VincSCalc - VincS Theorem
Contents
1. 1000 Up to now for XXLInt data type only basic operations are supported Other operations are currently under development 3 Operations with Integers 3 1 Dedicated keyboard and parameters When the BigInt data type is selected as well as in the coming implementation of XXInt data type a dedicated portion of keyboard will be shown enabled with suitable operations and function for such kind of data Also some settable parameters are shown enabled This parameters can be left as they are in default value or may be changed by the user to fit his her needs Modulo 0 pCert 200 baseXXL 1000 bitsz 128 3 2 Parameters Shortly explained these parameters one by one Modulo after every operation the final result will be automatically re calculated to be equal to result MOD Modulo Very useful working with modular arithmetic pCert is the certainty given when using the Java BigIntegers library functions related to determine if a number is a prime number or not This because of course these functions use probabilistic methods to determine it Taken from Oracle documentation certainty a measure of the uncertainty that the caller is willing to tolerate The probability that the new BigInteger represents a prime number will exceed 1 1 27 The execution time of this constructor is proportional to the value of this parameter Some functions affected by it are so x pP is x pri2. area that may become vertically scrollable for deeply nested calculation e Input Output operand fields horizontally scrollable to allow arbitrary hugeness of integers as huge as your hardware will allow e Digit Keyboard disabled automatically when data is consistent to avoid involuntary overwrite only operators or clears input are accepted e 5 Memories Absolute MAx on the left side of calculation area these are used by the calculator in order to give extra output see as example HMPx functions The panel can be horizontally shrinked to permit the widest calculation area as possible e 5 Memories Editable MEx on the right side of calculation area the user can store results of operation by input arrow key in the dedicated panel as well as input directly a value inside the field giving also a name to any stored value in order to remind the meaning of such data just close below the stored value Recall the value in the calculation area input it is so a simple as a click on the counter output arrow button in the panel The panel can be horizontally shrinked to permit the widest calculation area as possible e 3 Data Types Double BigInt eger XXLInt eger e 4 numeric bases only for integer types decimal octal hexdecimal binary e Calculations can be performed run time for a quick response or also postponed to the operator request to keep track and double check RunTm checkbox is run time by default In case
3. of postponed operations the user could also eventually go back BkS button in order to correct his input nteger calculations can be performed in Modulo settable directly in its field allowing experiments with modular arithmetic e Integers primality test in probabilistic and deterministic methods e Integers HowManyPrimes functions to test the Gauss formulas logarithmic Integral Logarithmic or the Riemann s derived formulas oon 2 3 Software s security The VincSCalc is written in Java source code Java offers the advantage of a great emphasis in security matters embedded in its constantly upgraded technology in order to avoid deployment of viruses and malicious software In facts the VincSCalc is a signed application that means that the identity of the software developer has been verified by a Certifications Authority Symantec Thawte and that the software cannot be modified in order to introduce viruses or similar hacking attacks because it has been encrypted with the same signature One of the main advantages of using Java is the availability of the Big nteger library a class derived from Numbers class particularly suitable for Numbers Theory experiments such as prime numbers research and application such as communication security cryptography and similar technology So the VincSCalc among classic Double precision data type has built in the BigInt data type that allows to perform such kind of calculation 2 4 Num
