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Check that the following linear combination is small.
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Finding a integer relation between non-algebraic constants.
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Using PSLQ to find the minimal polynomial for
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Approximate with
digits and round to
digits.
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The minimal polynomial for
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Check that
is a root of
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The next example involves complex numbers. First define a tenth root of unity.
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In the next example, a Gaussian integer relation is found. We subsequently find an integer relation from the Gaussian integer relation by eliminating I.
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The last example is of much larger degree requiring more than the default
digits of precision. In the example, we are using PSLQ to test if the algebraic number
is of degree
or less.
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Compute to
digits and round to
digits.
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Check.
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Thus, the minimal polynomial for
must be the degree 9 factor.
Here is what happens if we mistakenly assume that algebraic number
is of degree
or less. The output of PSLQ looks like random
digit integers, which indicates that it has not found anything interesting.
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| (38) |