PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.89, pp.203-221, 2016 (Journal Indexed in SCI)
Article / Article
Title of Journal :
carks, binary quadratic forms, reduction theory, representation problem of binary quadratic forms, minimum problem of binary quadratic forms
We give an interpretation of the reduction algorithm of Gauss in terms of carks, which are certain types of infinite ribbon graphs (or infinite dessins). We then describe an alternative reduction which is slightly faster than Gauss'. We also solve the minimal value problem and describe an algorithmic solution to the representation problem of indefinite binary quadratic forms.