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Roots of unity: Difference between revisions

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Roots of unity (view source)

Revision as of 12:41, 9 August 2008

364 bytes added ,  15 years ago
m
→‎[[Roots_of_unity#Python]]
(added Fortran)
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=={{header|Python}}==
{{works with|Python|2.5}}
<python>
import cmath
 
# format complex to 4 decimal places
Function <code>nthroots()</code> returns all n-th roots of unity.
class Complex(complex):
<python>from cmath import exp, pi
def nthroots__repr__(nself):
re_fmt = "%7.4f"
return [exp(k * 2j * pi / n) for k in range(1, n + 1)]</python>
im_fmt = ("+" if self.imag > 0 else "-") + "%6.4fj"
Example:
return (re_fmt+im_fmt) % (self.real, abs(self.imag))
>>> f = nthroots
 
>>> for nroot in range(12, 410+1):
... print map(lambda c: ("%.3f " + ("+" if c.imag > 0 else "-") + " %.3gj") % (c.real, abs(c.imag)), f(n))
print "%3d"%root, [Complex(cmath.exp(2j*cmath.pi*n/root)) for n in range(1, root/2+1)]
['1.000 - 2.45e-016j']
</python>
['-1.000 + 1.22e-016j', '1.000 - 2.45e-016j']
Output:
['-0.500 + 0.866j', '-0.500 - 0.866j', '1.000 - 2.45e-016j']
2 [-1.0000+0.0000j]
3 [-0.5000+0.8660j]
4 [ 0.0000+1.0000j, -1.0000+0.0000j]
5 [ 0.3090+0.9511j, -0.8090+0.5878j]
6 [ 0.5000+0.8660j, -0.5000+0.8660j, -1.0000+0.0000j]
7 [ 0.6235+0.7818j, -0.2225+0.9749j, -0.9010+0.4339j]
8 [ 0.7071+0.7071j, 0.0000+1.0000j, -0.7071+0.7071j, -1.0000+0.0000j]
9 [ 0.7660+0.6428j, 0.1736+0.9848j, -0.5000+0.8660j, -0.9397+0.3420j]
10 [ 0.8090+0.5878j, 0.3090+0.9511j, -0.3090+0.9511j, -0.8090+0.5878j, -1.0000+0.0000j]
 
=={{header|Seed7}}==
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