14 Dec 2012 (TK+MES)

engine work todo list:
1. gtest tests for engine code
  TK: play with gtest, to understand it
  add Makefile targets for a simple one
  get include files so we can link with all engine files (not interpreter files)
  write tests!
2. doxygen: start putting in better doxy-comments
  also: source code has no indentation, why not?!
  
3. interface to flint and top-level ring and mutable matrix code
4. same issue with RRR, CCC
5. same issue with finite fields
6. interface to mathicgb code that Bjarke is doing





-- 1/10/2007:
changed comp_* to comp-*
z_mod_p --> ZZp
int_bag --> int-bag

-- General speedup

  -- added gbvector stash: this made big difference
  -- resterm stash added
  -- stash: delete_elem, new_elem made inline
  -- monideal: added stash for Nmi_node's: this seemed to slow resolutions down!
  --

  -- things to still do/try:
    streamline monomial ops
-- Mike's to do list, new version, started 3/29/04

BUGS:
      Grassmannian(2,5)
      compress (uses submatrix)
      submatrix (vectors not yet re-implemented)
      terms RingElement
      sortColumns

packages:
        gin
        lexideal
        schur -- cauchy -- bott
        bgg
        special surfaces
        points
        complexes
        toric ideals
        markov
        borel -- generating sets of ideals

matrix2.m2 gg problems:
  divideByVariable DONE
  compress
  oldCoefficients
  selectInSubring
  Matrix::lead_var_coefficients -- needed for decompose
    changed to top_coefficients

random aspects of resolutions and GB's:
       matrices returned should NEVER be able to be changed by the computation.
       text_out, stats should maybe function for all these computations.
       quotients, skew commutative, Weyl: all needs to be done or checked.
       DONE (I think): Schreyer order for GB's
       DONE: HF code
       DONE: HF use in resolutions: this I think was not correct
       MAYBE: Frank Schreyer's suggestions
       AT SOME POINT: minimalization routine for resolutions (over fraction rings, ZZ,
         inhomog, etc).
       gb2: computation completion conditions are not used, except for degree...

routines to implement: gin, lexideal, macaulayRep, noetherNormalization, routines for
points, toric rings, LPP, what else?

pushforward, pushforward1 should be stashed too, and should work functorially and with
inhomogeneous maps and modules.

subring, quotient, and saturation computations need to be interruptable: so we must
stash the results.

factorization and decomposition from singular needs to be interruptable.

Groebner bases todo: HF use, mingens, subring elements, elements sorted in
decreasing monomial order?

random should take optional parameters for FractionNonZero, UpperTriangular, or something
like that.

DONE random matrices of scalars

skew multiplication: does it still work?  Get it working, test it.

DONE (I think) leadTerm needs to be made to work again

basis needs to be made to work again (engine part DONE)

basis needs to be functorial

DONE rawMonomials needs to be connected to front end (this is the new version which
takes a matrix instead a list of exponent vectors)

Monomial orders for free modules should obey what we agreed with Cox

DONE Add GroupRevLex to monomial order creation routines

Get resolutions back up and running

Get quotient rings functional: this includes getting fraction rings functional,
  and polynomial rings over that.  This includes having various routines
  like leadCoefficient do the right thing.

DONE Polynomial rings should take a degree ring instead of a degree monoid.  Then we need a
way of specifying the trivial ring.

Go back to having a MutableMatrix class, which does not have free module information.
All mutable operations must be switched back.  Need a routine: map(Module,Module,MutableMatrix)
  - Write the remaining mutable matrix operations.
  - Change the interface to some of the rawMatrix commands.
How does this interact with lapack matrices?

statistics routine for Computation
  summary or stats for a computation should be in the toString.
  -- rawSummary(computation)

------------
polynomial ring construction:

classes:
  PolynomialRing
    PolyRing
      Skew
      Weyl
    PolyFrac
      PolyFracQQ -- maybe
    QuotientPolyRing
    QuotientPolyFrac
  NCPolynomialRing
    QuotientNCPolyRing -- ??

to construct
  A = ZZ[s,t]
  B = A/I
  C = B[x,y,z]
  D = C/J
do:
  A = rawPolynomialRing(rawZZ(), [s,t]) -- [s,t] stands for that monoid
  B = rawQuotient(A, gens gb I)
  C1 = rawPolynomialRing(rawAmbientRing B, [x,y,z])
  C = rawQuotient(C1, B)  -- rawAmbientRing C == C1
  D = rawQuotient(C, gens gb J)  -- rawAmbientRing D == C1
------------

 term over position (TOP) :

       e_1 < e_2 < ... (bottom down, top up)

