On the Resolution of Index Form Equations

In the present paper we describe a new algorithm to determine the minimal index and all elements with minimal index in totally real biquadratic fields with Galois group D8. The method is based on sieving procedures and can be successfully applied in about 70 % of the cases. If the method applicable, then it produces the results very fast, moreover we can characterize the cases, when it is applicable. At the end of the paper we include some tables, demonstrating our computations by using this method. We also consider the possibilities of applying the Baker–Davenport reduction algorithm in our case. Further, we give an infinite family of

• Type: Conference
• Year: 1991
• Where: ISSAC
• Authors: István Gaál, Attila Pethö, Michael Pohst
• Keywords: ISSAC 1991, Mathematics, Minimal Index, Present Paper, Real Biquadratic fields