Opened 8 years ago
Closed 7 years ago
#16198 closed defect (fixed)
allow constant != 1 in log(power series)
Reported by:  rws  Owned by:  

Priority:  minor  Milestone:  sage7.0 
Component:  commutative algebra  Keywords:  log, function, series expansion 
Cc:  Merged in:  
Authors:  Ralf Stephan  Reviewers:  Volker Braun 
Report Upstream:  N/A  Work issues:  
Branch:  ee40e93 (Commits, GitHub, GitLab)  Commit:  ee40e93a8b09aa20721240e591c6cf4332abb06d 
Dependencies:  Stopgaps: 
Description (last modified by )
log(power series)
fails when the constant coefficient is not 1:
sage: R.<x> = PowerSeriesRing(RR) sage: log(2+x)  ArithmeticError Traceback (most recent call last) <ipythoninput449ca3295e0d6> in <module>() > 1 log(Integer(2)+x) /usr/local/src/sagegit/local/lib/python2.7/sitepackages/sage/functions/log.pyc in __call__(self, *args, **kwds) 311 if base is None: 312 if len(args) == 1: > 313 return GinacFunction.__call__(self, *args, **kwds) 314 # second argument is base 315 base = args[1] /usr/local/src/sagegit/local/lib/python2.7/sitepackages/sage/symbolic/function.so in sage.symbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.cpp:9120)() /usr/local/src/sagegit/local/lib/python2.7/sitepackages/sage/rings/power_series_ring_element.so in sage.rings.power_series_ring_element.PowerSeries.log (build/cythonized/sage/rings/power_series_ring_element.c:15894)() ArithmeticError: constant term of power series is not 1
Pari has no problems:
? log(2x) %1 = 0.69314718055994530941723212145817656807  1/2*x  1/8*x^2  1/24*x^3  1/64*x^4  1/160*x^5  1/384*x^6  1/896*x^7  1/2048*x^8  1/4608*x^9  1/10240*x^10  1/22528*x^11  1/49152*x^12  1/106496*x^13  1/229376*x^14  1/491520*x^15 + O(x^16)
Effectively the log of the constant is taken but this simply changes the base ring from whatever to SR if the constant is not equal to one.
Change History (12)
comment:1 Changed 8 years ago by
comment:2 followup: ↓ 7 Changed 8 years ago by
 Description modified (diff)
 Priority changed from major to minor
 Summary changed from replace default algorithm for log(power series) to allow constant <> 1 in log(power series)
So it looks like any constant from exp(n)
, n
in NN0
will leave this in PowerSeries(ZZ)
but anything else will make it necessary to rebase in PowerSeries(SR)
.
comment:3 Changed 8 years ago by
 Milestone changed from sage6.2 to sage6.3
comment:4 Changed 8 years ago by
 Milestone changed from sage6.3 to sage6.4
comment:5 Changed 8 years ago by
 Milestone changed from sage6.4 to sageduplicate/invalid/wontfix
 Status changed from new to needs_review
This was illconceived from the beginning, because only SR is a superset of the coefficients in the Pari result (floating point and rational). That's why Pari is questionable, even if it's convenient.
As I find it not useful to duplicate symbolics functionality in the power series ring, the best way to get such a power series is via SR and the newly available #16203:
sage: R.<x> = PowerSeriesRing(SR) sage: ex=(log(2y)).series(y,4); R(ex) log(2)  1/2*x  1/8*x^2  1/24*x^3 + O(x^4) sage: ex=(gamma(1y)).series(y,3); R(ex) 1 + euler_gamma*x + (1/2*euler_gamma^2 + 1/12*pi^2)*x^2 + O(x^3)
comment:6 Changed 8 years ago by
 Status changed from needs_review to positive_review
comment:7 in reply to: ↑ 2 Changed 8 years ago by
 Milestone changed from sageduplicate/invalid/wontfix to sage6.5
 Status changed from positive_review to needs_work
 Summary changed from allow constant <> 1 in log(power series) to allow constant != 1 in log(power series)
Replying to rws:
So it looks like any constant from
exp(n)
,n
inNN0
will leave this inPowerSeries(ZZ)
but anything else will make it necessary to rebase inPowerSeries(SR)
.
If the base ring is RR
, then log()
is perfectly defined for nonone constant terms, so that should certainly work.
comment:8 Changed 8 years ago by
 Description modified (diff)
comment:9 Changed 7 years ago by
 Branch set to u/rws/allow_constant____1_in_log_power_series_
comment:10 Changed 7 years ago by
 Commit set to ee40e93a8b09aa20721240e591c6cf4332abb06d
 Component changed from calculus to commutative algebra
 Milestone changed from sage6.5 to sage7.0
 Status changed from needs_work to needs_review
New commits:
ee40e93  16198: allow constant != 1 in log(power series)

comment:11 Changed 7 years ago by
 Reviewers set to Volker Braun
 Status changed from needs_review to positive_review
comment:12 Changed 7 years ago by
 Branch changed from u/rws/allow_constant____1_in_log_power_series_ to ee40e93a8b09aa20721240e591c6cf4332abb06d
 Resolution set to fixed
 Status changed from positive_review to closed
I don't think Ginac is actually involved. Take a look at the last piece of the traceback, which points to here. In particular, in sage/rings/power_series_ring_element.pyx,
So this is actually hardcoded in for some reason, referring eventually to
_solve_linear_de
which was factored out of this stuff a very long time ago.It could be worth asking around why/whether this is really necessary. I don't know that I want the above instead of
note the
log(2)
instead of an approximation.