            R = ZZ[x,y,z]
            R = ZZ[x,y,z, MonomialOrder => GRevLex ]
            R = ZZ[x,y,z, MonomialOrder => { GRevLex } ]
            R = ZZ[x,y,z, MonomialOrder => { GRevLex, Position } ]
            R = ZZ[x,y,z, MonomialOrder => { GRevLex, Position => Up} ]

       e_1 > e_2 > ... (top down, bottom up)

            R = ZZ[x,y,z, MonomialOrder => { GRevLex, Position => Down } ]

    position over term (POT) :

       e_1 < e_2 < ... (bottom down, top up)

            R = ZZ[x,y,z, MonomialOrder => Position ]
            R = ZZ[x,y,z, MonomialOrder => { Position } ]
            R = ZZ[x,y,z, MonomialOrder => { Position, GRevLex } ]
            R = ZZ[x,y,z, MonomialOrder => { Position => Up} ]
            R = ZZ[x,y,z, MonomialOrder => { Position => Up, GRevLex} ]

       e_1 > e_2 > ... (top down, bottom up)

            R = ZZ[x,y,z, MonomialOrder => { Position => Down } ]
            R = ZZ[x,y,z, MonomialOrder => { Position => Down, GRevLex } ]

    Many other ordering keywords can replace or supplement GRevLex:

            GRevLex => 3             (order just 3 variables this way)
            Lex
            Lex => 3
            RevLex
            RevLex => 3
            Eliminate 3
            ProductOrder {...}
            GroupLex
            NCLex
            ...

 Dear Dan: Up and Down are great.  The example we do using Macaulay 2 is
   the following very simple computation:

   R = QQ[a..d, MonomialOrder => {Position => Down}]

   M = matrix{{a2+b2, a3 - 2*b*c*d, a - b},{c2 - d2, b3 + a*c*d, c+d}}

   gens gb M

   The answer appears as equation (2.10) on page 205 of Using Algebraic
   Geometry.  We also do this example in Singular (and, in the 2nd edition,
   also in Maple).  In all three computations, we use TOP downward grevlex.
     It would be wonderful if you could check this in Macaulay 2.
       Many thanks, David

-- required engine routines:
   gcdExtended
   forceGB
   autoReduce
   someMinors
   compare of ring elements
   simplify (make it several?)
   findNonMember
   setRandomSeed
   schur
   compress
   topCoefficients

-- just need m2 file connecting, possibly debugging in engine
   monideal routines
   toField, getNonUnit, getZeroDivisor

