#hw14.txt; March 10, 2014; Frank Wagner ################### #####Problem 3##### ################### DelinZheng:=proc(lambda) local a,b,c: a:=[[],[1/2],[(1/2)-(1/lambda),1/lambda],[0,1-lambda/2,lambda/2]]: b:=[1/6,(4-lambda)/6,lambda/6,1/6]: c:=[0,1/2,1/2,1]: a,b,c: end: ################### #####Problem 4##### ################### #ProveB([DelinZheng(1)],4)=true while ProveB([DelinZheng(1)],5)=false, # so works for 1 #ProveB([DelinZheng(3)],4)=true while ProveB([DelinZheng(3)],5)=false, # so works for 3 #ProveB([DelinZheng(4)],4)=true while ProveB([DelinZheng(4)],5)=false, # so works for 4 #ProveB([DelinZheng(5)],4)=true while ProveB([DelinZheng(5)],5)=false, # so works for 5 # #The degree for lambda=2.5 is 1, while the degere for lambda=3.5 is 2 ################### #####Problem 5##### ################### RP:=proc(x,y,M,d): add(add(rand(1..M)()*x^i*y^j,j=0..d-i),i=0..d): end: ################### #####Problem 6##### ################### srProveB:=proc(B,d,M,K) local Y,h,i,f,Y1,Y2: Y:=h^(d+1): for i from 1 to K while ldegree(Y,h)>=d+1 do f:=RP(x,y,M,d): Y1:=GRK1s(op(B),f,x,y,0,0,h,d): Y2:=subs(x=h,Z(f,x,y,0,d)): Y:=expand(Y1-Y2): od: if ldegree(Y,h)>=d+1 then true: else false: fi: end: