Re: [sage-devel] Is 1 a prime power?
On Fri, Aug 29, 2014 at 10:53 AM, John Cremona wrote: > pari: > > ? isprimepower(1) > %4 = 0 > > magma: > >>> IsPrimePower(1); >^ > Runtime error in 'IsPrimePower': Argument 1 (1) should be >= 2 > > gap> IsPrimePowerInt(1); > false > > I'll let others try Maple. That seems like enough of an argument for Sage to return False to me. -- William > > John > > > On 29 August 2014 09:50, Vincent Delecroix <20100.delecr...@gmail.com> > wrote: >> >> What is the status of 1 in pari, GAP, Maple, Magma, Mathematica? >> >> Vincent >> >> 2014-08-29 10:31 UTC+02:00, Jeroen Demeyer : >> > Personally, I think "1" should not be considered a prime power, but Sage >> > thinks otherwise: >> > >> > sage: 1.is_prime_power() >> > True >> > >> > Of course, one could argue that 1 = p^0 for every prime p... >> > >> > Should this be changed, any opinions? >> > >> > -- >> > You received this message because you are subscribed to the Google >> > Groups >> > "sage-devel" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> > an >> > email to sage-devel+unsubscr...@googlegroups.com. >> > To post to this group, send email to sage-devel@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sage-devel. >> > For more options, visit https://groups.google.com/d/optout. >> > >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-devel" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-devel+unsubscr...@googlegroups.com. >> To post to this group, send email to sage-devel@googlegroups.com. >> Visit this group at http://groups.google.com/group/sage-devel. >> For more options, visit https://groups.google.com/d/optout. > > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- William Stein Professor of Mathematics University of Washington http://wstein.org wst...@uw.edu -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Is 1 a prime power?
pari: ? isprimepower(1) %4 = 0 magma: >> IsPrimePower(1); ^ Runtime error in 'IsPrimePower': Argument 1 (1) should be >= 2 gap> IsPrimePowerInt(1); false I'll let others try Maple. John On 29 August 2014 09:50, Vincent Delecroix <20100.delecr...@gmail.com> wrote: > What is the status of 1 in pari, GAP, Maple, Magma, Mathematica? > > Vincent > > 2014-08-29 10:31 UTC+02:00, Jeroen Demeyer : > > Personally, I think "1" should not be considered a prime power, but Sage > > thinks otherwise: > > > > sage: 1.is_prime_power() > > True > > > > Of course, one could argue that 1 = p^0 for every prime p... > > > > Should this be changed, any opinions? > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to sage-devel+unsubscr...@googlegroups.com. > > To post to this group, send email to sage-devel@googlegroups.com. > > Visit this group at http://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/d/optout. > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Is 1 a prime power?
1 is definitely not a prime power. It's basically the same reason that 1 is not a prime. Some reasons: (1) positive integers are uniqely products of prime powers (with 1 being the empty product!) Uniqueness would fail if 1 were allowed. (2) a positive integer n is a prime power iff nZ is a primary ideal of Z (that got you 2 marks in an exam I set this year), and the definition of primary ideal (as with prime ideal) explicitly requires the ideal to be proper. John On 29 August 2014 09:31, Jeroen Demeyer wrote: > Personally, I think "1" should not be considered a prime power, but Sage > thinks otherwise: > > sage: 1.is_prime_power() > True > > Of course, one could argue that 1 = p^0 for every prime p... > > Should this be changed, any opinions? > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Is 1 a prime power?
What is the status of 1 in pari, GAP, Maple, Magma, Mathematica? Vincent 2014-08-29 10:31 UTC+02:00, Jeroen Demeyer : > Personally, I think "1" should not be considered a prime power, but Sage > thinks otherwise: > > sage: 1.is_prime_power() > True > > Of course, one could argue that 1 = p^0 for every prime p... > > Should this be changed, any opinions? > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Is 1 a prime power?
Personally, I think "1" should not be considered a prime power, but Sage thinks otherwise: sage: 1.is_prime_power() True Of course, one could argue that 1 = p^0 for every prime p... Should this be changed, any opinions? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
