Does math-fun quietly discard BCCs? I BCCed them this suggestion to Support@wolfram.com but it never distributed. I also BCCed my list of eavesdroppers, but I don't know if they got it. Then I re-sent it to rcs asking if he knew where it went. Maybe he's off on a Thanksgubble holiday. Anyway, comments (as always) welcome on the following: ---------- Forwarded message ---------- From: Bill Gosper <billgosper@gmail.com> Date: Tue, Nov 26, 2013 at 2:05 PM Subject: Re: [CASE:423927] GCD suggestions To: Wolfram Technical Support <support@wolfram.com> Hi again Jason! Below, I should have said: Likewise. GCD[0,foo] is |foo|. (If foo ϵ Reals.) If your developers are leery of GCD[1,π]→0, I think I can muster authoritative corroborators, if not corroborative literature. Motivation: The gcd of two real quantities is the largest quantity that goes into each a whole number of times. In[642]:= Convergents[π, 4] Out[642]= {3, 22/7, 333/106, 355/113} In[643]:= GCD[%, 1] Out[643]= {1, 1/7, 1/106, 1/113} The better the approximation, the smaller the GCD. There is no positive GCD[π,1], so it must be 0. This extension isn't likely to save work for anyone. But increasingly, people use Mathematica as a source of expertise and instruction. --Bill Gosper On Tue, Nov 26, 2013 at 11:55 AM, Wolfram Technical Support < support@wolfram.com> wrote:
Hello Bill Gosper,
Thank you for bringing these issues to our attention.
I was able to reproduce the many results you found with GCD and I have filed a note with our development team about them. I will be sure to let you know if I hear anything back.
We are always interested in improving Mathematica and I want to thank you again for taking the time to contact us about this issue. If you have any further questions, or if you find any further issues, please feel free to contact us again.
Sincerely,
Jason Grigsby Wolfram Technology Group Wolfram Research, Inc www.wolfram.com
On: 11/25/2013 08:12pm billgosper@gmail.com submitted the following Case: In[576]:= FullSimplify[GCD[0, n], n \[Element] Integers]
Out[576]= Abs[n]
Good!
In[577]:= FullSimplify[GCD[0, n], n \[Element] Reals]
Out[577]= GCD[0, n]
Should be Abs[n]
In[578]:= FullSimplify[GCD[0, n], n \[Element] Rationals]
Out[578]= GCD[0, n]
Likewise. GCD[0,foo] is foo.
Correction: |foo|. (If foo ϵ Reals.) In[575]:= FullSimplify[GCD[\[Pi], 2*\[Pi]]] Out[575]= GCD[\[Pi], 2 \[Pi]] Should be ?. In my original mail, this says "Should be π"! Your mail system needs updating.
In[580]:= FullSimplify[GCD[Sqrt[2], Sqrt[8]]]
Out[580]= GCD[Sqrt[2], 2 Sqrt[2]]
Should be ?2.
This said √2 !
In[581]:= FullSimplify[GCD[1/Sqrt[2], 1/Sqrt[8]]]
Out[581]= GCD[1/(2 Sqrt[2]), 1/Sqrt[2]]
Should be 1/?8.
Hopefully, your developers got the undamaged version.
In[582]:= FullSimplify[GCD[1/Sqrt[2], 1]]
Out[582]= GCD[1, 1/Sqrt[2]]
Should be 0. Likewise GCD[1,?], GCD[?2,?3], GCD[?2,?].
I.e., GCD[1,π], GCD[√2,√3], GCD[√2,π]
And everybody knows GCD[E,?]=0, but nobody can prove it.
At any rate, PossibleZeroQ[GCD[E, π]] should not be False. --Bill Gosper
In[583]:= $LicenseID
Out[583]= "L3290-7570"