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Theorem 5.3. If a Garside group G has a finite index subgroup G0 that has the unique root property, then the generalized power problem and the generalized power conjugacy problem are solvable in G. Proof. Let r be a positive integer such that gr ∈ G0 for all g ∈ G. (It suffices ...
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Theorem 2. For each level k in the SB tree, we have: δk2 ≥ k 3 . Proof. By induction on the levels of the Stern-Brocot tree, we have δ12 = δ22 = 1; and δ32 ∈ {1, 2} while δ42 = 2. Hence the minimal value of δ32 (denoted min δ32) is equal to 1 and min...
Polefinding (and rootfinding if necessary) by a one-step eigenvalue problem. 2. Automatic determination of a type(m,n)for the rational approximant. This allows the user to obtainp,qfrom the inputfalone. In previous algorithms the type(m,n)has been a required input. ...
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