{"H":[[{"coeff":"-1/2","exponents":[0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2]}],[{"coeff":"3","exponents":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-2","exponents":[0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2]}],[{"coeff":"4","exponents":[0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-2","exponents":[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2]}],[{"coeff":"-1","exponents":[0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2]}],[{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2]}],[{"coeff":"-5","exponents":[0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"4","exponents":[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"2","exponents":[0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"2","exponents":[0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2]}],[{"coeff":"-1","exponents":[1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]}],[{"coeff":"3","exponents":[1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"1","exponents":[0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1]}],[{"coeff":"-7","exponents":[0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"1","exponents":[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"1","exponents":[0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1]},{"coeff":"-1","exponents":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2]}],[{"coeff":"-1","exponents":[2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]}],[{"coeff":"1","exponents":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]}],[{"coeff":"-3/2","exponents":[2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"1/2","exponents":[2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0]},{"coeff":"-1/2","exponents":[1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]}],[{"coeff":"12","exponents":[1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"1","exponents":[1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-3","exponents":[1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-3","exponents":[0,2,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-1","exponents":[0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0]}],[{"coeff":"3","exponents":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"1","exponents":[1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-3","exponents":[0,2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"7","exponents":[0,2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-1","exponents":[0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"1","exponents":[0,0,1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-1","exponents":[0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0]}],[{"coeff":"2","exponents":[1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]}],[{"coeff":"3","exponents":[2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}],[{"coeff":"-5","exponents":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-2","exponents":[1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0]},{"coeff":"6","exponents":[0,2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-14","exponents":[0,2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"2","exponents":[0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"-2","exponents":[0,0,1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"2","exponents":[0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0]}],[{"coeff":"-1","exponents":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]},{"coeff":"1","exponents":[1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]}],[]],"certificates":{"homogeneous_degree":3,"nilpotency_lower":17,"nilpotency_upper":18,"nonzero_entry_1_based":{"column":19,"row":4,"value":"-18*t^16*x^10*y^6*z^2"}},"collision_points":[["0","0","-1/4","0","0","1/2","0","0","0","0","0","0","0","0","0","0","0","0","1"],["1","-3/2","13/2","-9/4","9/2","-10","-3/2","3/4","-153/8","1","-13/2","17/4","45/8","-99/16","-9/2","9/2","177/8","-99/4","1"],["-1","3/2","13/2","-9/4","-9/2","-10","-3/2","-3/4","-153/8","1","13/2","-17/4","-45/8","-99/16","-9/2","-9/2","177/8","-99/4","1"]],"common_image":["0","0","-1/4","0","0","1/2","0","0","0","0","0","0","0","0","0","0","0","0","1"],"dimension":19,"field":"Q","format":"yagzhev-map-v1","map":"G_i = X_i + H_i","variable_order":["x","y","z","a","b","c","d","q","s","h","k","Y1","Y2","Y3","Y4","Y5","Y6","Y9","t"]}
