The function quadres will compute a generalized Legendre symbol  of a and b, which is defined to be 1 if a is a quadratic residue and -1 if a is a quadratic non-residue .  The number a is a quadratic residue mod b if it has a square root ;  i.e., an integer c exists such that  is congruent to .

The command with(numtheory,quadres) allows the use of the abbreviated form of this command.