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### `gcd`, `gcdz`

`gcd(poly1,poly2[,mod])`
`gcdz(poly1,poly2)`
  :: The polynomial greatest common divisor of poly1 and poly2.

return
  polynomial
poly1 poly2
  polynomial
mod
  prime

- Functions `gcd()` and `gcdz()` return the greatest common divisor (GCD) of the given two polynomials.
- Function `gcd()` returns an integral polynomial GCD over the rational number field. The coefficients are normalized such that their GCD is 1. It returns 1 in case that the given polynomials are mutually prime.
- Function `gcdz()` works for arguments of integral polynomials, and returns a polynomial GCD over the integer ring, that is, it returns `gcd()` multiplied by the contents of all coefficients of the two input polynomials.
- `gcd()` computes the GCD over GF(mod) if mod is specified.
- Polynomial GCD is computed by an improved algorithm based on Extended Zassenhaus algorithm.
- GCD over a finite field is computed by PRS algorithm and it may not be efficient for large inputs and co-prime inputs.

    [0] gcd(12*(x^2+2*x+1)^2,18*(x^2+(y+1)*x+y)^3);
    x^3+3*x^2+3*x+1
    [1] gcdz(12*(x^2+2*x+1)^2,18*(x^2+(y+1)*x+y)^3);
    6*x^3+18*x^2+18*x+6
    [2] gcd((x+y)*(x-y)^2,(x+y)^2*(x-y));
    x^2-y^2
    [3] gcd((x+y)*(x-y)^2,(x+y)^2*(x-y),2);
    x^3+y*x^2+y^2*x+y^3

`References`
  section `igcd`,`igcdcntl`.

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