singmathic.cc

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#include <kernel/mod2.h>

#ifdef HAVE_MATHICGB

#include <misc/auxiliary.h>

#include <misc/options.h>

#include <kernel/ideals.h>
#include <kernel/polys.h>

#include <Singular/ipid.h>
#include <Singular/mod_lib.h>

#include <mathicgb.h>

typedef mgb::GroebnerConfiguration::Coefficient Coefficient;
typedef mgb::GroebnerConfiguration::VarIndex VarIndex;
typedef mgb::GroebnerConfiguration::Exponent Exponent;
typedef mgb::GroebnerConfiguration::BaseOrder BaseOrder;

// Constructs a Singular ideal.
class MathicToSingStream {
public:
  MathicToSingStream(Coefficient modulus, VarIndex varCount):
    mModulus(modulus),
    mVarCount(varCount),
    mPolyCount(0),
    mTerm(0),
    mIdeal(0)
  {}

  ~MathicToSingStream() {deleteIdeal();}

  // Mathic stream interface

  Coefficient modulus() const {return mModulus;}
  VarIndex varCount() const {return mModulus;}

  void idealBegin(size_t polyCount) {
    deleteIdeal();
    mIdeal = idInit(polyCount);
    mPolyCount = 0;
  }

  void appendPolynomialBegin(size_t termCount) {}

  void appendTermBegin() {
    if (mTerm == 0)
      mTerm = mIdeal->m[mPolyCount] = pInit();
    else
      mTerm = mTerm->next = pInit();
  }

  void appendExponent(VarIndex index, Exponent exponent) {
    pSetExp(mTerm, index + 1, exponent);
  }

  void appendTermDone(Coefficient coefficient) {
    mTerm->coef = reinterpret_cast<number>(coefficient);
    pSetm(mTerm);
  }

  void appendPolynomialDone() {
    ++mPolyCount;
    mTerm = 0;
  }

  void idealDone() {}


  // Singular interface

  ::ideal takeIdeal() {
    ::ideal id = mIdeal;
    mIdeal = 0;
    return id;
  }

private:
  void deleteIdeal() {
    if (mIdeal != 0) {
      idDelete(&mIdeal);
      mIdeal = 0;
    }
  }

  const Coefficient mModulus;
  const VarIndex mVarCount;
  size_t mPolyCount;
  poly mTerm;
  ::ideal mIdeal;
};

#include <iostream>

bool setOrder(ring r, mgb::GroebnerConfiguration& conf) {
  const VarIndex varCount = conf.varCount();

  bool didSetComponentBefore = false;
  mgb::GroebnerConfiguration::BaseOrder baseOrder =
    mgb::GroebnerConfiguration::RevLexDescendingBaseOrder;

  std::vector<Exponent> gradings;
  for (int block = 0; r->order[block] != ringorder_no; ++block) {
    // *** ringorder_no

    const rRingOrder_t type = static_cast<rRingOrder_t>(r->order[block]);
    if (r->block0[block] < 0 || r->block1[block] < 0) {
      WerrorS("Unexpected negative block0/block1 in ring.");
      return false;
    }
    const VarIndex block0 = static_cast<VarIndex>(r->block0[block]);
    const VarIndex block1 = static_cast<VarIndex>(r->block1[block]);
    const int* const weights = r->wvhdl[block];
    if (block0 > block1) {
      WerrorS("Unexpected block0 > block1 in ring.");
      return false;
    }

    // *** ringorder_c and ringorder_C
    if (type == ringorder_c || type == ringorder_C) {
      if (block0 != 0 || block1 != 0 || weights != 0) {
        WerrorS("Unexpected non-zero fields on c/C block in ring.");
        return false;
      }
      if (didSetComponentBefore) {
        WerrorS("Unexpected two c/C blocks in ring.");
        return false;
      }
      didSetComponentBefore = true;
      if (r->order[block + 1] == ringorder_no) {
        conf.setComponentBefore
          (mgb::GroebnerConfiguration::ComponentAfterBaseOrder);
      } else
        conf.setComponentBefore(gradings.size() / varCount);
      conf.setComponentsAscending(type == ringorder_C);
      continue;
    }
    if (block0 == 0 || block1 == 0) {
      WerrorS("Expected block0 != 0 and block1 != 0 in ring.");
      return false;
    }
    if (block1 > varCount) {
      // todo: first handle any block types where this is not true
      WerrorS("Expected block1 <= #vars in ring.");
      return false;
    }

