/**************************************************************************\
MODULE: zz_pEX
SUMMARY:
The class zz_pEX represents polynomials over zz_pE,
and so can be used, for example, for arithmentic in GF(p^n)[X].
However, except where mathematically necessary (e.g., GCD computations),
zz_pE need not be a field.
\**************************************************************************/
#include <NTL/lzz_pE.h>
#include <NTL/vec_lzz_pE.h>
class zz_pEX {
public:
zz_pEX(); // initial value 0
zz_pEX(const zz_pEX& a); // copy
zz_pEX& operator=(const zz_pEX& a); // assignment
zz_pEX& operator=(const zz_pE& a);
zz_pEX& operator=(const zz_p& a);
zz_pEX& operator=(long a);
~zz_pEX(); // destructor
zz_pEX(long i, const zz_pE& c); // initilaize to X^i*c
zz_pEX(long i, const zz_p& c);
zz_pEX(long i, long c);
};
/**************************************************************************\
Comparison
\**************************************************************************/
long operator==(const zz_pEX& a, const zz_pEX& b);
long operator!=(const zz_pEX& a, const zz_pEX& b);
long IsZero(const zz_pEX& a); // test for 0
long IsOne(const zz_pEX& a); // test for 1
// PROMOTIONS: ==, != promote {long,zz_p,zz_pE} to zz_pEX on (a, b).
/**************************************************************************\
Addition
\**************************************************************************/
// operator notation:
zz_pEX operator+(const zz_pEX& a, const zz_pEX& b);
zz_pEX operator-(const zz_pEX& a, const zz_pEX& b);
zz_pEX operator-(const zz_pEX& a);
zz_pEX& operator+=(zz_pEX& x, const zz_pEX& a);
zz_pEX& operator+=(zz_pEX& x, const zz_pE& a);
zz_pEX& operator+=(zz_pEX& x, const zz_p& a);
zz_pEX& operator+=(zz_pEX& x, long a);
zz_pEX& operator++(zz_pEX& x); // prefix
void operator++(zz_pEX& x, int); // postfix
zz_pEX& operator-=(zz_pEX& x, const zz_pEX& a);
zz_pEX& operator-=(zz_pEX& x, const zz_pE& a);
zz_pEX& operator-=(zz_pEX& x, const zz_p& a);
zz_pEX& operator-=(zz_pEX& x, long a);
zz_pEX& operator--(zz_pEX& x); // prefix
void operator--(zz_pEX& x, int); // postfix
// procedural versions:
void add(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); // x = a + b
void sub(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); // x = a - b
void negate(zz_pEX& x, const zz_pEX& a); // x = - a
// PROMOTIONS: +, -, add, sub promote {long,zz_p,zz_pE} to zz_pEX on (a, b).
/**************************************************************************\
Multiplication
\**************************************************************************/
// operator notation:
zz_pEX operator*(const zz_pEX& a, const zz_pEX& b);
zz_pEX& operator*=(zz_pEX& x, const zz_pEX& a);
zz_pEX& operator*=(zz_pEX& x, const zz_pE& a);
zz_pEX& operator*=(zz_pEX& x, const zz_p& a);
zz_pEX& operator*=(zz_pEX& x, long a);
// procedural versions:
void mul(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); // x = a * b
void sqr(zz_pEX& x, const zz_pEX& a); // x = a^2
zz_pEX sqr(const zz_pEX& a);
// PROMOTIONS: *, mul promote {long,zz_p,zz_pE} to zz_pEX on (a, b).
void power(zz_pEX& x, const zz_pEX& a, long e); // x = a^e (e >= 0)
zz_pEX power(const zz_pEX& a, long e);
/**************************************************************************\
Shift Operations
LeftShift by n means multiplication by X^n
RightShift by n means division by X^n
A negative shift amount reverses the direction of the shift.
\**************************************************************************/
// operator notation:
zz_pEX operator<<(const zz_pEX& a, long n);
zz_pEX operator>>(const zz_pEX& a, long n);
zz_pEX& operator<<=(zz_pEX& x, long n);
zz_pEX& operator>>=(zz_pEX& x, long n);
// procedural versions:
void LeftShift(zz_pEX& x, const zz_pEX& a, long n);
zz_pEX LeftShift(const zz_pEX& a, long n);
void RightShift(zz_pEX& x, const zz_pEX& a, long n);
zz_pEX RightShift(const zz_pEX& a, long n);
/**************************************************************************\
Division
\**************************************************************************/
// operator notation:
zz_pEX operator/(const zz_pEX& a, const zz_pEX& b);
zz_pEX operator/(const zz_pEX& a, const zz_pE& b);
zz_pEX operator/(const zz_pEX& a, const zz_p& b);
zz_pEX operator/(const zz_pEX& a, long b);
zz_pEX operator%(const zz_pEX& a, const zz_pEX& b);
zz_pEX& operator/=(zz_pEX& x, const zz_pEX& a);
zz_pEX& operator/=(zz_pEX& x, const zz_pE& a);
zz_pEX& operator/=(zz_pEX& x, const zz_p& a);
zz_pEX& operator/=(zz_pEX& x, long a);
zz_pEX& operator%=(zz_pEX& x, const zz_pEX& a);
// procedural versions:
void DivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEX& b);
// q = a/b, r = a%b
void div(zz_pEX& q, const zz_pEX& a, const zz_pEX& b);
void div(zz_pEX& q, const zz_pEX& a, const zz_pE& b);
void div(zz_pEX& q, const zz_pEX& a, const zz_p& b);
void div(zz_pEX& q, const zz_pEX& a, long b);
// q = a/b
void rem(zz_pEX& r, const zz_pEX& a, const zz_pEX& b);
// r = a%b
long divide(zz_pEX& q, const zz_pEX& a, const zz_pEX& b);
// if b | a, sets q = a/b and returns 1; otherwise returns 0
long divide(const zz_pEX& a, const zz_pEX& b);
// if b | a, sets q = a/b and returns 1; otherwise returns 0
/**************************************************************************\
GCD's
These routines are intended for use when zz_pE is a field.
\**************************************************************************/
void GCD(zz_pEX& x, const zz_pEX& a, const zz_pEX& b);
zz_pEX GCD(const zz_pEX& a, const zz_pEX& b);
// x = GCD(a, b), x is always monic (or zero if a==b==0).
void XGCD(zz_pEX& d, zz_pEX& s, zz_pEX& t, const zz_pEX& a, const zz_pEX& b);
// d = gcd(a,b), a s + b t = d
/**************************************************************************\
Input/Output
I/O format:
[a_0 a_1 ... a_n],
represents the polynomial a_0 + a_1*X + ... + a_n*X^n.
On output, all coefficients will be polynomials of degree < zz_pE::degree() and
a_n not zero (the zero polynomial is [ ]). On input, the coefficients
are arbitrary polynomials which are reduced modulo zz_pE::modulus(),
and leading zeros stripped.
\**************************************************************************/
istream& operator>>(istream& s, zz_pEX& x);
ostream& operator<<(ostream& s, const zz_pEX& a);
/**************************************************************************\
Some utility routines
\**************************************************************************/
long deg(const zz_pEX& a); // return deg(a); deg(0) == -1.
const zz_pE& coeff(const zz_pEX& a, long i);
// returns a read-only reference to the coefficient of X^i, or zero if
// i not in range
const zz_pE& LeadCoeff(const zz_pEX& a);
// read-only reference to leading term of a, or zero if a == 0
const zz_pE& ConstTerm(const zz_pEX& a);
// read-only reference to constant term of a, or zero if a == 0
void SetCoeff(zz_pEX& x, long i, const zz_pE& a);
void SetCoeff(zz_pEX& x, long i, const zz_p& a);
void SetCoeff(zz_pEX& x, long i, long a);
// makes coefficient of X^i equal to a; error is raised if i < 0
void SetCoeff(zz_pEX& x, long i);
// makes coefficient of X^i equal to 1; error is raised if i < 0
void SetX(zz_pEX& x); // x is set to the monomial X
long IsX(const zz_pEX& a); // test if x = X
void diff(zz_pEX& x, const zz_pEX& a); // x = derivative of a
zz_pEX diff(const z
WinNTL-5_4_2 大数库
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2009-01-21
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WinNTL-5_4_2 大数库 （310个子文件） 
BerlekampTestIn 5KB BerlekampTestOut 5KB CanZassTestIn 5KB CanZassTestOut 5KB CharPolyTestIn 1KB CharPolyTestOut 55KB ZZXFactoring.cpp 81KB GF2X1.cpp 64KB lzz_pX.cpp 63KB ZZ_pEX.cpp 61KB lzz_pEX.cpp 61KB GF2EX.cpp 60KB ZZ_pX.cpp 57KB G_LLL_QP.cpp 47KB LLL_QP.cpp 46KB ZZX1.cpp 43KB ZZ.cpp 43KB GF2EXFactoring.cpp 39KB GF2X.cpp 38KB LLL_FP.cpp 38KB ZZ_pX1.cpp 37KB lzz_pX1.cpp 36KB lzz_pXFactoring.cpp 36KB ZZ_pXFactoring.cpp 35KB G_LLL_FP.cpp 34KB RR.cpp 34KB GF2XFactoring.cpp 32KB lzz_pEXFactoring.cpp 29KB ZZ_pEXFactoring.cpp 29KB G_LLL_XD.cpp 29KB LLL_RR.cpp 28KB G_LLL_RR.cpp 28KB LLL_XD.cpp 28KB mat_ZZ.cpp 25KB MakeDesc.cpp 25KB mat_lzz_p.cpp 18KB quad_float.cpp 18KB mat_lzz_pE.cpp 17KB mat_ZZ_pE.cpp 17KB mat_ZZ_p.cpp 16KB ZZX.cpp 16KB xdouble.cpp 16KB mat_GF2.cpp 15KB mat_GF2E.cpp 15KB LLL.cpp 13KB mat_RR.cpp 13KB vec_GF2.cpp 12KB gen_lip_gmp_aux.cpp 10KB FFT.cpp 9KB WordVector.cpp 8KB QuickTest.cpp 6KB ZZ_p.cpp 6KB newnames.cpp 5KB vec_lzz_p.cpp 5KB lzz_p.cpp 4KB vec_ZZ_p.cpp 4KB vec_lzz_pE.cpp 3KB vec_ZZ_pE.cpp 3KB GF2E.cpp 3KB vec_GF2E.cpp 3KB lzz_pE.cpp 3KB ZZ_pE.cpp 3KB LLLTest.cpp 3KB subset.cpp 3KB vec_RR.cpp 3KB vec_ZZ.cpp 3KB HNF.cpp 2KB ctools.cpp 2KB tools.cpp 2KB gen_gmp_aux.cpp 2KB GF2EXTest.cpp 2KB mat_poly_ZZ.cpp 2KB QuadTest.cpp 2KB mat_poly_ZZ_p.cpp 2KB mat_poly_lzz_p.cpp 2KB BitMatTest.cpp 2KB FacVec.cpp 2KB GF2XVec.cpp 2KB ZZVec.cpp 1KB ZZXCharPoly.cpp 1KB BerlekampTest.cpp 1KB CanZassTest.cpp 1KB lzz_pXCharPoly.cpp 1KB ZZ_pXCharPoly.cpp 1KB ZZXFacTest.cpp 1KB MoreFacTest.cpp 1KB fileio.cpp 1000B GF2.cpp 891B ZZ_pEXTest.cpp 889B lzz_pEXTest.cpp 884B MatrixTest.cpp 866B GetTime1.cpp 613B GetTime4.cpp 599B GetTime.cpp 599B GetTime3.cpp 550B GetTime2.cpp 515B MakeDescAux.cpp 510B pair_ZZ_pEX_long.cpp 416B pair_lzz_pEX_long.cpp 415B pair_lzz_pX_long.cpp 402B共 310 条
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