cartan(::Symbol,...) accepts a cartanType

jmichel7 · Oct 2, 2024 · c769746 · c769746
1 parent 11f0896
commit c769746
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diff --git a/src/InitChevie.jl b/src/InitChevie.jl
@@ -84,15 +84,16 @@ const needcartantype=Set([:Invariants,
                           :WeightInfo,
                           :CartanMat])
 
-const debug=Ref(false) # time each call
+debug::Bool=false # time each call
+
 "`getchev(t::TypeIrred,f::Symbol,extra...)` get `CHEVIE[field(t)][f](extra...)`"
 function getchev(t::TypeIrred,f::Symbol,extra...)
   n,args...=field(t)
 # println("d=$d f=$f extra=$extra")
   o=chevieget(n,f)
   if o isa Function
     if haskey(t,:orbit) t=t.orbit[1] end
-if debug[]
+if debug
     if haskey(t,:cartanType) && f in needcartantype
       println("$n.$f(",(args...,extra...,t.cartanType),")")
 @time o(args...,extra...,t.cartanType)
@@ -102,10 +103,8 @@ if debug[]
     end
 else
     if haskey(t,:cartanType) && f in needcartantype
-#     println("$f(",(args...,extra...,t.cartanType),")")
       o(args...,extra...,t.cartanType)
     else 
-#    println("$f(",(args...,extra...),")")
       o(args...,extra...)
     end
 end

diff --git a/src/PermRoot.jl b/src/PermRoot.jl
@@ -348,7 +348,7 @@ function asreflection(m::AbstractMatrix)
   if !isnothing(r) asreflection(m,rr[r,:]) end
 end
 #------------------------------------------------------------------------
-@GapObj struct TypeIrred end
+@GapObj mutable struct TypeIrred end
 
 Base.copy(t::TypeIrred)=TypeIrred(copy(t.prop))
 
@@ -642,18 +642,15 @@ end
 
 function cartan(t::TypeIrred;permute=false)
   if t.series==:ST return improve_type(toM(getchev(t,:CartanMat))) end
-  C=cartan(t.series,rank(t),haskey(t,:bond) ? t.bond : 0)
-  if haskey(t,:cartanType) ct=t.cartanType
-    T=promote_type(typeof(ct),eltype(C))
-    if T!=eltype(C) C=convert.(T,C) end
-    if     t.series in (:B,:G,:I) C[2,1]*=-C[1,2]//ct; C[1,2]=-ct
-    elseif t.series==:F C[3,2]*=-C[2,3]//ct; C[2,3]=-ct
-    end
-  end
-  if indices(t)!=1:rank(t) && permute
-    C=C[sortperm(indices(t)),sortperm(indices(t))]
+  C=haskey(t,:bond) ? haskey(t,:cartanType) ? 
+     cartan(t.series,rank(t),t.bond,t.cartanType) : 
+     cartan(t.series,rank(t),t.bond) : 
+     haskey(t,:cartanType) ? cartan(t.series,rank(t),t.cartanType) : 
+     cartan(t.series,rank(t))
+  if permute && indices(t)!=1:rank(t)
+    p=sortperm(indices(t));C=C[p,p]
   end
-  improve_type(C)
+  C
 end
 
 cartan(W::PermRootGroup,I)=[cartan(W,i,j) for i in I, j in I]

