Add KnotTheory as a provided package.

CHANGES.rst

@@ -126,6 +126,8 @@ Package update
 ++++++++++++++
 
 - SymPy 1.8
+- ``KnotTheory`` Mathics package added. This is largely not working, but provided so that others can try, report bugs, and help out.
+
 
 New variables and builtins
 ++++++++++++++++++++++++++

mathics/builtin/scoping.py

@@ -650,6 +650,10 @@ class BeginPackage(Builtin):
              Protect[System`Private`$ContextPathStack, System`$Packages];
              context
         """,
+        "BeginPackage[context_String, needs__List]": """
+             Print["Mathics does not support the second argument: ",needs,". Please add Needs[] explicitly inside the package."];
+             BeginPackage[context]
+        """,
     }
 
 

mathics/packages/KnotTheory/A2Invariant4TorusKnots.m

@@ -0,0 +1,33 @@
+BeginPackage["KnotTheory`A2Invariant4TorusKnots`", {"KnotTheory`"}]
+Message[KnotTheory::loading, "A2Invariant4TorusKnots`"]
+
+Begin["`Private`"]
+
+KOs = {
+  TorusKnot[3, 2], TorusKnot[5, 2], TorusKnot[7, 2], TorusKnot[4, 3],
+  TorusKnot[9, 2], TorusKnot[5, 3], TorusKnot[11, 2], TorusKnot[13, 2],
+  TorusKnot[7, 3], TorusKnot[5, 4], TorusKnot[15, 2]
+}
+
+Is = {
+ q^2 + q^4 + 2*q^6 + q^8 - q^12 - q^14, q^6 + q^8 + 2*q^10 + q^12 + q^14 - 
+  q^18 - q^20 - q^22, q^10 + q^12 + 2*q^14 + q^16 + q^18 - q^26 - q^28 - 
+  q^30, q^10 + q^12 + 2*q^14 + 2*q^16 + 2*q^18 - q^22 - 2*q^24 - 2*q^26 - 
+  q^28 + q^32, q^14 + q^16 + 2*q^18 + q^20 + q^22 - q^34 - q^36 - q^38, 
+ q^14 + q^16 + 2*q^18 + 2*q^20 + 2*q^22 + q^24 - 2*q^28 - 2*q^30 - 2*q^32 - 
+  q^34 + q^40, q^18 + q^20 + 2*q^22 + q^24 + q^26 - q^42 - q^44 - q^46, 
+ q^22 + q^24 + 2*q^26 + q^28 + q^30 - q^50 - q^52 - q^54, 
+ q^22 + q^24 + 2*q^26 + 2*q^28 + 2*q^30 + q^32 + q^34 - q^38 - 2*q^40 - 
+  2*q^42 - 2*q^44 - q^46 + q^56, q^22 + q^24 + 2*q^26 + 2*q^28 + 3*q^30 + 
+  2*q^32 + q^34 - q^36 - 2*q^38 - 3*q^40 - 3*q^42 - 2*q^44 - q^46 + q^48 + 
+  q^50 + q^52, q^26 + q^28 + 2*q^30 + q^32 + q^34 - q^58 - q^60 - q^62
+}
+
+Is = Function /@ (Is /. q -> #)
+
+MapThread[(A2Invariant[#1] = #2)&, {KOs, Is}]
+
+Clear[KOs, Is]
+
+End[]; EndPackage[]
+

mathics/packages/KnotTheory/ColouredJones4TorusKnots.m

@@ -0,0 +1,78 @@
