h.func

来自「强大的数学工具包」· FUNC 代码 · 共 430 行

                                * * * * * * *
                                *    func   *
                                * * * * * * *

        The following functions and operations are available in simcalc:

        +           aftopr      discec     linequ      putoct     
        -           arccos      discnf     ln          real        
        *           arccot      dmconstr   local       red        
        :           arcosh      dowhile    log2        reg      
        ^           arcoth      eccoef     log10       relcln      
        /           arcsin      ecgnp      mam2        resul
        !           arctan      ecinf      max         return
        [ ]         areptsli    ecnpscf    mcoef       rk
        ==          arsinh      egcd       mex         rk2d
        !=          artanh      eival      min         rkbsd
        <           aval        elform     minim       rkg2d
        <=          basismwg    elog       minor       root
        >           binom       elsubst    mod         rper
        >=          bitrans     exp        mtoi        scalar
        &&          break       fact p     mval        sfp
        ||          ceil        faintp     nftopol     sgn
                    chcoef      floor      norm        sgnfeq   
                    chinrem     fltoi      np          sin     
                    chpol       for        npfe        sinh    
                    classnum    forprime   nthei       sort    
                    coef        forstep    ntpair      sqrt
                    cond        fp         num         sum     
                    conjug      f1root     ord         swnf
                    cont        froot      ordtsg      taalg
                    continue    gcd        pconstr     tan
                    cos         getb       pfact       tanh
                    cosh        gethex     pgen        tavb2
                    cot         getoct     phi         tavb4
                    coth        gftopol    ppconstr    tavb6
                    cper        herm       prfunc      tavb8
                    curec       if         prim        tavc4
                    curgf       imag       print       tavc6
                    curgf2bit   intbas     pripgen     tofl 
                    curmod      intcoef    prod        tors
                    curnf       integr     proot       trace 
                    decl        irpgen     prtoaf      transp
                    declaw      ispprime   ptcoef      unit
                    deg         isprime    putb        vcoef
                    denom       isptec     putbits     whei
                    deriv       isqrt      putGF2bit   while
                    derivL      jacsym     puthex      zmconstr
                    det         jinv       puto        zvconstr
                    disc        lcm

        '+'             means   addition;

        '-'                     subtraction;

        '*'                     multiplication;

        ':'                     (integer part of) quotient;

        '^'                     exponentiation;

        '/'                     division;

        '!'                     factorial;

        '[ ]'                   absolute value;

        '=='                    equal;

        '!='                    not equal;

        '<'                     less;

        '<='                    less or equal;

        '>'                     greater;

        '>='                    greater or equal;

        '&&'                    and;

        '||'                    or;

        'aftopr'                conversion from affine to projective 
                                representation;

        'arccos'                arcus cosinus;

        'arccot'                arcus cotangens;

        'arcosh'                area cosinus hyperbolicus;

        'arcoth'                area cotangens hyperbolicus;

        'arcsin'                arcus sinus;

        'arctan'                arcus tangens;

        'areptsli'              are points linearly independent? ;

        'arsinh'                area sinus hyperbolicus;

        'artanh'                area tangens hyperbolicus;

        'aval'                  additive m-adic value;

        'basismwg'              basis of Mordell-Weil-group;

        'binom'                 binomial coefficient;

        'bitrans'               birational transformation of an elliptic
                                curve or a point;

        'break'                 break;

        'ceil'                  smallest integer greater or equal;

        'chcoef'                change coefficient of a polynomial;
         
        'chinrem'               chinese remainder algorithm;

        'chpol'                 characteristic polynomial;

        'classnum'              class number;

        'coef'                  coefficient of a polynomial;

        'cond'                  conductor;

        'conjug'                conjugate;

        'cont'                  content;

        'continue'              continue;

        'cos'                   cosinus;

        'cosh'                  cosinus hyperbolicus;

        'cot'                   cotangens;
 
        'coth'                  cotangens hyperbolicus;

        'cper'                  complex period;

        'curec'                 current elliptic curve;

        'curgf'                 current Galois-field;

        'curgf2bit'             current Galois-field over characteristic 2,
                                special bit representation;

        'curmod'                current modulus;

        'curnf'                 current algebraic number field;

        'decl'                  declaration of functions;

        'declaw'                decomposition law;

        'deg'                   degree;

        'denom'                 denominator;

        'deriv'                 derivation;
        
        'derivL'                derivation L-series;

        'det'                   determinant;

        'disc'                  discriminant of a polynomial;

        'discec'                discriminant of an elliptic curve;

        'discnf'                discriminant of a number field;

        'dmconstr'              diagonal matrix construction;

        'dowhile'               dowhile-loop;

        'eccoef'                elliptic curve coefficient;

        'ecgnp'                 elliptic curve with given number of points;
                                (only in SIEMENS-version)

        'ecinf'                 elliptic curve information;

        'ecnpscf'               elliptic curve with point order with small cofactor;

