An algorithm for computing a standard form for second-order linear \(q\)-difference equations (Q1358917)

This paper is devoted to so-called \(q\)-difference equations. For classic \(K=C(z)\), a suitable algebraic extension \(K_\infty\) with a \(C\)-linear operation \(\varphi\) is defined. Then the author considers the systems of linear difference equations \(\varphi y=Ay\), where \(A= GL(n,K_\infty)\) and announces results of Galois theory for such equations. The theory is analogous to Galois theory for differential equations. A case \(n=2\) is investigated in detail and results obtained are similar to \textit{J. Kovacic}'s results [J. Symb. Comput. 2, 3-43 (1986; Zbl 0603.68035)] for differential equations.