Pol

Represents a polynomial from F_2[X].

Members

benchmarkPolDeg void benchmarkPolDeg(): Undocumented in source. Be warned that the author may not have intended to support it.
benchmarkPolDiv void benchmarkPolDiv(): Undocumented in source. Be warned that the author may not have intended to support it.
benchmarkPolDivMod void benchmarkPolDivMod(): Undocumented in source. Be warned that the author may not have intended to support it.
benchmarkPolGetRandom void benchmarkPolGetRandom(): Undocumented in source. Be warned that the author may not have intended to support it.
benchmarkPolIrreducible void benchmarkPolIrreducible(): Undocumented in source. Be warned that the author may not have intended to support it.
benchmarkPolMod void benchmarkPolMod(): Undocumented in source. Be warned that the author may not have intended to support it.
expand string expand(): Returns the string representation of the polynomial x.
mulMod Pol mulMod(Pol f, Pol g): Computes this*f mod g.
opBinary Pol opBinary(Pol y): Returns this+y.
opBinary Pol opBinary(Pol y): Returns this*y. When an overflow occurs, throws an exception.
opBinary Pol opBinary(Pol d): Returns the integer division result this / d.
opBinary Pol opBinary(Pol d): Returns the remainder of this / d.
parseBin Pol parseBin(string s): Undocumented in source. Be warned that the author may not have intended to support it.
toString string toString(): Returns the coefficients in hex.

deg int deg [@property getter]: Returns the degree of the polynomial. If this is zero, -1 is returned.
irreducible bool irreducible [@property getter]: Returns true iff x is irreducible over F_2. This function uses Ben Or's reducibility test. For details see "Tests and Constructions of Irreducible Polynomials over Finite Fields".

derive Pol derive(R source): Returns an irreducible polynomial of degree 53 (largest prime number below 64-8) by reading bytes from source. There are (2^53-2/53) irreducible polynomials of degree 53 in F_2[X], c.f. Michael O. Rabin (1981): "Fingerprinting by Random Polynomials", page 4. If no polynomial could be found in one million tries, an error is returned.
divMod Pol[2] divMod(Pol x, Pol d): Returns quotient and remainder from division [x / d, x % d], see https://en.wikipedia.org/wiki/Division_algorithm
gcd Pol gcd(Pol x, Pol f): Computes the Greatest Common Divisor of x and f.
getRandom Pol getRandom(): Returns a new random irreducible polynomial of degree 53 using the default rndGen as source. It is equivalent to calling derive(generate!(() => uniform!ubyte)).