[GAP Forum] which function of dictionary can use polynomial or function as key

[Alexander Hulpke]

Dear Forum,

On Sep 24, 2014, at 9/24/14 3:21, Lee Martin CCNP <tesleft at hotmail.com> wrote:

> would like to use rational function as key in dictionary like table function in maple
> which function is a dictionary can use function as key and value as list to store ideals.

Lookup dictionaries currently work with rational functions, e.g:

gap> R:=PolynomialRing(Rationals,["x","y","z"]);AssignGeneratorVariables(R);   
Rationals[x,y,z]
#I  Assigned the global variables [ x, y, z ]

gap> d:=NewDictionary(x,true);
<object>
gap> AddDictionary(d,x,1);
gap> AddDictionary(d,y,2);
gap> LookupDictionary(d,x);
1
gap> LookupDictionary(d,z);
fail
gap> AddDictionary(d,x/y,2);
gap> LookupDictionary(d,z);
fail
gap> LookupDictionary(d,x/y);
2

Instead of numbers you should be able to store arbitrary associated information. However internally lists will be made immutable, so if your ideal list is expected to grow you would need to keep a separate (mutable) list of the ideal lists, storing only an index in the dictionary.

I note that

gap> RepresentationsOfObject(d);
[ "IsComponentObjectRep", "IsDictionaryDefaultRep", "IsListDictionary", 
  "IsListLookupDictionary", "IsSortDictionary", "IsSortLookupDictionary" ]

this currently uses sorted lists internally and not yet hashing. To enable hashing, one would have to add a method for SparseHashKey for rational functions, which currently is not on the list of features.

Best,

   Alexander Hulpke


> Regards,
> Martin 		 	   		  
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