Complex coefficient avoiding real number representation

[Roberto De Renzi]

Hello, I am manipulating symbolic Matrices with complex numeric coefficients (angular momentum operators).
Their real and imaginary parts are algebraic.  I have troubles diagonalizing them because the real representation of the coefficients produce numerical rounding errors. As long as I use only real coefficients I can define them as s=Fraction(int(n),int(m)), and use e.g.  sympy.sqrt(s*(s+1)),  thus avoiding numerical rounding errors. However

              Fraction(1,2)*1j is 0.5*I

and rounding errors are unavoidable. Is there a way out? I am thinking of a complex number with algebraic immutable real and imaginary part.

i) Is the concept sound? and ii) is it implemented (implementable) in sympy?

Thanks for your help

Roberto

[Aaron Meurer]

If you want an exact symbolic imaginary number, use sympy.I. For
instance, Rational(1, 2)*I (or just I/2) will give an exact number.

The reason you get 0.5*I above is that SymPy automatically evaluates
rational numbers to floats when you multiply them by a float. For
instance, Rational(1, 2)*1.0 gives 0.5. 1j is a Python floating point
complex number. They are always represented as floats, that is, 1j is
the same as 1.0j, so if you use it in a SymPy, it will act like float
would and cause things to evaluate to floats.

Aaron Meurer

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