4. VincSCalc User Manual Vincenzo Sambito Author VincSCalc gmail com Revision 20150903 draft Related Software Release 0 2 x x x beta File VincSCalc User Manual 20151115 Sw Rel 0 2 x x x ENG Revision history Revision date Description xx Yyy 2015 Draft Copyright O This User Manual is a creative intellectual property of Vincenzo Sambito All rights reserved 2015 All other marks and brands reported in this book are properties of related owners Index 1 User License for VincSCalc softWare 2 FAG REPTILES 2l Introducing the VineS Cale ic ilaele Ze hey Feist 2 3 SOftWare S coal D nadocca ian aaaomaaeeeaeseoreteienss 24A N mber Data TYPES seee TU 2 4 1 Double precision Data pesci 242 Bip int Data Vy pe T bata geidaneesd as SM pelare 3 Operations with ntegers iue deine leer een iste 3 1 Dedicated keyboard and Dar dmielef s cosssccucacncsnssniiabtonedivaacansdeancaendentaendseangnasasetanwidearaponasstcns 3 2 Patel UU ULT 33 Keyboard e 1 User License for VincSCalc software We here just remind that the use of the software is underling to the acceptance of some conditions The only valid text that is valid as contract with the user is what reported when the user launch the software for the first time and that might be recalled back whenever the user would like having so the chan
5. ber Data Types The user can select the preferred data type by proper radio buttons provided in the GUI as shown in the pictures here below Double Bigint O XXLInt If a section of the calculator keyboard make sense only in a specific Data Type as example operation among integers for BigInt this will be enabled shown when that specific Data Type is selected 2 4 1 Double precision Data Type The most common data type for commercial calculators It offers a limited precision and it uses exponent of 10 Exx to extend wideness of numbers Using the Double precision Data Type the choice of numeric base for viewing is limited to Decimal see also Chapter about these radio buttons 2 4 2 BigInt Data Type Documentation about this data type is widely available at Oracle s as its class of object is the BigInteger embedded in JDK since v1 1 Sumarizing operations just among integers e arbitrary precision it relies only on hardware capability e Java optimized bytecode available for operations e etc etc 2 4 3 XXLInt Data Type In case of doubts up to now this is a proprietary Data Type derived by BigInteger since every single digit of this data type is a BigInteger The aim of this class of object is to extend the capability of BigInteger data type Digits are separed by a dot or comma in the future in order to support other cultures The maximum value of every digit is represented and can be chosen by baseXXL
6. ce to confirm refuse or keep as it is Once accepted the license terms of use and distribution the choice is stored in the computer Next time that it will be launched the software will be executed straight to the application window 2 Features 2 1 Introducing the VincSCalc As easily you can guess the VincSCalc is primarily a calculator which aim is to give the same features in the average of such kind of software The user can take advantage in daily use of the calculator Differently from many other calculators the VincSCalc is a multi language multi data type multi base the numeric base as the number is shown and input calculator More than this the VincSCalc has many other not common features that will be illustrated later on T j VincSCalc 0 2 2 0 0 201511152241 beta L PrioF Double Cl Caret v Runtm Generi1 gt Bigint XXLInt C BooIT L StpCa L ShowP Generi3 baseXXL 1000 bitsz 128 Dirichlet 5 Jews fi the User Manual BkS il Manuale Utente wwww vines it mailto VincSCalc gmail com VincSCalc Youtube page VincSCalc Blog 2 2 Key Features e One of the few calculators with resizable window up to full screen in order to allow a wide input output field for huge numbers horizontal and deeply nested calculation vertical e Nesting of calculation kept shown in calculation
7. erand x pP is x a prime number The test is done using a probabilistic method using pCert parameter see above If yes the operand becomes 1 true if not the operand becomes 0 false x pD is x a prime number The test is done using a deterministic method a sieve If yes the operand becomes 1 true if not the operand becomes 0 false and xor or bitwise operations among BigInteger operands CriBit clears the bit indicated by the given second parameter To obtain the result press Example 5 ClrBit 2 1 SetBit sets the bit indicated by the given second parameter To obtain the result press Example 5 SetBit 1 7 x y 0 the operand x currently in the operand field left shifted by y digits and filled by Os Note the shift is made digit wise and not bit wise that s if you choose Binary data type x y lt lt 0 the operand x currently in the operand field right shifted by y digits and filled by Os Note the shift is made digit wise and not bit wise that s if you choose Binary data type not the operand is sign reverted and subtracted by 1 differently by negation xBy the Newton s Binomial coefficient Pascal s triangle etcetera Example for the 2nd coefficient in the 3rd row 1 3 3 1 insert 3 xBy 1 and you will get 3 Example for the 3rd coefficient in the 4th row 1 4 6 4 1 insert 4 xBy 2 and you will get 6 GCD the Greater Common Divisor among the two operands Example 15 GCD 6 3 Mod the Modulo o