diff --git a/src/Weyl.jl b/src/Weyl.jl
@@ -232,14 +232,15 @@ cartanmats[:a]=cartanmats[:A]=function(r)
   end
   m
 end
-cartanmats[:b]=cartanmats[:B]=function(r)
+cartanmats[:b]=cartanmats[:B]=function(r,cartanType=2)
   m=cartanmats[:A](r)
-  if r>1 m[1,2]=-2 end
+  if r>1 
+    if cartanType==2 m[1,2]=-2 
+    else m=typeof(cartanType//1).(m);m[1,2]=-cartanType;m[2,1]=-2//cartanType
+    end
+  end
   m
 end
-cartanmats[:isym]=cartanmats[:Isym]=function(b)
-  [2 -E(2*b)-E(2*b,-1);-E(2*b)-E(2*b,-1) 2]
-end
 cartanmats[:bsym]=cartanmats[:Bsym]=function(r)
   m=Cyc.(cartanmats[:A](r))
   m[1:2,1:2]=cartanmats[:Isym](4)
@@ -261,10 +262,12 @@ cartanmats[:e]=cartanmats[:E]=function(r)
   u=1:min(r,4); m[u,u]=[2 0 -1 0; 0 2 0 -1;-1 0 2 -1;0 -1 -1 2][u,u]
   m
 end
-cartanmats[:f]=cartanmats[:F]=function(r)
+cartanmats[:f]=cartanmats[:F]=function(r,cartanType=1)
   if r!=4 error("type :F is defined only for rank 4") end
   m=cartanmats[:A](r)
-  m[3,2]=-2
+  if cartanType==1 m[3,2]=-2 
+  else m=typeof(cartanType//1).(m);m[3,2]=-2//cartanType;m[2,3]=-cartanType
+  end
   m
 end
 cartanmats[:fsym]=cartanmats[:Fsym]=function(r)
@@ -273,10 +276,12 @@ cartanmats[:fsym]=cartanmats[:Fsym]=function(r)
   m[3,2]=m[2,3]=-root(2)
   m
 end
-cartanmats[:g]=cartanmats[:G]=function(r)
+cartanmats[:g]=cartanmats[:G]=function(r,cartanType=1)
   if r!=2 error("type :G is defined only for rank 2") end
   m=cartanmats[:A](r)
-  m[2,1]=-3
+  if cartanType==1 m[2,1]=-3
+  else m=typeof(cartanType//1).(m);m[1,2]=-cartanType;m[2,1]=-3//cartanType
+  end
   m
 end
 cartanmats[:gsym]=cartanmats[:Gsym]=r->cartanmats[:Isym](6)
@@ -286,9 +291,18 @@ cartanmats[:h]=cartanmats[:H]=function(r)
   m[1:2,1:2]=cartanmats[:Isym](5)
   m
 end
-cartanmats[:i]=cartanmats[:I]=function(b)
-  res=b%2==0 ? [2 (b==2 ? 0 : -1);-2-E(b)-E(b,-1) 2] : cartanmats[:Isym](b)
-  (b<5 || b==6) ? Int.(res) : res
+cartanmats[:isym]=cartanmats[:Isym]=function(bond)
+  c=improve_type(-E(2*bond)-E(2*bond,-1))
+  [2 c;c 2]
+end
+cartanmats[:i]=cartanmats[:I]=function(r,bond,cartanType=1)
+  if r!=2 error("$r should be 2") end
+  if isodd(bond) cartanmats[:Isym](bond)
+  elseif bond==2 
+    [2 0;0 2]
+  else 
+    improve_type([2 -cartanType;(-2-E(bond)-E(bond,-1))//cartanType 2])
+  end
 end
 """
 `cartan(type, rank [,bond])`
@@ -320,8 +334,8 @@ julia> cartan(:Bsym,2)
  -√2    2
 ```
 """
-function PermRoot.cartan(t::Symbol,r::Integer,b::Integer=0)
-  if haskey(cartanmats,t) b==0 ? cartanmats[t](r) : cartanmats[t](b)
+function PermRoot.cartan(t::Symbol,r::Integer,args::Number...)
+  if haskey(cartanmats,t) cartanmats[t](r,args...)
   else error("Unknown Cartan type $(repr(t)). Known types are:\n",
              join(sort(repr.(collect(keys(cartanmats)))),", "))
   end
@@ -405,10 +419,10 @@ function type_fincox_cartan(m::AbstractMatrix)
       if bond==1 t.series=:A
       elseif bond==2 t.series=:B
         if l(1)==-1 reverse!(s) end # B2 preferred to C2
-        t.cartanType=-l(1)
+        t.cartanType=improve_type(-l(1))
       elseif bond==3 t.series=:G
         if r(1)==-1 reverse!(s) end
-        t.cartanType=-l(1)
+        t.cartanType=improve_type(-l(1))
       else n=conductor(bond)
         if r(1)==-1 reverse!(s) end
         if bond==2+E(n)+E(n,-1) bond=n else bond=2n end
@@ -422,17 +436,18 @@ function type_fincox_cartan(m::AbstractMatrix)
         if l(2)*r(2)==1 t.series=:A
         else t.series=:F
           if r(2)==-1 reverse!(s) end
-          t.cartanType=-l(2)
+          t.cartanType=improve_type(-l(2))
         end
       else n=conductor(l(1)*r(1))
         if n==5 t.series=:H
         else t.series=:B
-          t.cartanType=-l(1)
+          t.cartanType=improve_type(-l(1))
         end
       end
     end
     t.indices=s::Vector{Int}
   end
+  return t
 # println("t=$t")
 # println("indices=",t.indices]," cartan=",cartan(t)," m=$m")
   if cartan(t,permute=true)==m return t end  # countercheck
@@ -797,8 +812,8 @@ julia> reflrep(W)
  [1 3; 0 -1]
 ```
 """
-CoxGroups.coxeter_group(t::Symbol,r::Int=0,b::Int=0;sc=false)=iszero(r) ? coxgroup() :
-sc ? rootdatum(permutedims(cartan(t,r,b)),Matrix{Int}(I,r,r)) : rootdatum(cartan(t,r,b))
+CoxGroups.coxeter_group(t::Symbol,r::Int=0,b::Int...;sc=false)=iszero(r) ? coxgroup() :
+sc ? rootdatum(permutedims(cartan(t,r,b...)),Matrix{Int}(I,r,r)) : rootdatum(cartan(t,r,b...))
 
