H0 %%%-(6(B(?):))8J.CK.$L.Dn6o6p6q6##:+$: %:,vA!wAxA2A=AA>FF FFM1MM;P@ P !PAUU UV.VV/]%] ]&]i4ii5@z(Az Bz)@'%P(GUESS( GUESS,Guess(GUESS,GuessPoly(GUESS,GuessRatioGUESS( GUESS,Guess(GUESS,GuessPoly(GUESS,GuessRatio((GUESS,GuessRatioU7VW"u Fv 'w G%%%-(6(B(?):))8J.CK.$L.Dn6o6p6q6##:+$: %:,vA!wAxA2A=AA>FF FFM1MM;P@ P !PAUU UV.VV/]%] ]&]i4ii5@z(Az Bz)@'%Pg as Guess(l) but it returns\n expressions without GAMMA functions.\n \n - Whenever there is a conflict between the function name Guess and another\n name used in the same session, use the long form GUESS['Guess'].\n \n EXAMPLES:\n > with(GUESS):\n > l := [seq(product(product(GAMMA(i)*i^2,i=1..j),j=1..k),k=1..10)]:\n \n > Guess( l, 1 );\n \{\}\n \n > Guess( l );\n \n _i[0] - 1 /_i[1] - 1 \\\n --------' | --------' 2|\n ' | | |' | | GAMMA(_i[2] + 3) |\n \{ | | 4 | | | -----------------|\}\n | | | | | GAMMA(2 + _i[2])|\n | | | | | |\n _i[1] = 1 \\_i[2] = 1 /\n \n > Guess( l , 'nogamma' );\n \n _i[0] - 1 /_i[1] - 1 /_i[2] - 1 \\\\\n --------' | --------' E({VERSION 2 2 "User Help Text" "2.2"} {USTYLETAB } {SECT 0 {PARA 0 "> " 0 "" {TEXT -1 1264 " \n HELP FOR: A package to guess closed form for a sequence of numbers.\n \n CALLING SEQUENCE:\n GUESS[](args)\n (args)\n \n SYNOPSIS:\n - This package provides functions to find a closed form for a sequence\n of numbers within the hierarchy of expressions of the form\n , , , etc.\n \n - Whenever there is a conflict between a function name in GUESS and another\n name used in the same session, use the long form GUESS[].\n \n - The available functions are:\n \n Guess GuessPoly GuessRatio\n \n - For help with a particular function, type either ?GUESS[] or\n ?GUESS, where is one from the above list.\n \n EXAMPLES:\n > with(GUESS):\n \n > Guess( [1,2,3] );\n \n 9< \{----------\}\n _i[0]\n \n SEE ALSO: GUESS, Guess, GuessPoly,"}}}- rational interpolation for a sequence of numbers\n \n CALLING SEQUENCE:\n GuessRatio(l)\n GUESS[GuessRatio](l)\n \n PARAMETERS:\n l - a list of numbers\n \n SYNOPSIS:\n - The return value of GuessRatio(l) is a rational function in the\n variable _i[0].\n \n - Whenever there is a conflict between the function name GuessRatio and\n another name used in the same session, use the long form\n GUESS['GuessRatio'].\n \n EXAMPLES:\n > with(GUESS):\n > l := [seq((i^2+1)/i,i=1..10)];\n \n 101\n l := [2, 5/2, 10/3, 17/4, 26/5, 37/6, 50/7, 65/8, 82/9, ---]\n 10\n \n > GuessRatio( l );\n \n 2\n 1 + _i[0]\n 0 \{----------\}\n _i[0]\n \n SEE ALSO: GUESS, Guess, GuessPoly,"}}}- rational interpolation for a sequence of numbers\n \n CALLING SEQUENCE:\n GuessRatio(l)\n GUESS[GuessRatio](l)\n \n PARAMETERS:\n l - a list of numbers\n \n SYNOPSIS:\n - The return value of GuessRatio(l) is a rational function in the\n variable _i[0].\n \n - Whenever there is a conflict between the function name GuessRatio and\n another name used in the same session, use the long form\n GUESS['GuessRatio'].\n \n EXAMPLES:\n > with(GUESS):\n > l := [seq((i^2+1)/i,i=1..10)];\n \n 101\n l := [2, 5/2, 10/3, 17/4, 26/5, 37/6, 50/7, 65/8, 82/9, ---]\n 10\n \n > GuessRatio( l );\n \n 2\n 1 + _i[0]\n 3( {VERSION 2 2 "User Help Text" "2.2"} {USTYLETAB } {SECT 0 {PARA 0 "> " 0 "" {TEXT -1 2216 " \n FUNCTION: Guess - products of rational interpolation\n - for a sequence of numbers\n \n CALLING SEQUENCE:\n Guess(l,)\n GUESS[Guess](l,)\n \n PARAMETERS:\n l - a list of numbers\n level - an integer (optional, as to be in second position)\n 'one' - the string 'one' (optional)\n 'nogamma' - the string 'nogamma' (optional)\n \n SYNOPSIS:\n - Guess(l) tries to find a closed form for a sequence within the hierarchy\n of expressions of the form , , , etc.