+BeginPackage["KnotTheory`ColouredJones4TorusKnots`", {"KnotTheory`"}]
+Message[KnotTheory::loading, "ColouredJones4TorusKnots`"]
+
+Begin["`Private`"]
+
+TK=TorusKnot[3, 2]
+ColouredJones[TK,2]=
+ #1^2 + #1^5 - #1^7 + #1^8 - #1^9 - #1^10 + #1^11 & 
+
+TK=TorusKnot[5, 2]
+ColouredJones[TK,2]=
+ #1^4 + #1^7 - #1^9 + #1^10 - #1^12 + #1^13 - 2*#1^15 + #1^16 - #1^18 + 
+  #1^19 & 
+
+TK=TorusKnot[7, 2]
+ColouredJones[TK,2]=
+ #1^6 + #1^9 - #1^11 + #1^12 - #1^14 + #1^15 - #1^17 + #1^18 - #1^20 - #1^23 + 
+  #1^24 - #1^26 + #1^27 & 
+
+TK=TorusKnot[4, 3]
+ColouredJones[TK,2]=
+ #1^6 + #1^9 + #1^12 - #1^13 - #1^16 - #1^19 + #1^20 - #1^22 + #1^23 & 
+
+TK=TorusKnot[9, 2]
+ColouredJones[TK,2]=
+ #1^8 + #1^11 - #1^13 + #1^14 - #1^16 + #1^17 - #1^19 + #1^20 - #1^22 + 
+  #1^23 - #1^25 + #1^26 - #1^27 - #1^28 + #1^29 - #1^31 + #1^32 - #1^34 + 
+  #1^35 & 
+
+TK=TorusKnot[5, 3]
+ColouredJones[TK,2]=
+ #1^8 + #1^11 + #1^14 - #1^15 + #1^17 - #1^18 - #1^19 + #1^20 - #1^21 - 
+  #1^22 + #1^23 - #1^25 + #1^26 - #1^28 + #1^29 & 
+
+TK=TorusKnot[11, 2]
+ColouredJones[TK,2]=
+ #1^10 + #1^13 - #1^15 + #1^16 - #1^18 + #1^19 - #1^21 + #1^22 - #1^24 + 
+  #1^25 - #1^27 + #1^28 - #1^30 + #1^31 - 2*#1^33 + #1^34 - #1^36 + #1^37 - 
+  #1^39 + #1^40 - #1^42 + #1^43 & 
+
+TK=TorusKnot[13, 2]
+ColouredJones[TK,2]=
+ #1^12 + #1^15 - #1^17 + #1^18 - #1^20 + #1^21 - #1^23 + #1^24 - #1^26 + 
+  #1^27 - #1^29 + #1^30 - #1^32 + #1^33 - #1^35 + #1^36 - #1^38 - #1^41 + 
+  #1^42 - #1^44 + #1^45 - #1^47 + #1^48 - #1^50 + #1^51 & 
+
+TK=TorusKnot[7, 3]
+ColouredJones[TK,2]=
+ #1^12 + #1^15 + #1^18 - #1^19 + #1^21 - #1^22 + #1^24 - #1^25 - #1^28 - 
+  #1^31 + #1^32 - #1^34 + #1^35 - #1^37 + #1^38 - #1^40 + #1^41 & 
+
+TK=TorusKnot[5, 4]
+ColouredJones[TK,2]=
+ #1^12 + #1^15 + #1^18 - #1^23 - #1^26 - #1^29 + #1^30 - #1^32 + #1^33 - 
+  #1^35 + #1^36 - #1^38 + #1^39 & 
+
+TK=TorusKnot[15, 2]
+ColouredJones[TK,2]=
+ #1^14 + #1^17 - #1^19 + #1^20 - #1^22 + #1^23 - #1^25 + #1^26 - #1^28 + 
+  #1^29 - #1^31 + #1^32 - #1^34 + #1^35 - #1^37 + #1^38 - #1^40 + #1^41 - 
+  #1^43 + #1^44 - #1^45 - #1^46 + #1^47 - #1^49 + #1^50 - #1^52 + #1^53 - 
+  #1^55 + #1^56 - #1^58 + #1^59 & 
+
+TK=TorusKnot[8, 3]
+ColouredJones[TK,2]=
