dae101ef400f3df95410a8d
comment:3 Changed 4 years ago by
 Dependencies set to #20043
 Status changed from new to needs_review
comment:4 Changed 4 years ago by
 Branch changed from u/dkrenn/asy/powvar to u/cheuberg/asy/powvar
comment:5 Changed 4 years ago by
 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:
29bffe0  Trac #20044: punctuation

comment:6 Changed 4 years ago by
 Branch changed from u/cheuberg/asy/powvar to 29bffe011e7e034e4807714e6a4a4918b439449f
 Resolution set to fixed
 Status changed from positive_review to closed
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Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
Trac #20044: NoConvergenceError
Trac #20044: extend __pow_number__ and test for convergence
Trac #20044: add shortcuts for exponents 0 and 1 in __pow__
Trac #20044: use new extension in __pow__
Merge branch 'u/dkrenn/asy/onetimeszero' of git://trac.sagemath.org/sage into t/20044/asy/powvar