canonical form of `(-1)^(1/4)` and/or `exp(pi*I/4)`

asked 2024-08-29 19:03:24 +0100

6540 ●9 ●47 ●153

updated 2024-08-29 19:07:07 +0100

If I ask explicitly, Sage confirms that (-1)^(1/4) and exp(pi*I/4) are equal. However, I'd like to reduce/simplify each of them into the same canonical form (whatever it is) so that I will see their equality with "naked eye". Is there a way to do so? I've tried full_simplify() but it does not help.

sage: bool( (-1)^(1/4) == exp(pi*I/4) )
True
sage: ((-1)^(1/4)).full_simplify()
(-1)^(1/4)
sage: exp(pi*I/4).full_simplify()
(1/2*I + 1/2)*sqrt(2)

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answered 2024-08-29 23:30:58 +0100

eric_g
8469 ●10 ●62 ●168 https://luth.obspm.fr/...

You may use rectform:

sage: ((-1)^(1/4)).rectform()
(1/2*I + 1/2)*sqrt(2)
sage: exp(pi*I/4).rectform()
(1/2*I + 1/2)*sqrt(2)

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FWIW

sage: QQbar(exp(I*pi/4)).radical_expression()
(-1)^(1/4)

HTH (but doubting it ...),

Emmanuel Charpentier ( 2024-08-30 09:39:13 +0100 )edit

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Asked: 2024-08-29 19:03:24 +0100

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Last updated: Aug 29

canonical form of `(-1)^(1/4)` and/or `exp(pi*I/4)` edit