    // dim is how many variables this block concerns.
    const size_t dim = static_cast<size_t>(block1 - block0 + 1);

    // *** single-graded/ungraded lex/revlex orders
    // a(w): w-graded and that's it
    // a64(w): w-graded with 64-bit weights (not supported here)
    //    lp:               lex from  left (descending)
    //    Dp:  1-graded,    lex from  left (descending)
    //    Ds: -1-graded,    lex from  left (descending)
    // Wp(w):  w-graded,    lex from  left (descending)
    // Ws(w): -w-graded,    lex from  left (descending)
    //    rp:               lex from right (ascending)
    //    rs:            revlex from right (descending)
    //    dp:  1-graded, revlex from right (descending)
    //    ds: -1-graded, revlex from right (descending)
    // wp(w):  w-graded, revlex from right (descending)
    // ws(w): -w-graded, revlex from right (descending)
    //    ls:            revlex from  left (ascending)

    if (type == ringorder_a64) {
      WerrorS("Block type a64 not supported for MathicGB interface.");
      return false;
    }

    // * handle the single-grading part
    const bool oneGrading = (type == ringorder_Dp || type == ringorder_dp);
    const bool minusOneGrading = (type == ringorder_Ds || type == ringorder_ds);
    const bool wGrading =
      (type == ringorder_a || type == ringorder_Wp || type == ringorder_wp);
    const bool minusWGrading = (type == ringorder_ws || type == ringorder_Ws);
    if (oneGrading || minusOneGrading || wGrading || minusWGrading) {
      const VarIndex begin = gradings.size();
      gradings.resize(begin + varCount);
      if (oneGrading || minusOneGrading) {
        if (weights != 0) {
          WerrorS("Expect wvhdl == 0 in Dp/dp/Ds/ds-block in ring.");
          return false;
        }
        const Exponent value = oneGrading ? 1 : -1;
        for (int var = block0 - 1; var < block1; ++var)
          gradings[begin + var] = value;
      } else {
        if (weights == 0) {
          WerrorS("Expect wvhdl != 0 in a/Wp/wp/ws/Ws-block in ring.");
          return false;
        }
        if (wGrading) {
          for (int var = 0; var < dim; ++var)
            gradings[begin + (block0 - 1) + var] = weights[var];
        } else {
          for (int var = 0; var < dim; ++var)
            gradings[begin + (block0 - 1) + var] = -weights[var];
        }
      }
    }
    if (type == ringorder_a)
      continue; // a has only the grading, so we are done already

    // * handle the lex/revlex part
    const bool lexFromLeft =
      type == ringorder_lp ||
      type == ringorder_Dp ||
      type == ringorder_Ds ||
      type == ringorder_Wp ||
      type == ringorder_Ws;
    const bool lexFromRight = type == ringorder_rp;
    const bool revlexFromLeft = type == ringorder_ls;
    const bool revlexFromRight =
      type == ringorder_rs ||
      type == ringorder_dp ||
      type == ringorder_ds ||
      type == ringorder_wp ||
      type == ringorder_ws;
    if (lexFromLeft || lexFromRight || revlexFromLeft || revlexFromRight) {
      const int next = r->order[block + 1];
      bool final = next == ringorder_no;
      if (!final && r->order[block + 2] == ringorder_no)
        final = next == ringorder_c || next == ringorder_C;
      if (final) {
        if (lexFromRight)
          baseOrder = mgb::GroebnerConfiguration::LexAscendingBaseOrder;
        else if (revlexFromRight)
          baseOrder = mgb::GroebnerConfiguration::RevLexDescendingBaseOrder;
        else if (lexFromLeft)
          baseOrder = mgb::GroebnerConfiguration::LexDescendingBaseOrder;
        else
          baseOrder = mgb::GroebnerConfiguration::RevLexAscendingBaseOrder;
        continue;
      }

      const size_t begin = gradings.size();
      gradings.resize(begin + dim * varCount);
      const Exponent value = (lexFromLeft || lexFromRight) ? 1 : -1;
      if (lexFromLeft || revlexFromLeft) {
        for (size_t row = 0; row < dim; ++row)
          gradings[begin + row * varCount + (block0 - 1) + row] = value;
      } else {
        for (size_t row = 0; row < dim; ++row)
          gradings[begin + row * varCount + (block1 - 1) - row] = value;
      }
      continue;
    }

