    /**************************************************************************\

    MODULE: vec_ZZ_p

    SUMMARY:

    Provides vectors over ZZ_p, along with some related operations.

    \**************************************************************************/

    #include <NTL/ZZ_p.h>
    #include <NTL/vec_ZZ.h>
    #include <NTL/vector.h>

    typedef Vec<ZZ_p> vec_ZZ_p; // backward compatibility

    void mul(vec_ZZ_p& x, const vec_ZZ_p& a, const ZZ_p& b);
    void mul(vec_ZZ_p& x, const vec_ZZ_p& a, long b);

    void mul(vec_ZZ_p& x, const ZZ_p& a, const vec_ZZ_p& b);
    void mul(vec_ZZ_p& x, long a, const vec_ZZ_p& b);
    // x = a * b

    void add(vec_ZZ_p& x, const vec_ZZ_p& a, const vec_ZZ_p& b);
    // x = a + b

    void sub(vec_ZZ_p& x, const vec_ZZ_p& a, const vec_ZZ_p& b);
    // x = a - b

    void clear(vec_ZZ_p& x);
    // x = 0 (length unchanged)

    void negate(vec_ZZ_p& x, const vec_ZZ_p& a);
    // x = -a

    long IsZero(const vec_ZZ_p& a);
    // test if a is the zero vector

    void InnerProduct(ZZ_p& x, const vec_ZZ_p& a, const vec_ZZ_p& b);
    // x = sum_{i=0}^{n-1} a[i]*b[i], where n = min(a.length(),
    // b.length())

    void InnerProduct(ZZ_p& x, const vec_ZZ_p& a, const vec_ZZ_p& b,
                      long offset);
    // x = sum_{i=offset}^{n-1} a[i]*b[i-offset], where n = min(a.length(),
    // b.length()+offset)

    void VectorCopy(vec_ZZ_p& x, const vec_ZZ_p& a, long n);
    vec_ZZ_p VectorCopy(const vec_ZZ_p& a, long n);
    // x = a copy of a of length exactly n.
    // The input is truncated or padded with zeroes, as necessary.

    void random(vec_ZZ_p& x, long n);  // x = random vector of length n
    vec_ZZ_p random_vec_ZZ_p(long n);

    // operator notation:

    vec_ZZ_p operator+(const vec_ZZ_p& a, const vec_ZZ_p& b);
    vec_ZZ_p operator-(const vec_ZZ_p& a, const vec_ZZ_p& b);

    vec_ZZ_p operator-(const vec_ZZ_p& a);

    // vector/scalar multiplication:

    vec_ZZ_p operator*(const vec_ZZ_p& a, const ZZ_p& b);
    vec_ZZ_p operator*(const vec_ZZ_p& a, long b);

    vec_ZZ_p operator*(const ZZ_p& a, const vec_ZZ_p& b);
    vec_ZZ_p operator*(long a, const vec_ZZ_p& b);

    // inner product:

    ZZ_p operator*(const vec_ZZ_p& a, const vec_ZZ_p& b);

    // assignment operator notation:

    vec_ZZ_p& operator+=(vec_ZZ_p& x, const vec_ZZ_p& a);
    vec_ZZ_p& operator-=(vec_ZZ_p& x, const vec_ZZ_p& a);

    vec_ZZ_p& operator*=(vec_ZZ_p& x, const ZZ_p& a);
    vec_ZZ_p& operator*=(vec_ZZ_p& x, long a);

    // Implementation note: the BlockConstruct routine has been customized
    // for ZZ_p so that when a vec_ZZ_p is grown, space for the needed
    // elements is allocated in one contiguous chunk.  This saves on calls to
    // malloc and free, and should also yield better locality of reference.
    // One connsequence of this is that swapping an element of a vec_ZZ_p
    // with another ZZ_p can not be implemented by pointer swap, and will in
    // this case be done by copy.