Hello, I made a new version of my inverter program. The file is at http://www.lacim.uqam.ca/%7Eplouffe/inverter.txt (563 kbytes). The text file is to be used with Maple, versions 9 and higher. There are 2 new funtions, pilll and pialg. They both use the new PSLQ routine, it needs a real number of at least 24 digits and up to 110 digits. The new function pilll uses 127 different tables of real numbers. The file can be downloaded and it is FREE, it can be copied at will as long as you mention the source. NOTE : the functions pismart() does not work this weekend because they are reconfiguring the machines at UQAM, please be patient. It should be back to normal in the next few days. Simon Plouffe Explanations on how to use it : ########################################################################################################## ########################################################################################################## # Plouffe's Inverter Maple interface, version of Sept. 18 2004. # Copyright (c) 1986-2004 by Simon Plouffe # # This program is to be used with Maple 7 or 8 on any platform. # A live connection is needed in order to work, preferably an ADSL, Cable modem, LAN or 56k modem. # This program makes a link to the website http://pi.lacim.uqam.ca/eng and can make request # to the website within a maple session. # The program is self-contained and DO not need anything else than maple and a connection to the internet. # There are 3 functions ; pilook, pismart and pidev (other functions are under development). # pilook makes a request to the Plouffe's Inverter and returns 1 answer (is there is any). # pismart is a personal souped-up version of the pilook function that makes 140 requests to the inverter. # the input needs to be a real floating point number or something that maple can evaluate to a real # number. The working precision is 24 digits, 16 are customary in order to return valid answers. # To make it to work : open a maple session, type read `inverter.txt`; # The name of the file can be anything. # Type any real number and watch it run. # pismart makes 200 variations on the input ans tries to see if there would not be any collision # against the tables. There are currently 201 million constants in the Inverter. # pidev expands the input x into 17 different development like the continued fractions, binary expansion, # Fibonacci representation and tries to find rational polynomial representation of x. # # Examples, pilook(X); minimal precision is 16 digits, this is a lookup to # Plouffe's inverter and returns the shortest answer (in characters). # # pilll(X); precision has to be from 24 to 110 digits, will try if the number # X is a linear combination of known constants like Pi, gamma, sqrt(2). # There are 127 tables of constants within the program. # # pismart(X); minimal precision is 16 digits, preferably 24. This portion # tries simple combination of the number X and simple functions. # There are 200 lookups made to the Inverter, uses the <socket> # function of Maple to make a request using <http://....>. # pidev(X); minimal precision is 16 digits. That portion expands the number # in various bases like base 2, Fibonacci base, Egyptian fraction etc # and tries if the result is a sequence which is a rational polynomial. # There are 17 different tests in this portion. # For example you may try pidev(tan(1.0)); to see the result. # # pialg(X); Minimal precision is preferably 24 digits. This routine will try # to find if X is the root of a polynomial equation of up to [sqrt(Digits)]. # For example with 64 digits will test if X is a root of a 8'th degree pol. # # piall(X); That one tries them all, pismart, pidev, pialg and pilll. The necessary # precision is adjusted within the routine. # # This program is FREE and can be distributed to anyone as long as the source is mentioned. ########################################################################################################### # # Plouffe's Inverter # # 1XS1?. .. # ?XXXXXXXSSXSSOIOXXXXXXXSSIIOSOC # ;;?1IC1?;;;: .:;;:. . # SXXXXXXXXXXXXXXXXXSXXXSOSOSOCIII1 # :?!!!!;!?!;::..::;;;;;;;!!!;!?. # ?IXXXXXXXXXXXSXSSSSSSSSSOSSSXXX=. # ?XXXXXXXXXXXXXXXXXXSSSSSCXX1IIICI? # =X :? S? : # 11 ;1 X: .:: # I= = X ;. :::. # ??;OI?=?;; ? C . # :;;;S=!!!?!: ?. ?? ;?? # I . : :S !! # ? ! O! # ! :? :C # .? !; !: # .! !. ?. # ;; =; : # !:; ; : # !;? !. # ?.I. !. # ?:XI :! # ;?XX. .???!;!!=I? ?! ;! # ;.XXC .!!?!;!!!!;!. ?O=?!! # ; OXX: :;; ;1XXX # ;C?. :::....... !SSO?!? # ?OII1CCOOO=. ?CXXX # !!!;!;;;;;: !? # # original drawing by Yves Chiricota (1995), Universite du Quebec a Chicoutimi ##############################################################################