Hey Guys,
I want to add a symbolic expression to CC representing an primitive n-th
root of unity analogous to 'I'.
Lets call this Element xi_n, besides the usual rules xi_n should satisfy
the following properties:
* (xi_n in CC) == true
* xi.parent() == CC
* (exp(2 * pi * I / n) == xi_n)
* latex(xi_n) == "\xi_n"
Maybe the first two conditions are equivalent. I played around with
sage.symbolic.expression.Expression and
sage.structure.element.CommutativeRingElement but did not get any idea
how to start.
I was also looking for a piece of code defining I, but i did not have
any success.
Is there already an implementation I can use (extend)? Or what is the
best way implement this?
My main idea is to inherit from a suitable base class and override the
_pow_ function.
But this results in this error:
sage: xi = NthRootOfUnity(3,parent=CC)
sage: xi**2
TypeError: unsupported operand parent(s) for '*': 'Complex Field with 53
bits of precision' and 'Complex Field with 53 bits of precision'
best regards,
Johannes
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