+ #1^14 + #1^17 + #1^20 - #1^21 + #1^23 - #1^24 + #1^26 - #1^27 + #1^29 - 
+  #1^30 - #1^31 + #1^32 - #1^33 - #1^34 + #1^35 - #1^37 + #1^38 - #1^40 + 
+  #1^41 - #1^43 + #1^44 - #1^46 + #1^47 & 
+
+TK=TorusKnot[17, 2]
+ColouredJones[TK,2]=
+ #1^16 + #1^19 - #1^21 + #1^22 - #1^24 + #1^25 - #1^27 + #1^28 - #1^30 + 
+  #1^31 - #1^33 + #1^34 - #1^36 + #1^37 - #1^39 + #1^40 - #1^42 + #1^43 - 
+  #1^45 + #1^46 - #1^48 + #1^49 - 2*#1^51 + #1^52 - #1^54 + #1^55 - #1^57 + 
+  #1^58 - #1^60 + #1^61 - #1^63 + #1^64 - #1^66 + #1^67 & 
+
+End[]; EndPackage[]
+

mathics/packages/KnotTheory/DTCode4KnotsTo11.m

@@ -0,0 +1,216 @@
+BeginPackage["KnotTheory`DTCode4KnotsTo11`", {"KnotTheory`"}]
+Message[KnotTheory::loading, "DTCode4KnotsTo11`"]
+
+Begin["`Private`"]
+
+DTStringsTo11 = {
+  "bca", "bcda", "bdeac", "cdeab", "bdeafc", "bdefac", "bdfeac",
+  "bdefagc", "bdfagce", "befgadc", "begfadc", "cefgabd", "cefgbad",
+  "defgabc", "bdegahcf", "bdfagche", "bdfaghce", "bdfahgce",
+  "bdgeahcf", "befgahcd", "befgahdc", "befghacd", "befghadc",
+  "beghfadc", "behgfadc", "cdefghab", "cdfaghbe", "cdfgbhae",
+  "cdgfbhae", "cefghbad", "cefhgbad", "cfehgbad", "bdFaGCHE",
+  "bdFagChe", "bdFaGHCE", "bdegahcif", "bdegahicf", "bdegaihcf",
+  "bdfahcieg", "bdfahgcie", "bdfgahiec", "bdgahicfe", "bdgaihcfe",
+  "bdgeahicf", "bdgeaihcf", "bdgfahiec", "befgaihcd", "befgaihdc",
+  "befghacid", "befghaidc", "befhadicg", "befhgaidc", "begfhacid",
+  "beghaidcf", "beghfaicd", "beghfaidc", "behgaidcf", "bfghiaecd",
+  "bfghiaedc", "bfhigadec", "bfhigaedc", "bfihgaedc", "cdehgibaf",
+  "cegfhaibd", "cegibhadf", "cegibhdaf", "cegihadbf", "cfghiabed",
+  "cfghibaed", "cfgihabed", "cfgihbaed", "chgfbaied", "dfghiabce",
+  "dfghiacbe", "dfhgibace", "efghiabcd", "bdeGaHCIF", "bdeGahCif",
+  "bdegaHcIF", "bdeGaHICF", "beGFHaCID", "beGFhaCid", "cdehgIbaF",
+  "cEGfHAiBD", "bdegahicjf", "bdegaicjfh", "bdegaihcjf", "bdehaijcgf",
+  "bdehajicgf", "bdfagicjeh", "bdfahciejg", "bdfahcijeg", "bdfahcjieg",
+  "bdfaigcjeh", "bdfgahjiec", "bdfiahjceg", "bdgahicjef", "bdgahicjfe",
+  "bdgahijcef", "bdgahijcfe", "bdgaihcfje", "bdgaijhcfe", "bdgajihcfe",
+  "bdgeaicjfh", "bdgfahjiec", "bdheaijcgf", "bdheajicgf", "bdifahjceg",
+  "befghajidc", "befgiacjdh", "befgiahcjd", "befhadijcg", "befhadjicg",
