{"version":9,"randomSeed":"91ef8b9c215b5bdee91a7a4b016d61fe","graph":{"viewport":{"xmin":-10,"ymin":-15.205405799598871,"xmax":10,"ymax":15.205405799598871}},"expressions":{"list":[{"type":"text","id":"20","text":"https://en.wikipedia.org/wiki/Interval_arithmetic#Interval_operators"},{"type":"text","id":"5","text":"subtract"},{"type":"expression","id":"6","color":"#6042a6","latex":"S_{i}\\left(a,b\\right)=\\left(a.x-b.y,a.y-b.x\\right)"},{"type":"text","id":"8","text":"multiply"},{"type":"expression","id":"10","color":"#2d70b3","latex":"M_{immh}\\left(a,b,c,d\\right)=\\left(\\min\\left(a,b,c,d\\right),\\max\\left(a,b,c,d\\right)\\right)"},{"type":"expression","id":"9","color":"#c74440","latex":"M_{i}\\left(a,b\\right)=M_{immh}\\left(a.x\\cdot b.x,a.x\\cdot b.y,a.y\\cdot b.x,a.y\\cdot b.y\\right)"},{"type":"text","id":"13","text":"reciprocate (we don't like multi-intervals)"},{"type":"expression","id":"15","color":"#c74440","latex":"R_{i}\\left(a\\right)=\\left\\{a.x<0<a.y:\\left(-\\infty,\\infty\\right),a.x=0:\\left(\\frac{1}{a.y},\\infty\\right),a.y=0:\\left(-\\infty,\\frac{1}{a.x}\\right),\\left(\\frac{1}{a.y},\\frac{1}{a.x}\\right)\\right\\}"}]}}