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revision of twists docstring
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dwbump committed Jun 29, 2020
1 parent 0974b08 commit e9de384
Showing 1 changed file with 9 additions and 7 deletions.
16 changes: 9 additions & 7 deletions src/sage/combinat/root_system/fusion_ring.py
Original file line number Diff line number Diff line change
Expand Up @@ -622,15 +622,16 @@ def weight(self):
return next(iter(self._monomial_coefficients))

def twist(self):
r"""
Compute the object's twist. This returns a rational number `h`
r"""Compute the object's twist. This returns a rational number `h`
such that `\theta = e^{i \pi h}` is the twist of ``self``.
This method is only available for simple objects.
We compute the twists following p.7 of [Row2006]_, noting that
the bilinear form is normalized so that
`\langle \alpha, \alpha \rangle = 2` for short roots.
This method is only available for simple objects. If
`\lambda` is the weight of the object, then
`h = \langle\lambda,\lambda+2\rho\rangle` where
`\rho` is half the sum of the positive roots.
As in [Row2006]_, this requires normalizing
the invariant bilinear form so that `\langle \alpha, \alpha
\rangle = 2` for short roots.
EXAMPLES::
Expand All @@ -644,6 +645,7 @@ def twist(self):
Finite family {(0, 0, 0, 0): F41(0,0,0,0), (1, 0, 0, 0): F41(0,0,0,1)}
sage: F41(0,0,0,1).twist()
4/5
"""
if not self.is_simple_object():
raise ValueError("quantum twist is only available for simple objects of a FusionRing")
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