+  "befhajcidg", "befhajdicg", "befhgajidc", "befhiajcdg", "befhiajdcg",
+  "befhjadicg", "begfahijdc", "begfiacjdh", "begfiahcjd", "beghadijfc",
+  "beghaidcjf", "beghaijcdf", "beghaijdcf", "beghajicdf", "beghajidcf",
+  "begiahcjdf", "begiahdjfc", "begiahjdfc", "behfadijcg", "behfadjicg",
+  "behgadijfc", "behgaidcjf", "behgajdicf", "behifajdcg", "beihfajdcg",
+  "bfghiaejdc", "bfghiajcde", "bfghiajced", "bfghiajedc", "bfghijacde",
+  "bfghijaced", "bfghijaedc", "bfghjiadce", "bfgihaejdc", "bfgihajedc",
+  "bfgihjaedc", "bfhgiadjec", "bfhgiajced", "bfhigaejcd", "bfhigaejdc",
+  "bfhijgaecd", "bfhijgaedc", "bfhjiadceg", "bfijghaedc", "bfijhgaedc",
+  "bfjihgaedc", "cdeghijabf", "cdeghjiabf", "cdfahbijeg", "cdgahibjef",
+  "cdgahibjfe", "cdgahijbef", "cdgahijbfe", "cdghbijaef", "cdghbijafe",
+  "cdgihbjeaf", "cdhgbijaef", "cdhgbijafe", "cdighbjaef", "cefgihjabd",
+  "cefjihdabg", "cegahijdbf", "cegahjidbf", "ceghaibjdf", "ceghbiajfd",
+  "ceghibjadf", "cegiahjbdf", "cegihbjadf", "cehgaidjbf", "cehgibjafd",
+  "cehjgaibdf", "cehjgbiafd", "ceifbhjdag", "ceigahjdbf", "ceighbjdaf",
+  "ceihgbjdaf", "cejghibdaf", "cfghiabjde", "cfghiabjed", "cfghibajed",
+  "cfghijbade", "cfghijbaed", "cfgijhbaed", "cfgjihbaed", "cgfhijbade",
+  "cgfhijbaed", "cgfijhbaed", "cgfjihbaed", "chfgibjade", "chfgibjaed",
+  "chigabjdef", "defghijabc", "deghaijcbf", "dehgaijcbf", "bdeGahiCjf",
+  "bdeGaHICJF", "bdeGaICJFH", "bdfaGIcJEH", "bdFagiCjeh", "bdFaGICJEH",
+  "bdfaHcIEJG", "bdFahCiejg", "bdFaHCIEJG", "bdfaHcIJEG", "bdFahCijeg",
+  "bdFaHCIJEG", "bdFaHCJIEG", "bdFIaHJCEG", "bdgaHIcJEF", "bdGahiCjef",
+  "bdGaHICJEF", "bdgaHIcJFE", "bdGahiCjfe", "bdGaHICJFE", "bdGaHIJCEF",
+  "bdGaHIJCFE", "bdIFaHJCEG", "beGfahiJdC", "beGHaiDCjf", "beGHaIDCJF",
+  "beGHaIJCDF", "beghaIJdcF", "beGHaijDCf", "beGHaIJDCF", "bfHgIadJEC",
+  "bfhGiaDjec", "bfHGIaDJEC", "cdeghIJabF", "cdeghJIabF", "cdfaHbIJEG",
+  "cdgihbJeaF", "cEFgIHjABD", "ceghibJadF", "cegihbJadF", "cEHgAIdjBF",
+  "cEIgAHjdBf", "bdegahjckfi", "bdegaicjfkh", "bdegaicjkfh",
+  "bdegaickjfh", "bdegajhckfi", "bdehaijcgkf", "bdehaijckfg",
+  "bdehaijckgf", "bdehaijkcfg", "bdehaijkcgf", "bdehajicgkf",
+  "bdehajkicgf", "bdehakjicgf", "bdfagicjekh", "bdfagicjkeh",