    // *** ringorder_M: a square invertible matrix
    if (type == ringorder_M) {
      if (weights == 0) {
        WerrorS("Expected wvhdl != 0 in M-block in ring.");
        return false;
      }
      const size_t begin = gradings.size();
      gradings.resize(begin + dim * varCount);
      for (size_t row = 0; row < dim; ++row)
        for (size_t col = block0 - 1; col < block1; ++col)
          gradings[begin + row * varCount + col] = weights[row * dim + col];
      continue;
    }

    // *** Miscellaneous unsupported or invalid block types
    if (
      type == ringorder_s ||
      type == ringorder_S ||
      type == ringorder_IS
    ) {
      // todo: Consider supporting this later.
      WerrorS("Schreyer order s/S/IS not supported in MathicGB interface.");
      return false;
    }
    if (type == ringorder_am) {
      // This block is a Schreyer-like ordering only used in Spielwiese.
      // todo: Consider supporting it later.
      WerrorS("Block type am not supported in MathicGB interface");
      return false;
    }
    if (type == ringorder_L) {
      WerrorS("Invalid L-block found in order of ring.");
      return false;
    }
    if (type == ringorder_aa) {
      // I don't know what an aa block is supposed to do.
      WerrorS("aa ordering not supported by the MathicGB interface.");
      return false;
    }
    if (type == ringorder_unspec) {
      WerrorS("Invalid unspec-block found in order of ring.");
      return false;
    }
    WerrorS("Unknown block type found in order of ring.");
    return false;
  }

  if (!didSetComponentBefore) {
    WerrorS("Expected to find a c/C block in ring.");
    return false;
  }

  if (!conf.setMonomialOrder(baseOrder, gradings)) {
    WerrorS("MathicGB does not support non-global orders.");
    return false;
  }
  return true;
}

bool prOrderMatrix(ring r) {
  const int varCount = r->N;
  mgb::GroebnerConfiguration conf(101, varCount);
  if (!setOrder(r, conf))
    return false;
  const std::vector<Exponent>& gradings = conf.monomialOrder().second;
  if (gradings.size() % varCount != 0) {
    WerrorS("Expected matrix to be a multiple of varCount.");
    return false;
  }
  const size_t rowCount = gradings.size() / varCount;
  std::cout << "Order matrix:\n";
  for (size_t row = 0; row < rowCount; ++row) {
    for (size_t col = 0; col < varCount; ++col)
      std::cerr << ' ' << gradings[row * varCount + col];
    std::cerr << '\n';
  }
  std::cerr
    << "Base order: "
    << mgb::GroebnerConfiguration::baseOrderName(conf.monomialOrder().first)
    << '\n';
  std::cerr << "Component before: " << conf.componentBefore() << '\n';
  std::cerr << "Components ascending: " << conf.componentsAscending() << '\n';
  std::cerr << "Schreyering: " << conf.schreyering() << '\n';
}

void prOrder(ring r) {
  std::cout << "Printing order of ring.\n";
  for (int block = 0; ; ++block) {
    switch (r->order[block]) {
    case ringorder_no: // end of blocks
      return;

    case ringorder_a:
      std::cout << "a";
      break;

    case ringorder_a64: ///< for int64 weights
      std::cout << "a64";
      break;

    case ringorder_c:
      std::cout << "c";
      break;

    case ringorder_C:
      std::cout << "C";
      break;

    case ringorder_M:
      std::cout << "M";
      break;

    case ringorder_S: ///< S?
      std::cout << "S";
      break;

    case ringorder_s: ///< s?
      std::cout << "s";
      break;

    case ringorder_lp:
      std::cout << "lp";
      break;

    case ringorder_dp:
      std::cout << "dp";
      break;

    case ringorder_rp:
      std::cout << "rp";
      break;

    case ringorder_Dp:
      std::cout << "Dp";
      break;

    case ringorder_wp:
      std::cout << "wp";
      break;

    case ringorder_Wp:
      std::cout << "Wp";
      break;

    case ringorder_ls:
      std::cout << "ls"; // not global
      break;

    case ringorder_ds:
      std::cout << "ds"; // not global
      break;

    case ringorder_Ds:
      std::cout << "Ds"; // not global
      break;

    case ringorder_ws:
      std::cout << "ws"; // not global
      break;

    case ringorder_Ws:
      std::cout << "Ws"; // not global
      break;

    case ringorder_am:
      std::cout << "am";
      break;

    case ringorder_L:
      std::cout << "L";
      break;