        'egcd'                  extended greatest common divisor;

        'eival'                 eigenvalues and irreducible factors of the 
                                characteristic polynomial;

        'elform'                elementary divisor form and cofactors;

        'elog'                  elliptic logarithm;

        'elsubst'               element substitution in matrices or vectors;

        'exp'                   exponential function;

        'fact'                  factorization;

        'faintp'                finding all integral points;

        'floor'                 greatest integer less or equal;

        'fltoi'                 floating points to integers;

        'for'                   for-loop;

        'forprime'              forprime-loop;

        'forstep'               forstep-loop;

        'fp'                    finding point;

        'f1root'                finding one root;

        'froot'                 finding root;

        'gcd'                   greatest common divisor;

        'getb'                  bit representation to integer;

        'gethex'                hexadecimal representation to integer;

        'getoct'                octal representation to integer;

        'gftopol'               Galois-field to polynomial;

        'herm'                  Hermite normal form;

        'if'                    if-statement;

        'imag'                  imaginary part;
 
        'intbas'                integral basis;

        'intcoef'               elliptic curve with integer coefficients;

        'integr'                integration;

        'irpgen'                irreducible polynomial generator;

        'ispprime'              is pseudoprime ? ;

        'isprime'               is prime ? ;

        'isptec'                is point on elliptic curve ? ; 

        'isqrt'                 integral part of square root;

        'jacsym'                Jacobi symbol;

        'jinv'                  j-invariant;

        'lcm'                   least common multiple;

        'linequ'                solution of a system of linear equations;

        'ln'                    natural logarithm;

        'local'                 local variable declaration;

        'log2'                  integer part of the logarithm, base 2;

        'log10'                 1 + integer part of the logarithm,
                                base 10;
       
        'mam2'                  matrix over Z/2Z in special bit notation;

        'max'                   maximum;

        'mcoef'                 matrix coefficient;

        'mex'                   exponentiation in Z/mZ;

        'min'                   minimum;

        'minim'                 global minimal model;

        'minor'                 minor matrix;

        'mod'                   module homomorphism;

        'mtoi'                  modular to integer;

        'mval'                  multiplicative m-adic value;

        'nftopol'               number field to polynomial;

        'norm'                  norm of an algebraic number;

        'np'                    number of points;

        'npfe'                  number of points after field extension;

        'num'                   numerator;

        'nthei'                 Neron-Tate height;

        'ntpair'                Neron-Tate pairing;

        'ord'                   order;

        'ordtsg'                order of Tate-Shafarevic-group;

        'pconstr'               prime construction; 

        'pfact'                 factorization modulo prime;

        'pgen'                  prime generator;

        'phi'                   Eulerian phi-function;

        'ppconstr'              pseudo prime construction; 

        'prfunc'                primitive function;

        'prim'                  primitive part;

        'print'                 print;

        'pripgen'               primitive polynomial generator;

        'prod'                  product;

        'proot'                 primitive root;

        'prtoaf'                conversion from projective to affine 
                                representation;

        'ptcoef'                point on elliptic curve coefficient;

        'putb'                  put bit representation;

        'putbits'               display bit representation;

        'putGF2bit'             put Galois-field element in characteristic 2, 
                                special bit representation"

        'puthex'                put hexadecimal representation;

        'puto'                  display internal representation;

        'putoct'                put octal representation;

        'real'		        real part;

        'red'                   reduction of an elliptic curve;

        'reg'                   regulator;

        'relcln'                relative class number;

        'resul'                 resultant;

        'return'                return;
        
        'rk'                    rank;

        'rk2d'                  rank via 2-descent;

        'rkbsd'                 rank via Birch and Swinnerton-Dyer conjecture;

        'rkg2d'                 rank via general 2-descent;

        'root'                  root;

        'rper'                  real period;

        'scalar'                euclidian scalar product;

        'sfp'                   squarefree part;

        'sgn'                   sign;

        'sgnfeq'                sign of functional equation;

        'sin'                   sinus;

        'sinh'                  sinus hyperbolicus;

        'sort'                  sort polynomial;

        'sqrt'                  square root;

        'sum'                   sum;

        'swnf'                  short Weierstrass normal form;

        'taalg'                 Tate's algorithm;

        'tan'                   tangens;

        'tanh'                  tangens hyperbolicus;

        'tavb2'                 Tate's value b2;

        'tavb4'                 Tate's value b4;

        'tavb6'                 Tate's value b6;

        'tavb8'                 Tate's value b8;

        'tavc4'                 Tate's value c4;

        'tavc6'                 Tate's value c6;

        'tofl'                  to floating points;

        'tors'                  torsion group;

        'trace'                 trace;

        'transp'                transpose;

        'unit'                  unit group;

        'vcoef'                 vector coefficient;

        'whei'                  Weil height;

        'while'                 while-loop;

        'zmconstr'              zero matrix construction;

        'zvconstr'              zero vector construction.