Printing system, method of dyeing medium, and ink set

A printing system comprising:

• a printing apparatus that performs printing of information on a medium by using an ink set including at least one other ink in addition to a magenta ink;
• a heat treatment apparatus that fixes the information printed on the medium by textile printing processing of the medium on which the information is printed;
• and
• a controller, wherein
• the controller includes:
• a print data generation unit that generates print data from input data of information to be printed on the medium;
• a print control unit that prints the information on the medium by controlling ejection of the ink onto the medium based on the generated print data;
• and
• a textile printing parameter setting unit that sets, as a parameter of the textile printing processing, at least a heating temperature of the medium and a heating time of the medium,
• each of the inks included in the ink set contains a sublimable dye as a color development component, and the dye contained in the magenta ink is a disperse red 146, and
• the textile printing parameter setting unit is configured to:
• set a heating temperature in the textile printing processing to a first temperature higher than a heating temperature when the dye contained in the magenta ink is a disperse red 60;
• and
• set a heating time in the textile printing processing to a first time longer than a heating time when the dye contained in the magenta ink is a disperse red 60.