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# Revision history [back]

ComplexField() (in short CC) is the field of floating-point numbers that are emulated by MPFR (with 53 bits of precision by default). If instead, you use the ComplexDoubleField() (in short CDF), that is the field of floating-point numbers that the processor can directly work with (with 53bits of precisions as well). Just replace ComplexField() with CDF in you code and you will see how faster it is.

ComplexField() (in short CC) is the field of floating-point numbers that are emulated by MPFR (with 53 bits of precision by default). If instead, you use the ComplexDoubleField() (in short CDF), that is the field of floating-point numbers that the processor can directly work with (with 53bits of precisions as well). Just replace ComplexField() with CDF in you code and you will see how faster it is.

That said, note that apparently you lose some roots on the way.

Note that exact computation does not give the same picture: if you use the rational field QQ instead of ComplexField() and look for the roots in the algebraic field QQbar, you get a different picture:

sage: sols=s.roots(QQbar, multiplicities=False)
sage: points((i.real(),i.imag()) for i in sols)