read FunEq: K1:=2: K2:=30: print(`This file contains some sample examples of the Gessel-Zeilberger method applied to Functional Equations`): print(`of the form`): eq:=GenBabFE(a,b,A,B,C,x,y,fxy,fx1): PrintFE(eq,x,y,fxy,fx1,f) : print(`For various a,b,A,B,C`): print(`---------------------------------------------------`): print(`Let's take a=0, b=1`): a:=0: b:=1: for A from 1 to K1 do for B from 1 to K1 do for C from 1 to K1 do gu:=Info(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400): if gu<>FAIL then print(`---------------------------------------------------`): print(`[A,B,C]=`, [A,B,C]): InfoV(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400); fi: od: od: od: print(`---------------------------------------------------`): print(`---------------------------------------------------`): print(`Let's take a=1, b=0`): a:=1: b:=0: for A from 1 to K1 do for B from 1 to K1 do for C from 1 to K1 do gu:=Info(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400): if gu<>FAIL then print(`---------------------------------------------------`): print(`[A,B,C]=`, [A,B,C]): InfoV(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400); fi: od: od: od: print(`---------------------------------------------------`): print(`---------------------------------------------------`): print(`Let's take a=1, b=1`): a:=1: b:=1: for A from 1 to K1 do for B from 1 to K1 do for C from 1 to K1 do gu:=Info(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400): if gu<>FAIL then print(`---------------------------------------------------`): print(`[A,B,C]=`, [A,B,C]): InfoV(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400); fi: od: od: od: print(`Let's take a=2, b=2`): a:=2: b:=2: for A from 1 to K1 do for B from 1 to K1 do for C from 1 to K1 do gu:=Info(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400): if gu<>FAIL then print(`---------------------------------------------------`): print(`[A,B,C]=`, [A,B,C]): InfoV(GenBabFE(a,b,A,B,C,x,y,fxy,fx1),x,y,fxy,fx1,K2,n,N,10,30,400); fi: od: od: od: print(`This ends this file, that took`, time(), `seconds. `): quit: