/**************************************************************************\
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);
typedef zz_pE coeff_type;
// ...
};
/**************************************************************************\
Accessing coefficients
The degree of a polynomial f is obtained as deg(f),
where the zero polynomial, by definition, has degree -1.
A polynomial f is represented as a coefficient vector.
Coefficients may be accesses in one of two ways.
The safe, high-level method is to call the function
coeff(f, i) to get the coefficient of X^i in the polynomial f,
and to call the function SetCoeff(f, i, a) to set the coefficient
of X^i in f to the scalar a.
One can also access the coefficients more directly via a lower level
interface. The coefficient of X^i in f may be accessed using
subscript notation f[i]. In addition, one may write f.SetLength(n)
to set the length of the underlying coefficient vector to n,
and f.SetMaxLength(n) to allocate space for n coefficients,
without changing the coefficient vector itself.
After setting coefficients using this low-level interface,
one must ensure that leading zeros in the coefficient vector
are stripped afterwards by calling the function f.normalize().
NOTE: the coefficient vector of f may also be accessed directly
as f.rep; however, this is not recommended. Also, for a properly
normalized polynomial f, we have f.rep.length() == deg(f)+1,
and deg(f) >= 0 => f.rep[deg(f)] != 0.
\**************************************************************************/
long deg(const zz_pEX& a); // return deg(a); deg(0) == -1.
const zz_pE& coeff(const zz_pEX& a, long i);
// returns the coefficient of X^i, or zero if i not in range
const zz_pE& LeadCoeff(const zz_pEX& a);
// returns leading term of a, or zero if a == 0
const zz_pE& ConstTerm(const zz_pEX& a);
// returns 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
zz_pE& zz_pEX::operator[](long i);
const zz_pE& zz_pEX::operator[](long i) const;
// indexing operators: f[i] is the coefficient of X^i ---
// i should satsify i >= 0 and i <= deg(f).
// No range checking (unless NTL_RANGE_CHECK is defined).
void zz_pEX::SetLength(long n);
// f.SetLength(n) sets the length of the inderlying coefficient
// vector to n --- after this call, indexing f[i] for i = 0..n-1
// is valid.
void zz_pEX::normalize();
// f.normalize() strips leading zeros from coefficient vector of f
void zz_pEX::SetMaxLength(long n);
// f.SetMaxLength(n) pre-allocate spaces for n coefficients. The
// polynomial that f represents is unchanged.
/**************************************************************************\
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&
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共311个文件
c:102个
h:90个
txt:58个
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ntl-6.0.0.tar.gz_rsa (311个子文件)
BerlekampTestIn 5KB
BerlekampTestOut 5KB
ZZXFactoring.c 77KB
GF2X1.c 69KB
ZZ_pEX.c 58KB
lzz_pEX.c 58KB
lzz_pX.c 57KB
GF2EX.c 57KB
ZZ_pX.c 53KB
G_LLL_QP.c 45KB
LLL_QP.c 44KB
ZZX1.c 41KB
ZZ.c 41KB
GF2X.c 40KB
GF2EXFactoring.c 37KB
LLL_FP.c 36KB
ZZ_pX1.c 34KB
lzz_pX1.c 34KB
lzz_pXFactoring.c 34KB
ZZ_pXFactoring.c 33KB
G_LLL_FP.c 33KB
RR.c 32KB
GF2XFactoring.c 31KB
G_LLL_XD.c 28KB
lzz_pEXFactoring.c 28KB
ZZ_pEXFactoring.c 28KB
LLL_RR.c 27KB
LLL_XD.c 26KB
G_LLL_RR.c 26KB
FFT.c 25KB
MakeDesc.c 24KB
mat_ZZ.c 24KB
mat_lzz_p.c 17KB
quad_float.c 17KB
mat_lzz_pE.c 16KB
mat_ZZ_pE.c 16KB
mat_ZZ_p.c 15KB
ZZX.c 15KB
xdouble.c 15KB
mat_GF2E.c 14KB
LLL.c 12KB
mat_GF2.c 12KB
vec_GF2.c 12KB
mat_RR.c 12KB
gen_lip_gmp_aux.c 10KB
WordVector.c 7KB
QuickTest.c 7KB
ZZ_p.c 6KB
newnames.c 5KB
vec_lzz_p.c 4KB
lzz_p.c 4KB
vec_ZZ_p.c 4KB
GF2E.c 3KB
vec_ZZ_pE.c 3KB
vec_lzz_pE.c 3KB
Poly1TimeTest.c 3KB
vec_GF2E.c 3KB
lzz_pE.c 3KB
ZZ_pE.c 3KB
LLLTest.c 3KB
subset.c 3KB
tools.c 2KB
MulTimeTest.c 2KB
ctools.c 2KB
HNF.c 2KB
DispSettings.c 2KB
vec_RR.c 2KB
PolyTimeTest.c 2KB
vec_ZZ.c 2KB
GF2XTimeTest.c 2KB
gen_gmp_aux.c 2KB
InitSettings.c 2KB
GF2EXTest.c 2KB
mat_poly_ZZ.c 2KB
GF2XTest.c 2KB
QuadTest.c 2KB
mat_poly_ZZ_p.c 2KB
mat_poly_lzz_p.c 2KB
BitMatTest.c 1KB
GF2XVec.c 1KB
FacVec.c 1KB
ZZVec.c 1KB
ZZXCharPoly.c 1KB
BerlekampTest.c 1KB
CanZassTest.c 1KB
lzz_pXCharPoly.c 1KB
TestGetTime.c 1KB
ZZ_pXCharPoly.c 1KB
ZZXFacTest.c 1KB
MoreFacTest.c 1006B
fileio.c 925B
ZZ_pEXTest.c 832B
lzz_pEXTest.c 827B
MatrixTest.c 808B
GetTime1.c 584B
GetTime4.c 566B
GetTime3.c 525B
GetTime2.c 491B
MakeDescAux.c 487B
GF2.c 451B
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