\n \n - Guess(l,level) does the same thing as Guess(l) but it searches only\n within the first 'level' levels\n \n - Guess(l,'one') does the same thing as Guess(l) but it returns the first\n solution it finds.\n \n - Guess(l,'nogamma') does the same thin* \{_i[0]\}\n \n > Guess( [1,2,7,42,429,7436,218348,10850216] );\n \n _i[0] - 1\n --------' _i[1] _i[1] 2 1/2\n ' | | (3/4) (3 ) GAMMA(_i[1] + 4/3) GAMMA(_i[1] + 2/3) 3\n \{ | | 3/4 ---------------------------------------------------------------\n | | _i[1] 2\n | | (2 ) GAMMA(_i[1] + 3/2) GAMMA(_i[1] + 1/2)\n _i[1] = 1\n \n \}\n "}}}oduct of product\n of rational function>, etc.\n \n - Whenever there is a conflict between a function name in GUESS and another\n name used in the same session, use the long form GUESS[].\n \n - The available functions are:\n \n Guess GuessPoly GuessRatio\n \n - For help with a particular function, type either ?GUESS[] or\n ?GUESS, where is one from the above list.\n \n EXAMPLES:\n > with(GUESS):\n \n > Guess( [1,2,3] );\n \n 9x o{VERSION 2 2 "User Help Text" "2.2"} {USTYLETAB } {SECT 0 {PARA 0 "> " 0 "" {TEXT -1 940 " \n FUNCTION: GuessRatio - rational interpolation for a sequence of numbers\n \n CALLING SEQUENCE:\n GuessRatio(l)\n GUESS[GuessRatio](l)\n \n PARAMETERS:\n l - a list of numbers\n \n SYNOPSIS:\n - The return value of GuessRatio(l) is a rational function in the\n variable _i[0].\n \n - Whenever there is a conflict between the function name GuessRatio and\n another name used in the same session, use the long form\n GUESS['GuessRatio'].\n \n EXAMPLES:\n > with(GUESS):\n > l := [seq((i^2+1)/i,i=1..10)];\n \n 101\n l := [2, 5/2, 10/3, 17/4, 26/5, 37/6, 50/7, 65/8, 82/9, ---]\n 10\n \n > GuessRatio( l );\n \n 2\n 1 + _i[0]\n 0(o{VERSION 2 2 "User Help Text" "2.2"} {USTYLETAB } {SECT 0 {PARA 0 "> " 0 "" {TEXT -1 940 " \n FUNCTION: GuessRatio - rational interpolation for a sequence of numbers\n \n CALLING SEQUENCE:\n GuessRatio(l)\n GUESS[GuessRatio](l)\n \n PARAMETERS:\n l - a list of numbers\n \n SYNOPSIS:\n - The return value of GuessRatio(l) is a rational function in the\n variable _i[0].\n \n - Whenever there is a conflict between the function name GuessRatio and\n another name used in the same session, use the long form\n GUESS['GuessRatio'].\n \n EXAMPLES:\n > with(GUESS):\n > l := [seq((i^2+1)/i,i=1..10)];\n \n 101\n l := [2, 5/2, 10/3, 17/4, 26/5, 37/6, 50/7, 65/8, 82/9, ---]\n 10\n \n > GuessRatio( l );\n \n 2\n 1 + _i[0]\n 3(T{VERSION 2 2 "User Help Text" "2.2"} {USTYLETAB } {SECT 0 {PARA 0 "> " 0 "" {TEXT -1 674 " \n FUNCTION: GuessPoly - polynomial interpolation for a sequence of numbers\n \n CALLING SEQUENCE:\n GuessPoly(l)\n GUESS[GuessPoly](l)\n \n PARAMETERS:\n l - a list of numbers\n \n SYNOPSIS:\n - The return value of GuessPoly(l) is a polynomial in the variable _i[0].\n \n - Whenever there is a conflict between the function name GuessPoly and\n another name used in the same session, use the long form\n GUESS['GuessPoly'].\n \n EXAMPLES:\n > with(GUESS):\n > GuessPoly( [1,4,9,16] );\n \n 2\n _i[0]\n \n > GuessPoly( [1,3,6,10] );\n \n 1/2 _i[0] (1 + _i[0])\n \n SEE ALSO: GUESS, Guess, GuessRatio,"}}}n - Guess(l,'one') does the same thing as Guess(l) but it returns the first\n solution it finds.\n \n - Guess(l,'nogamma') does the same thing as Guess( | --------' 2||\n ' | | |' | | |' | | 9 + 6 _i[3] + _i[3] ||\n \{ | | 4 | | | 18 | | | --------------------||\}\n | | | | | | | | 2 + _i[3] ||\n | | | | | | | | ||\n _i[1] = 1 \\_i[2] = 1 \\_i[3] = 1 //\n \n SEE ALSO: GUESS, GuessPoly, GuessRatio,"}}} \\\n --------' | --------' 2|\n ' | | |' | | GAMMA(_i[2] + 3) |\n \{ | | 4 | | | -----------------|\}\n | | | | | GAMMA(2 + _i[2])|\n | | | | | |\n _i[1] = 1 \\_i[2] = 1 /\n \n > Guess( l , 'nogamma' );\n \n _i[0] - 1 /_i[1] - 1 /_i[2] - 1 \\\\\n --------' | --------' E