96 lines
2.9 KiB
Plaintext
96 lines
2.9 KiB
Plaintext
in knotkit/
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- my (or Kh) tangle algebra over Z
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- enumerate 2-connect sum knots to test mutation invariance over Z
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- add homology orientations for odd Khovanov homology and spectral
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sequence over Z
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- unify smoothing, resolution_diagram wiring (and knot_diagram?)
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- speed up construction of chain maps in chain_complex_simplifer
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- move chain_complex_simplifier to algebra/
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- unify chain_complex_simplifer and build_sseq
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- remove hardcoded limits (max_...)
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- revive testlib
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- figure out proper copy interface and consistently support copy and
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deepcopy
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in lib/
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- between interoperation between sets that require bounds (bitset,
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ullmanset) and those that don't (set, hashset)
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in algebra/
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- linear_combnation can be more efficient (eg no searching when
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coefficients die)
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- monomial ideals and maybe groebner bases
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- cleaner interface for gcd, etc. in fraction_field
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- support kernel, cokernel of torsion modules
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- change gcd et al so gcd is always positive
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- split linear_combination into internal and external versions
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git:
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- fix bug in Josh's version
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- make this master, merge into Josh's version
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- merge in square to master => then write paper!
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- merge in other improvements (sped up linear algebra? multivariate (laurent) polynomial?)
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- should exponents on polynomials be Z or unsigned?
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general:
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- unify simplify_chain_complex, sseq, kernel/image/homology (as much as possible)
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- sseq over Z
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- quadratic linear solver (enumerator?)
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- classes should either COPY or fully SHARE, but not some of each
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(e.g. knot_diagram, resolution_diagram, etc.) -- this is the right
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semantics.
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- clean up/delete setcommon, mapcommon
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- incorporate sage dump into standard classes
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- update use of tuples in steenrod square
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- test mutation invariance, other questions of Robert and Sucharit
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- write paper
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c++11:
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- make vector wrap std::vector (probably faster)
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- use tuple instead of pair, triple; and use tie, a great idiom
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- standardize ring, field interface so test_ring works for everything
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- get clear on default semantics: prefer default when possible
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- standardize use of {} for initializers
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- initializer_list for container types
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- support for iterator
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- compress Steenrod square data
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- get mpimain running again, run 15 xing mutants
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- simplifications to run (5, 8) with symmetries.
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notes:
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all rings (R): multivariate_laurentpoly<R>
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fields (F): Z2 Zp Q fraction_field<E> (for just pids?)
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euclidean domains (E): Z polynomial<F>
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euclidean domain interface:
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num/demon : denom must be a unit
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= num.operator / (denom)
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denom.divides (num)
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denom | num
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num.divide_exact (denom)
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(q, r) = num.divide_with_remainder (denom)
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(q, r) = num / denom
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(q, r) = num.operator / (denom)
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satisfies r = 0 or f(r) < f(denom) and num = q*denom + r
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gcd (a, b)
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lcm (a, b)
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r = num.mod (denom)
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satisfies r = 0 or f(r) < f(denom)
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(d, s, t) = a.extended_gcd (b)
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satifies d is the gcd and d = a*s + b*t
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