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Summary:
A) Resuming Grobnerloop
- better documentation is needed, preferably in the form of a well documented
example (new or modified ?) example07m.g is a bit of a start, but a new
example might be better.
- documentation of new functions should be checked as well
B) Examples (in particular for all functions)
- There is a list as below. Some examples could be extended. A plan of
approach should be made.
- inventarisation
- example with NP <-> GP conversion: not fully done
- example with printing: not fully done
- example with NP arithmetic: not fully done
- example with Grobner (instead of SGrobner): not present
- example needed for interrupted
SGrobner/IsGrobnerPair/MakeGrobnerPair/IsGrobnerBasis
(see above)
- section needed where these functions are described:
SGrobner/IsGrobnerPair/MakeGrobnerPair/IsGrobnerBasis
- example with quotient algebras and representations/calculations
why use compressed matrices ?
StrongNormalForm (and how to make it quicker)
- example with finiteness: split between 13-16: create one combined example
- example for trace exists: colagen, add EvalTrace, PrintTraceList
- example for trunc exists: two weighted homogeneous polynomials
- example for modules: 4,18-22 combine all functions in one (?)
C) Other
- Is 0 homogeneous ? The implementations says no, is that correct ?
D) Some things for the next version
- make a list here
some draft items below
=======================================
First version of time schedule
now: 22 april
summary of todo items:
- make inventarisation of tasks *mostly done*
- make elaborate time schedule allowing to finish in May *mostly done*
- look at examples (usage of functions) (4) *mostly done*
! finish grobnerloop resuming (1,3,5) *check*
29th of april
- add new examples where needed/reference to examples (4)
- JW: test truncated code
-> examples seem good (although A.3 does not use truncation and does not say
anything about being homogeneous, so it might be confusing, *discuss with
Arjeh*)
-> code review:
. check NondivMonsByLevel zero case (*done*)
! for CheckHomogeneousNPs : is zero homogeneous ? (answer seems to be no,
*ask Arjeh*) (*urgent*)
+ false should become fail (-> next version)
+ it would make sense for GBNP.CheckHom to use WieghtedDegreeMon (> next version)
+ ObsTrunc might be made quicker by using the normal function to get
Obstructions using lists
- check new theory (2)
8 may
- new versions (what does this mean)
- add other todo items that need to be done here
15 may
- final reading and testing
20 may
- spare week, for things that take longer and things that come up after
inventarisation and can not be done earlier
URGENT:
SHORT TERM:
- MakeGrobnerPair function (create a [weak] partial pair)
DONE:
- first version
- automatically stop (S)Grobner calculations after a certain number of
iterations
TODO:
- (1) check difference between IsGrobnerPair and IsGrobner
-> 1) elements of a Grobner basis don't have to be monic (can contain <0>)
or leading coefficients different from <1>
-> 2) how about being able to reduce with itself /multiple entries ?
-> seems to be allowed in both cases.
- decide what to do : combine ?
- (2) amc: check updated documentation for (S)Grobner (jwk: ok)
- (3)create example that (first version 7m)
- (S)Grobner stopping after a certain number of iterations
- IsGrobnerPair (leaving out something from or adding something to todo)
- MakeGrobnerPair
- possibly IsGrobner
- Examples for more functions
TODO: (4)
- inventarisation
- example with NP <-> GP conversion: not fully done
- example with printing: not fully done
- example with NP arithmetic: not fully done
- example with Grobner (instead of SGrobner): not present
- example needed for interrupted
SGrobner/IsGrobnerPair/MakeGrobnerPair/IsGrobnerBasis
(see above)
- section needed where these functions are described:
SGrobner/IsGrobnerPair/MakeGrobnerPair/IsGrobnerBasis
- example with quotient algebras and representations/calculations
why use compressed matrices ?
StrongNormalForm (and how to make it quicker)
- example with finiteness: split between 13-16: create one combined example
- example for trace exists: colagen, add EvalTrace, PrintTraceList
- example for trunc exists: two weighted homogeneous polynomials
- example for modules: 4,18-22 combine all functions in one (?)
- create examples
DONE
- name change (if amc agrees) (to be done by jwk)
- make GBNP.IsGrobnerPair global
- make GBNP.MakeGrobnerPair global
- rename IsGrobnerBasisTest IsGrobnerBasis
- rename IsStrongGrobnerBasisTest IsStrongGrobnerBasis
- document new global functions where no documentation was available
- also rename in documentation/examples/top of files
========================================
- options.gi: describe better how options work, which options there are and
where they are used -> already in OPTIONS
- jwk: check status: tree/occurtree vs graphs
- jwk: describe cancellation
- jwk: printing.gi: fix code duplication in PrintNP and GBNP.PrintNPnonewline
- jwk: make kary-heap optional/remove it (too complicated)
- jwk: tree.gi: see if code using tree.gi can be rewritten to use occurtree
- jwk: describe various functions for (strong) normal form
- jwk: make inventarization which functions have multiple versions (and add documenting these to the todo list)
- make test cases for performance testing
NOT urgent:
- occurtree: idea: make interface easier with objects
- check whether all functions use funcs.strong
- combine ReducePolTails/ReducePolTailsPTS
- ReducePol2 can be faster: remove Occur (at XXX)
Urgent but not directly possible:
- fix reducepol functions (what/how?)
- functions for splitting np/npm polynomials (???)
- PTS + Cancellation (what is required here, now prefix generators cannot be
cancelled, is this wat is intended)
- DimQA that gets pg from the GBR record
- DimQA that does not calculate the whole QA but only counts (depth first)
- reduce the number of prefix functions further (by using the two-sided
functions instead)
- options in a record for every calculation, possibly initialized with standard
options at the beginning of the calculation
- make cleancount/cleanpolys options
- possible to use lt, gt everywhere (add ?/conditions)
- Gröbner basis record / objects
- remove function StrongNormalForm2 (by adding occur trees to a Gröbner basis
record)
- put the prefix generators in the end of the list for trees -> saves space
NOTES:
ReducePol2:
- trace.gi:GBNP.ReducePolTrace2
ReducePol: (probably no changing)
- trace.gi:GBNP.ReducePolTrace
ReducePol functions:
grobner.gi:GBNP.ReducePol
calls ReducePol2
grobner_t.gi:GBNP.ReducePol2 G, GLOT
trees, poss prefix-unaware: StrongNormalForm2TS
trace.gi:GBNP.ReducePolTrace2
trace.gi:GBNP.ReducePolTrace
grobnerloops2.gi:GBNP.ReducePolTailsPTS
not a reduce function -> Cleans -> Name is confusing
functions that need to know pg:
-> now in occurtree, only CreateOccurTreeLR remains
for CreateOccurTreeLR: nog doen tree.g graphs.g fincheck.g
AllObs, LeftObsT, RightObsT, ReducePol2, StrongNormalFormT (grobner_t.gi)
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2026-03-28
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