-- add GB type
-------------------------------------------------
-- gg engine lines, as found on 8/2/04, 9am. ----
-------------------------------------------------
-- files:
--    factor.m2
        gggcdextended
        rawTopCoefficients -- DONE
--    galois.m2
        GF Ring
--    gb.m2
        forceGB
        GroebnerBasis == GroebnerBasis
        autoReduce
--    genmat.m2
        random: add Options
--    matrix.m2
        Matrix * Vector
--    matrix1.m2
        fixDegree, called from matrixTable
        matrix(List)
--    matrix2.m2
        oldCoefficients
        compress -- DONE
--    modules2.m2
        truncate(List,Module)
--    monideal.m2
        monomialIdeal MonomialIdeal  REMOVED
        poincare MonomialIdeal DONE EXCEPT: need rawHilbert MonomialIdeal
        minprimes MonomialIdeal DONE: except the name is bad
--    multilin.m2
        someMinors -- this is never called? But we want the functionality
--    ofcm.m2
        promote(MonoidElement,RingElement): BUG: (1_ZZ has no RawRingElement, 1_(ZZ/5) does)
--    orderedmonoidrings.m2
        is skew ring degree info correct?
        RM ? RM
--    overviewC.m2
        remove Ring ^ Matrix
        add routine: leadTerm(ZZ,RingElement)
        at end of file: some suggestions for routines to implement
--    primdecomp-SY.m2
        simplify
        newdecompose -- this routine looks awful
        findNonMember
--    primdecomp-fastgb.m2
        fastmingens  -- these routines should become part of the mainstream routines?
        fastgb
        fastquotient
        fastequal
--    quotring.m2
        toField
        getNonUnit
        getZeroDivisor
--    ringmap.m2
        RingMap * RingMap -- should be easy to replace
--    sagbi.m2 -- is this functional?
        sagbi
        subduction
--    schur.m2
        Schur ZZ
--    system.m2
        setRandomSeed
--
-- these represent the following routines/computations:
--   factorization/char series
--   GF
--   forceGB
--   autoReduceGB
--   random
--   multiply matrix by a vector
--   leadTerm
--
indigo:~/src/M2/Macaulay2/m2 mike$ grep gg *.m2
exports.m2:     symbol sendgg,
factor.m2:     error "gggcdextended not re-implemented";
factor.m2:     sendgg(ggPush f, ggPush g, gggcdextended);
factor.m2:     sendgg(ggpop);
factor.m2:     sendgg(ggPush f, ggfactor1);
factor.m2:     sendgg(ggPush f, ggfactor2);
factor.m2:     sendgg(ggPush f, ggcoeffs);
galois.m2:        sendgg(ggPush S, ggGF);
galois.m2:        sendgg (ggPush g, ggGF);
galois.m2:        F.ConvertToExpression, sendgg(ggPush t, ggtonet)
galois.m2:        sendgg ( ggPush x, ggPush y, ggdiv);
gb.m2:          ggPush minmat,
gb.m2:          ggPush f,
gb.m2:          ggPush changemat,
gb.m2:          ggPush syzmat,
gb.m2:          gggb);
gb.m2:            sendgg(ggPush g, ggPush h, ggisequal);
gb.m2:     sendgg(ggPush m, ggautoreduce);
genmat.m2:     sendgg(ggPush R, ggPush r, ggPush c, ggrandom);
matrix.m2:     sendgg(ggPush m, ggPush v, ggmult);
matrix.m2:     sendgg(ggPush m, ggINT, gg i, gginitial);
matrix.m2:     sendgg(ggPush m, gginitial);
matrix.m2:     sendgg (
matrix.m2:        ggPush m, ggINT, gg 0, ggmonideal,  -- get monomial lead ideal
matrix.m2:        ggborel,                            -- monomial borel now on stack
matrix.m2:        ggmatrix);
matrix1.m2:     sendgg (
matrix1.m2:       ggPush cover M,
matrix1.m2:       ggPush cover N,
matrix1.m2:       ggPush m,
matrix1.m2:       ggPush degreeCheck(d,R),
matrix1.m2:       ggmatrix);
matrix1.m2:            h := newHandle(ggPush\m, ggPush rawM, ggPush (#m), ggmatrix);
matrix1.m2:                    N := (sendgg(ggPush h,gggetcols); new Module from R);
matrix2.m2:    sendgg(ggPush m, ggPush v, ggcoeffs);
matrix2.m2:     sendgg(ggPush f, ggPush v, ggcoeffs);
matrix2.m2:     sendgg(ggPush m, ggdup, ggPush i, ggelim, ggsubmatrix);
matrix2.m2:     sendgg(ggPush m, ggPush index v, ggPush (-1), ggsat);
matrix2.m2:     sendgg(ggPush m, ggPush index v, ggPush d, ggsat);
matrix2.m2:--     sendgg( ggPush m, ggcompress );
modules2.m2:     sendgg(ggPush top, ggPush bottom, ggPush deg, ggtruncate);
monideal.m2:          sendgg(ggPush I, ggcopy);
monideal.m2:        sendgg(ggPush ZZn, ggPush M, gghilb);
