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aidevnn / FastGoat

What C# can do for studying Finite Groups, quotient groups, semi-direct products, homomorphisms, automorphisms group, characters table, minimalistic rings and fields manipulations, polynomials factoring, fields extensions and many more...
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Algebraic Integer Relation with LLL #40

Open aidevnn opened 1 year ago

aidevnn commented 1 year ago

https://github.com/aidevnn/FastGoat/blob/c312d8b87dccc100cc37fe8d096a817f52abb1f2/FastGoat/Examples/AlgebraicIntegerRelationLLL.cs#L171-L193

O1 represents the minimum number of digits required in the lattice, while O2 represents the maximum number of digits required for precise computation before populating the lattice, both of which are typically determined through trial and error. However, a more efficient approach involves using a minorant to predict O1 and O2 based on the polynomial degree and its coefficients. Although this method may be challenging, it represents a significant improvement for future applications.

aidevnn commented 1 year ago

The normality of the polynomial P must also be checked before continuing with LLL.