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The following table gives the total number of real fields of discriminant up to for , as well as the elapsed time on a DEC Alpha.

The following table gives the total number of complex fields of discriminant
greater or equal to to **-X** with for , as well as the
elapsed time on a DEC Alpha.

It should be remarked that, thanks to the notion of reducedness, our algorithm
gives for every cubic field a canonical equation, which we can call
* reduced*, and which in addition has all the
nice properties described in Section 4. In particular the integral basis
and decomposition of primes is immediate. One consequence is that, when the
cubic number field does not have a power basis, the equation that we will
find will not be monic. On the other hand, if there exists a power basis,
the reduced equation produced by our algorithm is not necessarily monic.
We give a few examples.

- The cyclic number field with discriminant
**961**can be given by the monic equation , but does not have a power basis (an integral basis is , where is a root of the above equation). Our algorithm finds the nonmonic reduced equation . - The noncyclic number field of discriminant
**1304**can be given by the monic equation , but does not have a power basis (an integral basis is ). Our algorithm finds the nonmonic reduced equation . - The noncyclic number field of discriminant
**2228**can be given by the monic equation , and this times it has a power basis. On the other hand our algorithm finds the nonmonic reduced equation .

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