+  "bdfagickjeh", "bdfahcjekgi", "bdfahcjiekg", "bdfahicjkge",
+  "bdfaicjkehg", "bdfaickjehg", "bdfaigcjkeh", "bdfaigckjeh",
+  "bdfaihcjkge", "bdfaijcekgh", "bdfajicekgh", "bdfgaikjehc",
+  "bdfhaijkecg", "bdfhaikjecg", "bdfiahjcekg", "bdgahickjef",
+  "bdgahickjfe", "bdgahijcekf", "bdgahijckfe", "bdgahikcjfe",
+  "bdgahjcfkei", "bdgahjickfe", "bdgaihjcekf", "bdgaijckfeh",
+  "bdgaijhckef", "bdgaijhckfe", "bdgajhcfkei", "bdgajhcifke",
+  "bdgajhicfke", "bdgajickfeh", "bdgajihcfke", "bdgajkicfhe",
+  "bdgeahjckfi", "bdgeaicjkfh", "bdgeaickjfh", "bdgeajhckfi",
+  "bdgfaikjehc", "bdghaijkefc", "bdghaijkfec", "bdhaijkcgef",
+  "bdhaijkcgfe", "bdhajkicfge", "bdhajkicgfe", "bdhakjicgfe",
+  "bdheaijckfg", "bdheaijckgf", "bdheaijkcfg", "bdheaijkcgf",
+  "bdheajkicgf", "bdheakjicgf", "bdhfaijkecg", "bdhfaikjecg",
+  "bdhgaijkefc", "bdhgaijkfec", "bdifahjcekg", "befgakijcdh",
+  "befgakijdch", "befghaijkcd", "befgiacjkdh", "befgiackjdh",
+  "befgiajdkch", "befgiakjdhc", "befgjahckdi", "befgjaidkch",
+  "befgkaijcdh", "befgkaijdch", "befhakijcgd", "befhakijdgc",
+  "befhakjicgd", "befhakjidgc", "befhiajcdkg", "befhiajdckg",
+  "befhiajkdcg", "befhiakcjdg", "befhiakjdcg", "befhjakidcg",
+  "befhkaijdgc", "befhkajidgc", "befiadjkchg", "befiadkjchg",
+  "befigakdjch", "befihajkdcg", "befihakjdcg", "befjhaidkcg",
+  "befjhakdgci", "begfajikcdh", "begfiacjkdh", "begfiackjdh",
+  "begfjahckdi", "beghajdckfi", "beghajicdkf", "beghajidckf",
+  "beghajkicdf", "beghajkidcf", "beghakjicdf", "beghakjidcf",
+  "beghiajckfd", "beghiajkdfc", "begiahckjdf", "begiajckfdh",
+  "begiajdkcfh", "begiakdjchf", "begifadjkch", "begifadkjch",
+  "begifakcjdh", "begifakdjch", "begihajkdfc", "begjadikcfh",
+  "begjahdkfci", "begjahidkcf", "begjahkdfci", "begjakidfch",
+  "begjhacfkdi", "begjhaikfcd", "begjhaikfdc", "begkiajcdfh",
+  "behfiajckdg", "behgajdckfi", "behgajdickf", "behgfaijkdc",
+  "behgiadjkfc", "behgiajckfd", "behgiajkfdc", "behiajkdcgf",
+  "behiakjdcgf", "behifadjkgc", "behifajkcdg", "behifajkdcg",
+  "behifakjcdg", "behifakjdcg", "behigajkcfd", "behjakidfcg",
+  "behjfaickdg", "behjfaidkgc", "behjfaikdgc", "behjgaikfcd",
+  "behjgaikfdc", "beifadjkchg", "beifadkjchg", "beifahjdkgc",
