h.irpgen

来自「强大的数学工具包」· IRPGEN 代码 · 共 42 行

                            * * * * * * *
                            *  irpgen   *
                            * * * * * * *

        "irreducible polynomial generator"
        SYNTAX: X = irpgen(p,A,n,t)
                X = irpgen(A,n,t)
                X = irpgen(A,n)

        p is a single precision prime.
        A is a variable.
        n is a single precision positive integer.
        If p or the current modulus is 2, then t=0 or t is an odd
        single precision integer, > 1 and <=(n+1). Otherwise t=0 or t=3. 

        In the first two cases, X is assigned a univariate irreducible 
        polynomial of degree n in the variable A over Z/pZ, where in the 
        second case p is the current modulus, which must be a single 
        precision prime. If t=0, then X is any irreducible polynomial. 
        Otherwise, X is an irreducible polynomial with t nonzero 
        coefficients, if such a polynomial exists. If such a polynomial 
        does not exist, X is any irreducible polynomial of degree n.

        In the third case, X is assigned a univariate irreducible
        polynomial of degree n in the variable A over GF(p^m), which
        is the current Galois field.


        Example 1: (correct)

                X = irpgen(2,A,8,3)

        
        Example 2: (correct)

                X = irpgen(A,8,0) 


        Example 3: (correct)

                X = irpgen(A,8)