monideal.m2:        sendgg(ggPush M.cache.poincareComputation, ggPush (-1), ggcalc);
monideal.m2:    sendgg(ggPush M.cache.poincareComputation, gggetvalue);
monideal.m2:     sendgg(ggPush m, ggprimes);
multilin.m2:     sendgg(
multilin.m2:      ggPush m,                       -- m
multilin.m2:      ggPush j,
multilin.m2:      ggPush strat,          -- 0: bareiss, 1: cofactor.
multilin.m2:      ggdets);                        -- create computation
multilin.m2:         sendgg(
multilin.m2:       ggPush h,
multilin.m2:       ggPush nsteps,
multilin.m2:       ggPush 0,  -- don't discard previous (there are none...)
multilin.m2:       ggPush options.First#0,
multilin.m2:       ggPush options.First#1,
multilin.m2:       ggcalc))
multilin.m2:       sendgg(
multilin.m2:      ggPush h,
multilin.m2:      ggPush nsteps,
multilin.m2:      ggcalc);
multilin.m2:     sendgg(ggPush h,
multilin.m2:      ggPush 0,
multilin.m2:      ggindex);
obsolete.m2:scan({sendgg,ggPush,ConvertJoin,ConvertRepeat,ConvertApply,newHandle},
ofcm.m2:          sendgg(ggPush R, ggPush one, ggPush m, ggterm);
orderedmonoidrings.m2:--                         ggPush degRing,
orderedmonoidrings.m2:--                         ggPush flatten apply((options M).Degrees, (options M).Adjust), <<<<< ---- do we have to do something with this???
orderedmonoidrings.m2:--                         ggPush R,
orderedmonoidrings.m2:--                         ggPush M,
orderedmonoidrings.m2:--                         ggPush skews,
orderedmonoidrings.m2:--                         ggskewpolyring
orderedmonoidrings.m2:         sendgg(ggPush f, ggleadmonom, ggPush g, ggleadmonom, ggcompare);
overviewC.m2:Ring ^ Matrix := (R,m) -> (sendgg(ggPush m, ggfree); new Module from R)
overviewC.m2:  -- leadTerm should call a ggleadterm routine?  DO THIS
primdecomp-SY.m2:     sendgg(ggPush m, ggPush n, ggsimplify);
primdecomp-SY.m2:     sendgg(ggPush m, ggPush n, ggissubset);
primdecomp-fastgb.m2:     sendgg(ggPush m, -- the matrix
primdecomp-fastgb.m2:     ggPush 0, -- collect syzygyies?
primdecomp-fastgb.m2:     ggPush 0, -- how many rows
primdecomp-fastgb.m2:     ggPush 0, -- 0 for now
primdecomp-fastgb.m2:     gggb);
primdecomp-fastgb.m2:     sendgg(ggPush g,
primdecomp-fastgb.m2:     ggPush {}, -- degree bound
primdecomp-fastgb.m2:     ggPush {-1, -- generator limit
primdecomp-fastgb.m2:     sendgg ggcalc;
primdecomp-fastgb.m2:     sendgg(ggPush g,
primdecomp-fastgb.m2:       gggetmingens,
primdecomp-fastgb.m2:            ggdup, ggPush 1, ggPush (-1), ggsortcolumns, ggsubmatrix);
primdecomp-fastgb.m2:     sendgg(ggPush m, -- the matrix
primdecomp-fastgb.m2:     ggPush 0, -- collect syzygyies?
primdecomp-fastgb.m2:     ggPush 0, -- how many rows
primdecomp-fastgb.m2:     ggPush 0, -- 0 for now
primdecomp-fastgb.m2:     gggb);
primdecomp-fastgb.m2:     sendgg(ggPush g,
primdecomp-fastgb.m2:     ggPush {}, -- degree bound
primdecomp-fastgb.m2:     ggPush {-1, -- generator limit
primdecomp-fastgb.m2:     sendgg ggcalc;
primdecomp-fastgb.m2:     sendgg(ggPush g, gggetgb);
primdecomp-fastgb.m2:     sendgg(ggPush m,
primdecomp-fastgb.m2:     ggPush 1,
primdecomp-fastgb.m2:     ggPush 1,
primdecomp-fastgb.m2:     ggPush 0,
primdecomp-fastgb.m2:     gggb);
primdecomp-fastgb.m2:     sendgg(ggPush g, ggPush {}, ggPush {-1,-1,-1,-1,0,-1,0});
primdecomp-fastgb.m2:     sendgg ggcalc;
primdecomp-fastgb.m2:     sendgg(ggPush g, gggetsyz);
primdecomp-fastgb.m2:     sendgg(ggPush m, ggPush n, ggisequal);
quotring.m2:      sendgg(ggPush R, ggdeclarefield);
quotring.m2:                sendgg(ggPush x, ggPush y, ggdiv);
quotring.m2:              sendgg(ggPush R, gggetzerodivisor);
quotring.m2:              sendgg(ggPush R, gggetzerodivisor);
ringmap.m2:       symbol handle => newHandle(ggPush m, ggringmap),
sagbi.m2:         sendgg(ggPush M, ggsagbi);
sagbi.m2:     sendgg(ggPush M.SagbiComputation, ggPush {}, ggPush {}, ggcalc);
sagbi.m2:     time sendgg(ggPush m, ggPush FRStoRS, ggPush g, ggsubduction);
sagbi.m2:sendgg(ggPush m.SagbiComputation, gggetgb)
sagbi.m2:     sendgg(ggPush g, ggPush f, ggsubduction);
schur.m2:         error "ggdim for Schur rings not re-implemented yet";
schur.m2:         sendgg(ggPush s, ggdim);
system.m2:     (callgg(ggrandomseed, seed);)