+  "beifgadjkch", "beifhajdkcg", "beigahjdkcf", "beigakdjchf",
+  "beigakjdfch", "beigfadjkch", "beighacjkfd", "beighajdkfc",
+  "beighajkfcd", "beihajkdcgf", "beihakjdcgf", "beihfadjkgc",
+  "beihgajdkfc", "beihgajkcfd", "beijahcdkgf", "beijakcdfgh",
+  "beikgajdcfh", "bejgadikcfh", "bfghiakcjde", "bfghiakcjed",
+  "bfghiakjdce", "bfghiakjdec", "bfghiakjedc", "bfghijacdke",
+  "bfghijacked", "bfghijadcke", "bfghijakdec", "bfghijakedc",
+  "bfghikajdec", "bfghikajedc", "bfghjaeckdi", "bfghjakdcei",
+  "bfghjiacked", "bfghkiajecd", "bfgihakjdce", "bfgijaekcdh",
+  "bfgijaekdch", "bfgijhakedc", "bfgjhiakecd", "bfgjihakedc",
+  "bfgjkiadech", "bfhgiadkjec", "bfhgiakcjed", "bfhgijacked",
+  "bfhgjaeckdi", "bfhgjiacked", "bfhigjadcke", "bfhijakecdg",
+  "bfhijakedcg", "bfhijgaekdc", "bfhijgakcde", "bfhijgakced",
+  "bfhijgakedc", "bfhjgiadkec", "bfhjigaekdc", "bfhjigakedc",
+  "bfhkiadcjeg", "bfhkiajecgd", "bfhkjiacged", "bfighakjecd",
+  "bfigjakdech", "bfigjhadkce", "bfihjgadkec", "bfihjgakced",
+  "bfijgaekdch", "bfijghaekcd", "bfijghaekdc", "bfijhakdecg",
+  "bfijhakedcg", "bfijhgaekcd", "bfijhgaekdc", "bfikhadjecg",
+  "bfikjgadceh", "bfjigaekdch", "bfjihakedcg", "bgeficajkdh",
+  "bgehkiajcfd", "bgejkiadcfh", "bghijkafcde", "bghijkafced",
+  "bghijkafedc", "bghikjafdce", "bghjikafedc", "bgijkcadefh",
+  "bgijkhaefcd", "bgijkhaefdc", "bgijkhafecd", "bgijkhafedc",
+  "bgikhjadfce", "bgjkhiafedc", "bgjkihafedc", "bgkjihafedc",
+  "cdeihjkbagf", "cdeihkjbagf", "cdfagibjkeh", "cdfahibjkge",
+  "cdfaihbjkge", "cdfaijbekgh", "cdfajibekgh", "cdfjhikbeag",
+  "cdfjihkbeag", "cdgahijbkfe", "cdgahjibkfe", "cdgaijbkfeh",
+  "cdgajibkfeh", "cdghbijakfe", "cdghbjiakfe", "cdhajkibfge",
+  "cdhgbijakfe", "cdhgbjiakfe", "cefghikjbad", "cefgjikdbah",
+  "cefijhkbadg", "cefjhikdbag", "cefjihkbadg", "cefkhidjbag",
+  "cefkihjbagd", "ceghjbiakfd", "cegiajkbfdh", "cegjaibkfdh",
+  "cegjbiakdfh", "cehfbijkadg", "cehfbikjadg", "cehfiajkbdg",
+  "cehfiakjbdg", "cehfjaibkdg", "cehgbijkafd", "cehgiajkbfd",
+  "cehgjbiakdf", "cehgjiakfbd", "cehigajbkfd", "cehijadbkfg",
+  "cehijbdakgf", "cehjbidkafg", "cehjiadkbfg", "cehkbijadfg",
+  "cehkbijadgf", "cehkbijdafg", "cehkbijdagf", "cehkiajdbfg",
