{"version":9,"randomSeed":"ab7ef1cb28fb3fbcd24c5f58aa848102","graph":{"viewport":{"xmin":-10,"ymin":-10.000000000000002,"xmax":10.000000000000004,"ymax":10.000000000000002}},"expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"G=\\left[\\left(0,1\\right),\\left(3,2\\right),\\left(4,-1\\right),\\left(6,0\\right),\\left(-3,2\\right),\\left(8,-4\\right)\\right]"},{"type":"expression","id":"2","color":"#2d70b3","latex":"F\\left(P,x\\right)=\\sum_{i=1}^{\\operatorname{length}\\left(P\\right)}\\left(P\\left[i\\right].y\\prod_{j=1}^{\\operatorname{length}\\left(P\\right)}\\left\\{i=j:1,\\frac{x-P\\left[j\\right].x}{P\\left[i\\right].x-P\\left[j\\right].x}\\right\\}\\right)"},{"type":"expression","id":"3","color":"#388c46","latex":"F\\left(G,x\\right)"},{"type":"expression","id":"107","color":"#c74440","latex":"Z\\left(p,k,x\\right)=F\\left(\\left\\{k=0:\\operatorname{join}\\left(\\left(0,1\\right),\\left(\\left[1...p-1\\right],0\\right)\\right),k=p-1:\\operatorname{join}\\left(\\left(\\left[0...p-2\\right],0\\right),\\left(p-1,1\\right)\\right),\\operatorname{join}\\left(\\left(\\left[0...\\left(k-1\\right)\\right],0\\right),\\left(k,1\\right),\\left(\\left[\\left(k+1\\right)...\\left(p-1\\right)\\right],0\\right)\\right)\\right\\},x\\right)"},{"type":"expression","id":"121","color":"#000000","latex":"K\\left(P,k,t\\right)=\\left\\{k<\\operatorname{length}\\left(P\\right):P\\left[k+1\\right]Z\\left(\\operatorname{length}\\left(P\\right),k,t\\right),\\left(0,0\\right)\\right\\}"},{"type":"text","id":"123","text":"come on, Desmos, let us sum points!"},{"type":"expression","id":"119","color":"#388c46","latex":"S\\left(P,t\\right)=\\left(\\sum_{k=0}^{\\operatorname{length}\\left(P\\right)-1}P\\left[k+1\\right].x\\cdot Z\\left(\\operatorname{length}\\left(P\\right),k,t\\right),\\sum_{k=0}^{\\operatorname{length}\\left(P\\right)-1}P\\left[k+1\\right].y\\cdot Z\\left(\\operatorname{length}\\left(P\\right),k,t\\right)\\right)"},{"type":"expression","id":"120","color":"#6042a6","latex":"S\\left(\\operatorname{sort}\\left(G,G.x\\right),t\\right)","parametricDomain":{"min":"","max":"5"},"domain":{"min":"0","max":"5"}}]}}