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4 results for “simontatham”

1. 

   Simon Tatham @[email protected] · 2026-09-29 · 16:37 UTC

   #TIL that in #SageMath you can accidentally write a comparison expression that doesn't do a comparison. (Reposted after the previous version was subtly wrong)

   x = QQbar(UniversalCyclotomicField().gen(3))
   if x == (-1 + sqrt(3)*i) / 2:
   print("All is well")
   if x != (-1 + sqrt(3)*i) / 2:
   print("Disaster!")

   The canonical primitive cube root of unity really is (−1+i√3)/2. So we expect "All is well" and not "Disaster". But in fact we get both:

   $ sage z.sage
   All is well
   Disaster!

   Turns out this is because when you compare a QQbar value with some more general algebraic expression, it doesn't do a comparison. It constructs a symbolic expression object that just represents the _notion_ of equality or inequality:

   sage: print(x != (-1 + sqrt(3)*i) / 2)
   (-0.500000000000000? + 0.866025403784439?*I) != 1/2*I*sqrt(3) - 1/2

   And those expression objects can evaluate true in a boolean context, simply because they aren't None or False. But they don't _always_. The == comparison seems to work OK, but the != evaluates true unconditionally. #wat

   (The workaround is to coerce the RHS of the expression to QQbar too: 'if x != QQbar(...)'. Then you're comparing elements of the same field and Sage is happy.)

   #til #sagemath #wat
2. 

   Simon Tatham @simontatham · 2026-09-29 · 16:37 UTC

   #TIL that in #SageMath you can accidentally write a comparison expression that doesn't do a comparison. (Reposted after the previous version was subtly wrong)

   x = QQbar(UniversalCyclotomicField().gen(3))
   if x == (-1 + sqrt(3)*i) / 2:
   print("All is well")
   if x != (-1 + sqrt(3)*i) / 2:
   print("Disaster!")

   The canonical primitive cube root of unity really is (−1+i√3)/2. So we expect "All is well" and not "Disaster". But in fact we get both:

   $ sage z.sage
   All is well
   Disaster!

   Turns out this is because when you compare a QQbar value with some more general algebraic expression, it doesn't do a comparison. It constructs a symbolic expression object that just represents the _notion_ of equality or inequality:

   sage: print(x != (-1 + sqrt(3)*i) / 2)
   (-0.500000000000000? + 0.866025403784439?*I) != 1/2*I*sqrt(3) - 1/2

   And those expression objects can evaluate true in a boolean context, simply because they aren't None or False. But they don't _always_. The == comparison seems to work OK, but the != evaluates true unconditionally. #wat

   (The workaround is to coerce the RHS of the expression to QQbar too: 'if x != QQbar(...)'. Then you're comparing elements of the same field and Sage is happy.)

   #til #sagemath #wat
3. 

   Simon Tatham @[email protected] · 2026-09-29 · 16:37 UTC

   #TIL that in #SageMath you can accidentally write a comparison expression that doesn't do a comparison. (Reposted after the previous version was subtly wrong)

   x = QQbar(UniversalCyclotomicField().gen(3))
   if x == (-1 + sqrt(3)*i) / 2:
   print("All is well")
   if x != (-1 + sqrt(3)*i) / 2:
   print("Disaster!")

   The canonical primitive cube root of unity really is (−1+i√3)/2. So we expect "All is well" and not "Disaster". But in fact we get both:

   $ sage z.sage
   All is well
   Disaster!

   Turns out this is because when you compare a QQbar value with some more general algebraic expression, it doesn't do a comparison. It constructs a symbolic expression object that just represents the _notion_ of equality or inequality:

   sage: print(x != (-1 + sqrt(3)*i) / 2)
   (-0.500000000000000? + 0.866025403784439?*I) != 1/2*I*sqrt(3) - 1/2

   And those expression objects can evaluate true in a boolean context, simply because they aren't None or False. But they don't _always_. The == comparison seems to work OK, but the != evaluates true unconditionally. #wat

   (The workaround is to coerce the RHS of the expression to QQbar too: 'if x != QQbar(...)'. Then you're comparing elements of the same field and Sage is happy.)

   #wat #sagemath #til
4. 

   Simon Tatham @[email protected] · 2026-09-29 · 16:37 UTC

   #TIL that in #SageMath you can accidentally write a comparison expression that doesn't do a comparison. (Reposted after the previous version was subtly wrong)

   x = QQbar(UniversalCyclotomicField().gen(3))
   if x == (-1 + sqrt(3)*i) / 2:
   print("All is well")
   if x != (-1 + sqrt(3)*i) / 2:
   print("Disaster!")

   The canonical primitive cube root of unity really is (−1+i√3)/2. So we expect "All is well" and not "Disaster". But in fact we get both:

   $ sage z.sage
   All is well
   Disaster!

   Turns out this is because when you compare a QQbar value with some more general algebraic expression, it doesn't do a comparison. It constructs a symbolic expression object that just represents the _notion_ of equality or inequality:

   sage: print(x != (-1 + sqrt(3)*i) / 2)
   (-0.500000000000000? + 0.866025403784439?*I) != 1/2*I*sqrt(3) - 1/2

   And those expression objects can evaluate true in a boolean context, simply because they aren't None or False. But they don't _always_. The == comparison seems to work OK, but the != evaluates true unconditionally. #wat

   (The workaround is to coerce the RHS of the expression to QQbar too: 'if x != QQbar(...)'. Then you're comparing elements of the same field and Sage is happy.)

   #til #sagemath #wat