+  "cehkiajdbgf", "cehkjiadfbg", "ceiahjkbdgf", "ceiahkjbdgf",
+  "ceigajkdfbh", "ceighbkjfad", "ceigjbkdfah", "ceikhbdjfag",
+  "cejgaidkfbh", "cfekhijdbag", "cfghijbaked", "cfghjibaked",
+  "cfgijabkedh", "cfgijbakedh", "cfgjiabkedh", "cfgjibakedh",
+  "cfhgijakbed", "cfhgjiakbed", "cfhigbjkade", "cfhikbjeadg",
+  "cfhjkbieagd", "cfhjkiaebgd", "cfhkiajbdge", "cfhkibjadeg",
+  "cfhkibjaedg", "cfhkijadbeg", "cfhkjbidaeg", "cfhkjbieagd",
+  "cfhkjiadbeg", "cfhkjiaebgd", "cfigkbjdeah", "cfihgbjkaed",
+  "cfihkbjdaeg", "cfikgbjdaeh", "cfikhbjdeag", "cfikhbjedag",
+  "cgeiakjbfdh", "cgfhjibaked", "cghijkabfde", "cghijkabfed",
+  "cghijkbafde", "cghijkbafed", "cghjkiabefd", "cghjkiabfed",
+  "cghjkibaefd", "cghjkibafed", "cghkjiabfed", "cghkjibafed",
+  "cgihjkbdafe", "cgihkjbdafe", "chfijbkeadg", "chfjibkeadg",
+  "cihfbajkedg", "cihfbakjedg", "cihgbajkefd", "cihgjbakfde",
+  "cihgjbakfed", "dfhikbjaceg", "dfhjaikcbeg", "dghijkabcfe",
+  "dghijkacbfe", "dghijkcbafe", "dghikjabcfe", "dghikjacbfe",
+  "dghikjcbafe", "dgihjkbacfe", "dgihkjbacfe", "dhgikjcbafe",
+  "eghijkabcdf", "eghijkabdcf", "eghijkbadcf", "fghijkabcde",
+  "bdegaHJcKFI", "bdeGahjCkfi", "bdeGaHJCKFI", "bdegaicJfKH",
+  "bdegaIcjFkh", "bdegaIcJFKH", "bdeGaiCjfkh", "bdeGaICJFKH",
+  "bdegaIcJKFH", "bdeGaiCjkfh", "bdeGaICJKFH", "bdeGaICKJFH",
+  "bdehaIJcKFG", "bdeHaijCkfg", "bdeHaIJCKFG", "bdehaIJcKGF",
+  "bdeHaijCkgf", "bdeHaIJCKGF", "bdeHaIJKCFG", "bdeHaIJKCGF",
+  "bdfaGIcJEKH", "bdFagiCjekh", "bdFaGICJEKH", "bdfagIcJKEH",
+  "bdfaGIcJKEH", "bdFagiCjkeh", "bdFaGICJKEH", "bdfaGIcKJEH",
+  "bdFagiCkjeh", "bdFaGICKJEH", "bdfaHcJEKGI", "bdFahCjekgi",
+  "bdFaHCJEKGI", "bdfaHIcJKGE", "bdFahiCjkge", "bdFaHICJKGE",
+  "bdFaICJKEHG", "bdFaICKJEHG", "bdfaIHcJKGE", "bdFaihCjkge",
+  "bdFaIHCJKGE", "bdfaIJcEKGH", "bdFaijCekgh", "bdFaIJCEKGH",
+  "bdfaJIcEKGH", "bdFajiCekgh", "bdFaJICEKGH", "bdFHaIJKECG",
+  "bdFHaIKJECG", "bdFIaHJCEKG", "bdgaHIcKJEF", "bdGahiCkjef",
+  "bdGaHICKJEF", "bdgaHIcKJFE", "bdGahiCkjfe", "bdGaHICKJFE",
+  "bdGaHIJCEKF", "bdgaHIJcKFE", "bdGahijCkfe", "bdGaHIJCKFE",
+  "bdGaHIKCJFE", "bdgaHJIcKFE", "bdGahjiCkfe", "bdGaHJICKFE",
+  "bdgaihJceKF", "bdgaIHjcEkf", "bdgaIHJcEKF", "bdGaihjCekf",
+  "bdGaIHJCEKF", "bdGaIJCKFEH", "bdgaJhcifKE", "bdGajhCifke",
