Infrastructure (number theory)

In mathematics, an infrastructure is a group-like structure appearing in global fields. == Historic development == In 1972, D. Shanks first discovered the infrastructure of a real quadratic number field and applied his baby-step giant-step algorithm to compute the regulator of such a field in O ( D 1 / 4 + ε ) {\displaystyle {\mathcal {O}}(D^{1/4+\varepsilon })} binary operations (for every ε > 0 {\displaystyle \varepsilon >0} ), where D {\displaystyle D} is the discriminant of the quadratic field; previous methods required O ( D 1 / 2 + ε ) {\displaystyle {\mathcal {O}}(D^{1/2+\varepsilon })} binary operations.

Source: Wikipedia — Infrastructure (number theory) (CC BY-SA 4.0)

Infrastructure (number theory)

In mathematics, an infrastructure is a group-like structure appearing in global fields. == Historic development == In 1972, D. Shanks first discovered the infrastructure of a real quadratic number field and applied his baby-step giant-step algorithm to compute the regulator of such a field in O ( D 1 / 4 + ε ) {\displaystyle {\mathcal {O}}(D^{1/4+\varepsilon })} binary operations (for every ε > 0 {\displaystyle \varepsilon >0} ), where D {\displaystyle D} is the discriminant of the quadratic field; previous methods required O ( D 1 / 2 + ε ) {\displaystyle {\mathcal {O}}(D^{1/2+\varepsilon })} binary operations.

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Source: Wikipedia "Infrastructure (number theory)" · CC BY-SA 4.0

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