antipode()

ring_elem SkewPolynomialRing::antipode ( const ring_elem f ) const

virtual

Reimplemented from Ring.

Definition at line 37 of file skewpoly.cpp.

{
  Nterm head;
  Nterm *inresult = &head;
 
  exponents_t EXP = ALLOCATE_EXPONENTS(exp_size);
 
  for (Nterm& s : f)
    {
      M_->to_expvector(s.monom, EXP);
      int deg = skew_.skew_degree(EXP);
      // sign is (-1)^ (binomial(deg,2))
      // deg = 0: sign is 1
      // deg = 1: sign is 1
      // deg = 2: sign is -1
      // deg = 3: sign is -1
      // deg = 4: sign is 1, and so on
      int mod4 = deg % 4;
      int sign = sign4[mod4];
      Nterm *t = new_term();
      t->next = nullptr;
      t->coeff = (sign == 1 ? s.coeff : K_->negate(s.coeff));
      M_->copy(s.monom, t->monom);
      inresult->next = t;
      inresult = inresult->next;
    }
  inresult->next = nullptr;
  return head.next;
}

References ALLOCATE_EXPONENTS, Nterm::coeff, PolynomialRing::exp_size, PolynomialRing::K_, PolynomialRing::M_, Nterm::monom, PolyRing::new_term(), Nterm::next, s, sign4, and PolynomialRing::skew_.