HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 186

Finite arithmetic rings in the calculator All along we have defined our finite arithmetic operation so that the results are always positive. The modular arithmetic system in the calculator is set so that the ring of modulus n includes the numbers -n/2+1, ...,-1, 0, 1,...,n/2-1, n/2, if n is even, and -(n-1)/2, -(n-3)/2,...,-1,0,1,...,(n-3)/2, (n-1)/2, if n is odd. For example, for n = 8 (even), the finite arithmetic ring in the calculator includes the numbers: (-3,-2,-1,0,1,3,4), while for n = 7 (odd), the corresponding calculator's finite arithmetic ring is given by (-3,-2,-1,0,1,2,3). Modular arithmetic in the calculator To launch the modular arithmetic menu in the calculator select the MODULO sub-menu within the ARITHMETIC menu („Þ). The available menu includes functions: ADDTMOD, DIVMOD, DIV2MOD, EXPANDMOD, FACTORMOD, GCDMOD, INVMOD, MOD, MODSTO, MULTMOD, POWMOD, and SUBTMOD. Brief descriptions of these functions were provided in an earlier section. Next we present some applications of these functions. Setting the modulus (or MODULO) The calculator contains a variable called MODULO that is placed in the {HOME CASDIR} directory and will store the magnitude of the modulus to be used in modular arithmetic. The default value of MODULO is 13. To change the value of MODULO, you can either store the new value directly in the variable MODULO in the subdirectory {HOME CASDIR} Alternatively, you can store a new MODULO value by using function MODSTO. Modular arithmetic operations with numbers To add, subtract, multiply, divide, and raise to a power using modular arithmetic you will use the functions ADDTMOD, SUBTMOD, MULTMOD, DIV2MOD and DIVMOD (for division), and POWMOD. In RPN mode you need to enter the two numbers to operate upon, separated by an [ENTER] or an [SPC] entry, and then press the corresponding modular arithmetic function. For example, using a modulus of 12, try the following operations: Page 5-15