todo.txt

in knotkit/
 - my (or Kh) tangle algebra over Z
 - enumerate 2-connect sum knots to test mutation invariance over Z
 - add homology orientations for odd Khovanov homology and spectral
   sequence over Z
 - unify smoothing, resolution_diagram wiring (and knot_diagram?)
 - speed up construction of chain maps in chain_complex_simplifer
 - move chain_complex_simplifier to algebra/
 - unify chain_complex_simplifer and build_sseq
 - remove hardcoded limits (max_...)
 - revive testlib
 - figure out proper copy interface and consistently support copy and
   deepcopy

in lib/
 - between interoperation between sets that require bounds (bitset,
   ullmanset) and those that don't (set, hashset)

in algebra/
 - linear_combnation can be more efficient (eg no searching when
   coefficients die)
 - monomial ideals and maybe groebner bases
 - cleaner interface for gcd, etc. in fraction_field
 - support kernel, cokernel of torsion modules
 - change gcd et al so gcd is always positive
 - split linear_combination into internal and external versions

git:
 - fix bug in Josh's version
 - make this master, merge into Josh's version
 - merge in square to master => then write paper!
 - merge in other improvements (sped up linear algebra?  multivariate (laurent) polynomial?)
 - should exponents on polynomials be Z or unsigned?

general:
 - unify simplify_chain_complex, sseq, kernel/image/homology (as much as possible)
 - sseq over Z
 - quadratic linear solver (enumerator?)
 - classes should either COPY or fully SHARE, but not some of each
   (e.g. knot_diagram, resolution_diagram, etc.)  -- this is the right
   semantics.
 - clean up/delete setcommon, mapcommon
 - incorporate sage dump into standard classes
 - update use of tuples in steenrod square

 - test mutation invariance, other questions of Robert and Sucharit
 - write paper

c++11:
 - make vector wrap std::vector (probably faster)
 
 - use tuple instead of pair, triple; and use tie, a great idiom
 - standardize ring, field interface so test_ring works for everything
 - get clear on default semantics: prefer default when possible
 
 - standardize use of {} for initializers
 - initializer_list for container types
 - support for iterator

 - compress Steenrod square data
 - get mpimain running again, run 15 xing mutants

 - simplifications to run (5, 8) with symmetries.

notes:

all rings (R): multivariate_laurentpoly<R>

fields (F): Z2 Zp Q fraction_field<E> (for just pids?)

euclidean domains (E): Z polynomial<F>

euclidean domain interface:

num/demon : denom must be a unit
 = num.operator / (denom)

denom.divides (num)
denom | num

  num.divide_exact (denom)

(q, r) = num.divide_with_remainder (denom)
  (q, r) = num / denom
  (q, r) = num.operator / (denom)
satisfies r = 0 or f(r) < f(denom) and num = q*denom + r

 gcd (a, b)
 lcm (a, b)
 r = num.mod (denom)
satisfies r = 0 or f(r) < f(denom)


(d, s, t) = a.extended_gcd (b)
 satifies d is the gcd and d = a*s + b*t