[was@laptop mlogs]$ [was@laptop mlogs]$ Magma V2.9-11 Mon Oct 7 2002 10:51:10 on laptop [Seed = 967154440] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > Integers; Intrinsic 'Integers' Signatures: () -> RngInt Create the ring of integers Z ( m) -> RngIntRes Create the residue class ring Z/mZ ( Q) -> RngIntRes Create the residue class ring Z/mZ, where Q is the factorization of m ( K) -> RngInt ( K) -> RngOrd ( K) -> RngPad The ring of integers of field K ( K) -> Rng The polynomial ring from which K is constructed as its field of fractions ( L) -> RngLoc ( Z) -> RngInt Returns Z ( O) -> RngOrd Returns the order O > Kronecker(7,5); >> Kronecker(7,5); ^ User error: Identifier 'Kronecker' has not been declared or assigned > KroneckerSymbol(7,5); -1 > [[p,KroneckerSymbol(p,5)] : p in PrimeSeq(7,40)]; [ [ 7, -1 ], [ 11, 1 ], [ 13, -1 ], [ 17, -1 ], [ 19, 1 ], [ 23, -1 ], [ 29, 1 ], [ 31, 1 ], [ 37, -1 ] ] > [[p,KroneckerSymbol(p,5)] : p in PrimeSeq(7,70)]; [ [ 7, -1 ], [ 11, 1 ], [ 13, -1 ], [ 17, -1 ], [ 19, 1 ], [ 23, -1 ], [ 29, 1 ], [ 31, 1 ], [ 37, -1 ], [ 41, 1 ], [ 43, -1 ], [ 47, -1 ], [ 53, -1 ], [ 59, 1 ], [ 61, 1 ], [ 67, -1 ] ] > PrimeSeq; Intrinsic 'PrimeSeq' Signatures: ( start, stop) -> SeqEnum > [[p,KroneckerSymbol(p,5),p mod 5] : p in PrimeSeq(7,80)]; [ [ 7, -1, 2 ], [ 11, 1, 1 ], [ 13, -1, 3 ], [ 17, -1, 2 ], [ 19, 1, 4 ], [ 23, -1, 3 ], [ 29, 1, 4 ], [ 31, 1, 1 ], [ 37, -1, 2 ], [ 41, 1, 1 ], [ 43, -1, 3 ], [ 47, -1, 2 ], [ 53, -1, 3 ], [ 59, 1, 4 ], [ 61, 1, 1 ], [ 67, -1, 2 ], [ 71, 1, 1 ], [ 73, -1, 3 ], [ 79, 1, 4 ] ] >