read `GenBeukersZeta2.txt`: K:=3000: print(`For the original Zeta(2)`): TheoremZ2(0,0,0,0,K, [[ [1,0],[1,0],[] ],[ [1,0],[1,2],[] ]]): print(`--------------------------------------------------`): print(`-----------------------`): print(`The following examples give positive delta, i.e. yielding irrationality proofs`): print(``): print(`For GBC(0,0,1/2,0) (alias 2*log(2)) `): TheoremZ2(0,0,1/2,0,K,[ [[2,2],[1,0],[]],[[1, 1], [1, 0], [ [0,1/2,0,1,{0},1], [1/2,1,0,2,{0},1]$2 ] ]]): print(`-----------------------`): print(``): print(`For GBC(0,0,1/3,-2/3) (conjecturally -6+4*Pi/sqrt(3)), try: `): TheoremZ2(0,0,1/3,-2/3,K,[[[1, 0], [1, 0], [[1/3, 2/3, 0, 3, {2}, 3]]],[[1, 0], [1, 0], [[1/3, 2/3, 0, 3, {1}, 3]$2, [0, 1/3, 0, 3/2, {0}, 1], [2/3, 1, 0, 3/2, {0}, 1]]]]): print(`-----------------------`): print(`For the equivalent GBC(0,-2/3,2/3,-2/3), conjecturally ( 45/8-5*sqrt(3)*Pi/6) but much simpler`): TheoremZ2(0,-2/3,2/3,-2/3,K,[[[1, 0], [1, 0], []],[[3, 3/2], [1, 0], [[0, 1/3, 0, 1, {0}, 1]]]]): print(`-----------------------`): print(``): print(`For GBC(-3/4,-3/4,-1/4,-1/4), conjecturally 92-64*sqrt(2) `): TheoremZ2(-3/4,-3/4,-1/4,-1/4, K,[[[1, 0], [1, 0], []], [[2, 2], [1, 0], [[1/2, 3/4, 0, 2, {0}, 1]] ]],K): print(`-----------------------`): print(`For GBC( -4/5, -4/5, -2/5, 2/5), conjecturally, -65/4+65/8*5^(1/2) `): TheoremZ2( -4/5, -4/5, -2/5, 2/5, K,0): print(`-----------------------`): print(``): print(`For GBC(0, -1/2, 1/6, -1/2), (not yet identified, possibly not yet proved to be irrational) , also no INTEGERating factor yet.`): TheoremZ2(0,-1/2,1/6,-1/2,K,0): print(`----------------------------------`): print(``): print(`For GBC( -5/6, -5/6, -1/2, -1/2), conjecturally, -1344/5+16384/105*3^(1/2) `): TheoremZ2( -5/6, -5/6, -1/2, -1/2, K,0): print(`----------------------------------`): print(``): print(`For GBC( -5/6, -5/6, -1/3, -2/3), conjecturally, 972/5*2^(2/3)-1536/5 `): TheoremZ2( -5/6, -5/6, -1/3, -2/3, K,0): print(`----------------------------------`): print(`For GBC( -2/3, -1/2, 1/2, -1/2 ), not yet identified, also no INTEGERating factor yet , try: `): print(`Comment:The delta is very small, so this case is questionable`): TheoremZ2(-2/3, -1/2, 1/2, -1/2 , K,0): print(`----------------------------------`): print(``): print(`For GBC( -6/7, -6/7, -4/7, -5/7 ), not yet identified, also no INTEGERating factor yet , try: `): TheoremZ2( -6/7, -6/7, -4/7, -5/7, K,0): print(`----------------------------------`): print(``): print(`For GBC( -6/7, -6/7, -4/7, 4/7), conjecturally`): print(`the root of -110592*x^3+1225728*x^2+45000816*x-101163391=0 `): print(`or, using Cardano`): print(`-665/576*(28+84*I*3^(1/2))^(1/3)-4655/144/(28+84*I*3^(1/2))^(1/3)+133/36-133/96*I*3^(1/2)*(5/6*(28+84*I*3^(1/2))^(1/3)-70/3/(28+84*I*3^(1/2))^(1/3))`): TheoremZ2( -6/7, -6/7, -4/7, 4/7, K,0): print(`----------------------------------`): print(``): print(`For GBC( -6/7, -5/7, -3/7, -5/7 ), not yet identified, also no INTEGERating factor yet , try: `): TheoremZ2( -6/7, -5/7, -3/7, -5/7, K,0): print(``): print(`For GBC( -6/7, -5/7, -2/7, -1/7 ), not yet identified, also no INTEGERating factor yet , try: `): print(` TheoremZ2( -6/7, -5/7, -2/7, -1/7, 2000,0); `): print(``): print(`For GBC( -6/7, -4/7, -1/7, -1/7 ), not yet identified, also no INTEGERating factor yet , try: `): TheoremZ2( -6/7, -4/7, -1/7, -1/7, K,0): print(``): print(`For GBC((-6/7, -3/7, -5/7, -3/7 ), not yet identified, also no INTEGERating factor yet , try: `): TheoremZ2(-6/7, -3/7, -5/7, -3/7, K,0): print(``): print(`For GBC( -6/7, -1/7, 4/7, 2/7), conjecturally`): print(`the root of 2299968*x^3+7074144*x^2-11234916*x-12663217=0 `): print(`or, using Cardano`): print(`245/792*(-28+84*I*3^(1/2))^(1/3)+1715/198/(-28+84*I*3^(1/2))^(1/3)-203/198`): TheoremZ2( -6/7, -1/7, 4/7, 2/7, K,0): print(``): print(`For GBC( -5/7, -3/7, -4/7, -2/7 ), not yet identified, also no INTEGERating factor yet `): TheoremZ2( -5/7, -3/7, -4/7, -2/7, K,0): print(``): print(`----------------------------------------------------`): print(`The following examples are for constants that yield negative deltas, but it is still interesting`): print(``): print(`For GBC(1/2,-1/2,-1/2,1/2), (conjecturally 4-8/Pi) `): TheoremZ2(1/2,-1/2,-1/2,1/2,2000,[[[1, 0], [1, 0], []],[[2, 4], [1, 0], [[0, 1/2, 0, 1, {0}, 1]]]]): print(`----------------------------------------------------`): print(``): print(`For GBC(1/2,0,0,1/2), twice the Catalan constant`): TheoremZ2(1/2,0,0,1/2,K,[[[1, 0], [1, 0], []],[[2, 4], [2, 2], [ ]]]): print(`----------------------------------------------------`): print(`For GBC(1/3,0,0,1/3), whatever it is`): TheoremZ2(1/3,0,0,1/3,K,[[[1, 0], [1, 0], []],[[3,3], [3/2, 2], [ [1/3,2/3,3/2,3,{2},3]$2 ] ]]): print(`--------------------------------`): print(`--------------------------------`): print(`This took`, time(), `seconds `): quit: