|Bill Allombert on Wed, 15 Feb 2012 16:09:59 +0100|
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Hello PARI developers, I noticed the complex AGM function in PARI do not always return the so-called 'optimal' AGM. However this is documented: ??agm ... In the case of complex or negative numbers, the principal square root is always chosen. ... So I am not sure whether this should be fixed. However, do we have a proof of that PARI agm never diverges to zero ? Example of bad case are: agm(1,-.00001) which gives -0.0403257332 - 0.00327376459*I. but the optimal AGM is 0.114955789 + 0.0279973724*I Cheers, Bill.