    // the following are only used internally
    case ringorder_aa: ///< for idElimination, like a, except pFDeg, pWeigths ignore it
      std::cout << "aa";
      break;

    case ringorder_rs: ///< opposite of ls
      std::cout << "rs";
      break;

    case ringorder_IS: ///< Induced (Schreyer) ordering
      std::cout << "IS";
      break;

    case ringorder_unspec:
      std::cout << "unspec";
      break;
    }
    const int b0 = r->block0[block];
    const int b1 = r->block1[block];
    std::cout << ' ' << b0 << ':' << b1 << " (" << r->wvhdl[block] << ")" << std::flush;
    if (r->wvhdl[block] != 0 && b0 != 0) {
      for (int v = 0; v <= b1 - b0; ++v)
        std::cout << ' ' << r->wvhdl[block][v];
    } else
      std::cout << " null";
    std::cout << '\n';
  }
}

BOOLEAN prOrderX(leftv result, leftv arg) {
  if (currRing == 0) {
    WerrorS("There is no current ring.");
    return TRUE;
  }
  prOrder(currRing);
  prOrderMatrix(currRing);
  result->rtyp=NONE;
  return FALSE;
}

BOOLEAN setRingGlobal(leftv result, leftv arg) {
  currRing->OrdSgn = 1;
  result->rtyp=NONE;
  return FALSE;
}

BOOLEAN mathicgb(leftv result, leftv arg)
{
  result->rtyp=NONE;

  if (arg == NULL || arg->next != NULL || arg->Typ() != IDEAL_CMD) {
    WerrorS("Syntax: mathicgb(<ideal>)");
    return TRUE;
  }
  if (!rField_is_Zp(currRing)) {
    WerrorS("Polynomial ring must be over Zp.");
    return TRUE;
  }

  const int characteristic = n_GetChar(currRing);
  const int varCount = currRing->N;
  mgb::GroebnerConfiguration conf(characteristic, varCount);
  if (!setOrder(currRing, conf))
    return TRUE;
  if (TEST_OPT_PROT)
    conf.setLogging("all");

  mgb::GroebnerInputIdealStream toMathic(conf);

  const ideal id = static_cast<const ideal>(arg->Data());
  const int size = IDELEMS(id);
  toMathic.idealBegin(size);
  for (int i = 0; i < size; ++i) {
    const poly origP = id->m[i];
    int termCount = 0;
    for (poly p = origP; p != 0; p = pNext(p))
      ++termCount;
    toMathic.appendPolynomialBegin(termCount);

    for (poly p = origP; p != 0; p = pNext(p)) {
      toMathic.appendTermBegin();
      for (int i = 1; i <= currRing->N; ++i)
        toMathic.appendExponent(i - 1, pGetExp(p, i));
      const long coefLong = reinterpret_cast<long>(pGetCoeff(p));
      toMathic.appendTermDone(static_cast<int>(coefLong));
    }
    toMathic.appendPolynomialDone();
  }
  toMathic.idealDone();

  MathicToSingStream fromMathic(characteristic, varCount);
  mgb::computeGroebnerBasis(toMathic, fromMathic);

  result->rtyp=IDEAL_CMD;
  result->data = fromMathic.takeIdeal();
  return FALSE;
}

template class std::vector<Exponent>;
template void mgb::computeGroebnerBasis<MathicToSingStream>
  (mgb::GroebnerInputIdealStream&, MathicToSingStream&);

int SI_MOD_INIT(singmathic)(SModulFunctions* psModulFunctions)
{
  PrintS("Initializing Singular-Mathic interface Singmathic.\n");
  psModulFunctions->iiAddCproc(
    (currPack->libname ? currPack->libname : ""),
    "mathicgb",
    FALSE,
    mathicgb
  );
  psModulFunctions->iiAddCproc(
    (currPack->libname ? currPack->libname : ""),
    "mathicgb_prOrder",
    FALSE,
    prOrderX
  );
  psModulFunctions->iiAddCproc(
    (currPack->libname ? currPack->libname : ""),
    "mathicgb_setRingGlobal",
    FALSE,
    setRingGlobal
  );
  return MAX_TOK;
}

/* #else

int SI_MOD_INIT(singmathic)(SModulFunctions* psModulFunctions)
{
  WerrorS(
    "Cannot initialize the Singular interface to MathicGB "
    "as this Singular executable was built without support "
    "for MathicGB."
  );
  return 1;
}
*/

#endif /* HAVE_MATHICGB */