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// Copyright 1997 Michael E. Stillman
#ifndef _weylalg_hh_
#define _weylalg_hh_
#include "poly.hpp"
#include "gbring.hpp"
///// Ring Hierarchy ///////////////////////////////////
class WeylAlgebra : public PolyRing
{
int _nderivatives;
bool _homogeneous_weyl_algebra;
int _homog_var; // Only used if 'homogeneous_weyl_algebra' is true.
int *_derivative; // a value _derivative[i] = r >= 0 means that i is diff(r).
// If < 0 : the variable i does not have a diff op.
int *_commutative; // Same as above, but in opposite direction.
static int binomtop;
static int diffcoeffstop;
static int **binomtable;
static int **diffcoeffstable;
void initialize1();
bool initialize_weyl(M2_arrayint derivs, M2_arrayint comms, int homog_var);
WeylAlgebra() {}
virtual ~WeylAlgebra() {}
protected:
void extractDerivativePart(const int *exponents, int *result) const;
void extractCommutativePart(const int *exponents, int *result) const;
ring_elem binomial(int top, int bottom) const;
ring_elem multinomial(const ring_elem a,
const int *exptop,
const int *expbottom) const;
bool increment(int *current_derivative, const int *top_derivative) const;
bool divides(const int *expbottom, const int *exptop) const;
ring_elem diff_coefficients(const ring_elem c,
const int *derivatives,
const int *exponents) const;
Nterm *weyl_diff(const ring_elem c,
const int *expf, // The exponent vector of f
const int *derivatives,
const Nterm *g) const; // An entire polynomial
vec weyl_diff(const ring_elem c,
const int *expf, // The exponent vector of f
const int *derivatives,
const vec g) const; // An entire polynomial
vec weyl_diff(const FreeModule *resultF,
const ring_elem c,
const int *expf, // The exponent vector of f
int component,
const int *derivatives,
const Nterm *g) const; // An entire polynomial
gbvector *gbvector_weyl_diff(
GBRing *GR,
const ring_elem c, // in K
int comp, // adds this component to each component of g.
const int *expf, // The exponent vector of f
const int *derivatives,
const FreeModule *Fg, // Free module of g, unless g is a ring element
const gbvector *g) const; // An entire polynomial
public:
static WeylAlgebra *create(const Ring *K,
const Monoid *M,
M2_arrayint derivs,
M2_arrayint comms,
int homog_var);
virtual bool is_commutative_ring() const { return false; }
virtual bool is_weyl_algebra() const { return true; }
virtual const WeylAlgebra *cast_to_WeylAlgebra() const { return this; }
virtual void text_out(buffer &o) const;
virtual ring_elem power(const ring_elem f, mpz_srcptr n) const;
virtual ring_elem power(const ring_elem f, int n) const;
ring_elem multinomial(const int *exptop, const int *exp) const;
public:
virtual ring_elem mult_by_term(const ring_elem f,
const ring_elem c,
const int *m) const;
gbvector *gbvector_mult_by_term(
gbvectorHeap &result,
const gbvector *f,
const ring_elem c, // in the base K
const int *m, // monomial, in M
int comp) const; // comp is either 0 or a real component.
};
#endif
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e "
// indent-tabs-mode: nil
// End:
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