8. me probabilistically pNext next prime HMPP How Many Primes probabilistically etcetera bitSz is the number of bit size used to create for example a random prime number with the function pRandom random prime number Very useful with cryptography applications baseXXL the boundary of a digit in XXLInt data type Dirichlet a couple of parameters dedicated to the mathematician but not used to prove his theorem used by HMPC HowManyPrimesCalculated and HMPR HowManyPrimes in Range functions to determine not only how many primes there are in a given range but also how many primes of those are in the format z K w where z and w are the input parameters As we know the famous Dirichlet theorem says that z and w must not have common factors but as already told we don t care it s not a method to prove his theorem Note default value are z 6 and w 1 just because it s easy and funny to verify and also to prove that all prime numbers are in the format 6 K 1 but also how many of them are in the format 6 K versus how many are in the format 6 K 1 3 3 Keyboard Let s go now to calculator keys explained one by one pNext next prime greater than the number in the operand field Examples 0 gt 2 20 gt 23 pRand a random prime number with a bit size given by bitSz parameter Examples bitSz 8 and so 127 lt x lt 256 191 167 157 163 x the factorial of the given operand xit the primorial of the given op
9. onizzazione gt DTS Audio Control Panel ll Gestione credenziali Icone area di notifica amp Opzioni di indicizzazione Wl Personalizzazione e Programmi predefiniti VE SAP GUI Configuration Strumenti di amministrazione Windows CardSpace amp Attivit iniziali uL Barra delle applicazioni e menu Start Centro gestione dispositivi Windows Connessione RemoteApp e desktop Flash Player a Gestione dispositivi Java D Posta elettronica 6 Riconoscimento vocale I Schermo 2 Tastiera kid Windows Defender 0160 mq X Audio RA Caratteri Y Centro operativo 1 Data e ora lili Gadget per il desktop E Grafica HD Intel P Mouse A Opzioni risparmio energia MA Prestazioni del sistema Ripristino Sensore di posizione e altri sensori E Telefono e modem Windows Firewall Cerca nel Pannello di controllo P Visualizza per Icone piccole AutoPlay eo Centro accessibilit Fili Centro PC portatile Windows A Dispositivi e stampanti E Gestione colori wj Gruppo Home E Opzioni cartella S Paesee lingua a Programmi e funzionalit Risoluzione dei problemi gE Sistema 2 Windows Anytime Upgrade Windows Update B Pannello di controllo Java Visualizza le informazioni sulla versione del pannello di controllo Java Informazioni su Impostazioni di rete Le impostazioni di rete vengono utilizzate per effettuare le connessioni a Internet Per impos
10. perator Example 11 Mod 5 1 SHA1 the Secure Hash Algorithm revision 1 HowManyPrimes functions where x stands for Gauss s function symbol HMPR Mey how many primes calculated in a given range Note don t exceed a range of 10000000 numbers calculation lasts about 30 secs Example 100 HMPR 200 z 21 there are 21 primes among 100 and 200 HMPC Tx how many primes calculated in a given range starting from 0 Example 100 HMPC 25 there are 25 primes among 0 and 100 HMPP 7090 how many primes counted with probabilistic method in a given range starting from 0 Note don t exceed 1000000 calculation lasts about 10 secs range starting from 0 Note don t exceed 100000 calculation lasts about 10 secs Note HMPR and HMPC functions output is enhanced in MAx memories block also with the calculation of how many primes are in a specific format that the user can trim with dedicated Dirichlet parameters see above To be continued Appendix Sambito Vincenzo Documenti Immagini Musica Oggetti recenti Computer Pannello di controllo Dispositivi e stampanti Programmi predefiniti Guida e supporto tecnico Arresta i sistema gt JC B8 Pannello di controllo Tutti gli elementi del Pannello di controllo IA Modifica le impostazioni del computer EA Account utente 3 Backup e ripristino SE Centro connessioni di rete e condivis Centro sincr
11. tazione predefinita Java utilizza le impostazioni di rete del browser Web La modifica di queste impostazioni destinata ai soli utenti avanzati File temporanei Internet I file utilizzati nelle applicazioni Java vengono memorizzati in una speciale cartella per una successiva esecuzione pi rapida La modifica di queste impostazioni o l eliminazione dei file sono destinate ai soli utenti avanzati Java nel browser abilitato Vedere la scheda Sicurezza Note in case View Visualizza is not enlighted cannot be pressed click before on Apply button Applicazione
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