aring.h

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#ifndef _aring_h_
#  define _aring_h_
` annotations on individual entries
 * mark those that already have a matching `d/` binding ---
 * notably `rawARingTower1`/`_2`/`_3` are **not** marked
 * connected. Adding a new `aring` requires declaring it
 * here, implementing in `aring.cpp`, and wiring the M2-side
 * `.dd` binding.
 *
 * @see aring.cpp
 * @see engine-includes.hpp
 */
 
#  include "engine-includes.hpp"
 
// TODO: fix this
#  if defined(__cplusplus)
class Ring;
class RingElement;
#  else
typedef struct Ring Ring;
typedef struct RingElement RingElement;
#  endif

 
#  if defined(__cplusplus)
extern "C" {
#  endif
 
const Ring /* or null */ *rawARingZZp(unsigned long p); /* connected */
/* Expects a prime number p in range 2 <= p <= 32749 */
 
const Ring /* or null */ *rawARingGaloisField1(
    const RingElement *prim); /* connected */
/* same interface as rawGaloisField, but uses different internal code */
 
const Ring /* or null */ *rawARingGaloisFieldFlintBig(
    const RingElement *prim); /* connected */
/* same interface as rawGaloisField, but uses Flint GF code designed for
   wordsize p, but too big for lookup tables */
 
const Ring /* or null */ *rawARingGaloisFieldFlintZech(
    const RingElement *prim); /* connected */
/* same interface as rawGaloisField, but uses Flint GF code designed for
   wordsize p, and uses lookup tables */
 
const Ring /* or null */ *rawARingGaloisField(int p, int n); /* connected */
/* creates a ring GF(p^n).  Constraints on p, n? */
/* returns null if the values p,n are too large  */
 
const Ring /* or null */ *rawARingGaloisFieldFromQuotient(
    const RingElement *prim); /* connected */
/* same interface as rawGaloisField, but uses Givaro */
 
M2_arrayintOrNull rawARingGFPolynomial(const Ring *R);
/* given an ARingGF, return the coefficient array of the quotient polynomial.
   So, if R = kk[a]/(f(a)), where kk = ZZ/p, then the (integer) coefficients
   {f0, f1, f2, ..., f_(degree f)} is returned.
 */
 
M2_arrayintOrNull rawARingGFCoefficients(const RingElement *f);
/* f can be written as a polynomial in the generator a, e.g.
   f = f0 + a*f1 + ... + a^(d-1) * f_(d-1), where d = deg of the
   ring over ZZ/p.  This function returns {f0, f1, ..., f_(d-1)},
   where each entry is an integer */
 
const Ring /* or null */ *rawARingTower1(const Ring *K, M2_ArrayString names);
 
const Ring /* or null */ *rawARingTower2(const Ring *R1,
                                         M2_ArrayString new_names);
 
const Ring /* or null */ *rawARingTower3(const Ring *R1,
                                         engine_RawRingElementArray eqns);
 
const RingElement *rawMultiplicativeGenerator(const Ring *R);
/* given an ARingGF, return the  the generator of the multiplicative group.
 */

 
const Ring /* or null */ *rawARingZZFlint(); /* connected */
 
const Ring /* or null */ *rawARingQQFlint(); /* connected */
 
const Ring /* or null */ *rawARingZZpFlint(unsigned long p); /* connected */
/* Expects a prime number p in range 2 <= p <= 2^64-1 */
 
#  if defined(__cplusplus)
}
#  endif
 
#endif /* _aring_h_ */
 
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