+  "bdGajHCIFke", "bdGaJhCifKE", "bdGaJHCIFKE", "bdgaJhicfKE",
+  "bdGajHICFke", "bdGaJHICFKE", "bdGaJICKFEH", "bdgeaIcJKFH",
+  "bdHaJKICFGE", "bdHFaIJKECG", "bdHFaIKJECG", "bdIFaHJCEKG",
+  "befGhaIjkCd", "befGHaIJKCD", "befgiajdKcH", "befhiaJcdKG",
+  "befHIajCDkg", "befhiaJdcKG", "befHIajDCkg", "befJHaIDKCG",
+  "begFaJikcDh", "begfajiKcdH", "begFaJiKcDH", "beGFaJIKCDH",
+  "begfIacJKDH", "beGFiaCjkdh", "beGFIaCJKDH", "begfIacKJDH",
+  "beGFiaCkjdh", "beGFIaCKJDH", "begfJahcKDI", "beGHaJKICDF",
+  "beghaJKidcF", "beGHajkIDCf", "beGHaJKIDCF", "beGHiajCkfd",
+  "beGhiajKdfC", "begHIajkDfc", "beGHIaJKDFC", "begiajdKcfH",
+  "beGihajKdfC", "begihaJkdFc", "begIHajkDfc", "beGIHajKDfC",
+  "beGIHaJKDFC", "beGjaHIDKcF", "begJahidkCf", "beGJaHIDKCF",
+  "beHFiaJCkdG", "beHFIaJCKDG", "beHGfaIJKDC", "behGIaDjkFc",
+  "beHIgajkCfd", "beIFaHJDKGC", "beiFHaJDkcG", "beIGHaCJKFD",
+  "beIGHaJDKFC", "beIGHaJKFCD", "beiHGajDkfc", "beIHGaJDKFC",
+  "beIJaHCDKGF", "beIKGaJDCFH", "bfgHkIaJECd", "bfHgiadKjeC",
+  "bfHGijaCked", "bfHGIJaCKED", "bfhgJIacKED", "bfHGjiaCked",
+  "bfHGJIaCKED", "bfHJGIaDKEC", "bfHkIaJECGd", "bfiGhakJecD",
+  "bgEJKiaDCfH", "bgejkIadcFh", "bgEJKIaDCFH", "bgIJKCaDEFH",
+  "cdeihJKbaGF", "cdeihKJbaGF", "cdfaHIbJKGE", "cdfaIJbEKGH",
+  "cdfjhiKbeaG", "cdfjHIkbEag", "cdfjihKbeaG", "cEfghIkjBad",
+  "cEFgHIkjBAd", "cefijhKbadG", "cefIJhkbaDg", "cEfjhIkdBag",
+  "cefjihKbadG", "cEfkhIdjBag", "cEFkHIdjBAg", "cEghJBIakFD",
+  "cEghjBiakfd", "ceGiajkBfdh", "cegjaIbkFdh", "cegjbIakdFh",
+  "cEHfIAjkBDg", "cehfiaKJbdG", "cEHfIAkjBDg", "ceHfjaiBkdg",
+  "cEhfjAibkdg", "cEhgjBiakdf", "cEHgJIAkFBD", "ceHijadBkfg",
+  "cEhijAdbkfg", "cEhijBdakgf", "cEJgAIdkFBh", "cFHgIJAkBED",
+  "cFHgJIAkBED", "cFhigBjkade", "cGeIakjBfDh", "cGeiakjBfdh",
+  "cihgJbakfDE"
+}
+
+Module[
+  {K, Type, dts, at, n, k, dt, t},
+  at = 0;
+  Do[
+    Type = {Alternating, NonAlternating}[[t]];
+    Do[
+      dts = DTStringsTo11[[++at]];
+      K = Knot[n, Type, k];
+      dt = If[# >= 97, 2(# - 96), -2(# - 64)] & /@ ToCharacterCode[dts];
+      dt = DTCode @@ dt;
+      DTCode[K] = dt,
+      {k, NumberOfKnots[n, Type]}
+    ],
+    {n, 3, 11}, {t, 2}
+  ]
+]
+
+Clear[DTStringsTo11]
+
+End[]; EndPackage[]