 """
 `rootdatum(C::AbstractMatrix)`  adjoint root datum  from Cartan matrix `C`.

diff --git a/src/makefile b/src/makefile
@@ -1,4 +1,4 @@
-JULIA=1.10.4
+JULIA=1.10.5
 test: *.jl
 	~/julia-$(JULIA)/bin/julia ../tools/gentest.jl *.jl
 	mv runtests.jl ../test

diff --git a/test/runtests.jl b/test/runtests.jl
@@ -750,6 +750,7 @@ end
 @test mytest("Symbols.jl","defectsymbol([[1,5,6],[1,2]])","1")
 @test mytest("Symbols.jl","degree_fegsymbol([[1,5,6],[1,2]])","88")
 @test mytest("Symbols.jl","valuation_fegsymbol([[1,5,6],[1,2]])","16")
+@test mytest("Symbols.jl","stringsymbol.(rio(),symbols(3,3,0))","12-element Vector{String}:\n \"(1+)\"\n \"(1ζ₃)\"\n \"(1ζ₃²)\"\n \"(01,12,02)\"\n \"(01,02,12)\"\n \"(012,012,123)\"\n \"(0,1,2)\"\n \"(0,2,1)\"\n \"(01,01,13)\"\n \"(0,0,3)\"\n \"(012,,)\"\n \"(012,012,)\"")
 @test mytest("Symbols.jl","stringsymbol.(symbols(3,2))","14-element Vector{String}:\n \"(12,0,0)\"\n \"(02,1,0)\"\n \"(02,0,1)\"\n \"(012,12,01)\"\n \"(01,1,1)\"\n \"(012,01,12)\"\n \"(2,,)\"\n \"(01,2,0)\"\n \"(01,0,2)\"\n \"(1,012,012)\"\n \"(,02,01)\"\n \"(,01,02)\"\n \"(0,,012)\"\n \"(0,012,)\"")
 @test mytest("Symbols.jl","stringsymbol.(symbols(3,3,0))","12-element Vector{String}:\n \"(1+)\"\n \"(1E(3))\"\n \"(1E(3,2))\"\n \"(01,12,02)\"\n \"(01,02,12)\"\n \"(012,012,123)\"\n \"(0,1,2)\"\n \"(0,2,1)\"\n \"(01,01,13)\"\n \"(0,0,3)\"\n \"(012,,)\"\n \"(012,012,)\"")
 @test mytest("Symbols.jl","fegsymbol([[1,5,6],[1,2]])","q¹⁶Φ₅Φ₇Φ₈Φ₉Φ₁₀Φ₁₁Φ₁₄Φ₁₆Φ₁₈Φ₂₀Φ₂₂")

diff --git a/tools/timings.jl b/tools/timings.jl
@@ -8,7 +8,7 @@ using Chairmarks
 
 #julia> @b test_w0(6)
 #1.10.3  11.648 ms (182389 allocs: 12.981 MiB)
-#1.11.α2 11.671 ms (237323 allocs: 13.295 MiB)
+#1.11.rc 11.671 ms (237323 allocs: 13.295 MiB)
 function test_w0(n)
   W=coxsym(n+1)
   Tbasis(hecke(W,Pol()))(longest(W))^2
@@ -22,7 +22,7 @@ end;
 
 #julia> @b CyclotomicNumbers.testmat(9)^2 seconds=2
 #1.10.3  42.501 ms (286780 allocs: 49.168 MiB)
-#1.11.α2 34.639 ms (349995 allocs: 48.217 MiB)
+#1.11.rc 34.639 ms (349995 allocs: 48.217 MiB)
 #
 #testmat(9)^2 in GAP3 85ms in GAP4 60ms
 """
@@ -33,17 +33,17 @@ end;
 
 #julia> @b collect(symmetric_group(10)) seconds=4
 #1.10.3  240.491 ms (4043780 allocs: 336.001 MiB)
-#1.11.α2 189.171 ms (8083258 allocs: 335.999 MiB)
+#1.11.rc 189.171 ms (8083258 allocs: 335.999 MiB)
 #Elements(Group(List([1..9],i->(i,i+1)),()));; GAP3 takes 0.56s
 
 #julia> @b elements(coxgroup(:E,6))
 #1.10.3  4.092 ms (60997 allocs: 12.434 MiB)
-#1.11.α2 3.473 ms (118243 allocs: 13.182 MiB)
+#1.11.rc 3.473 ms (118212 allocs: 13.208 MiB)
 #Elements(CoxeterGroup("E",6));; #GAP3 15.5ms
 
 #julia> @b test_kl(coxgroup(:A,4))
 #1.10.3  5.870 ms (155260 allocs: 9.243 MiB)
-#1.11.α2 5.558 ms (205790 allocs: 8.980 MiB)
+#1.11.rc 5.558 ms (205766 allocs: 8.983 MiB)
 function test_kl(W)
   q=Pol([1],1)
   H=hecke(W,q^2,rootpara=q)
@@ -61,7 +61,7 @@ end;
 
 #julia> @b test_kl1(coxgroup(:A,4))
 #1.10.2  24.752 ms (403416 allocs: 43.278 MiB)
-#1.11.α2 22.338 ms (702082 allocs: 42.648 MiB)
+#1.11.rc 22.338 ms (702087 allocs: 42.652 MiB)
 function test_kl1(W)
   q=Pol([1],1)
   H=hecke(W,q^2,rootpara=q)
@@ -78,7 +78,7 @@ end;
 
 #julia> @b test_kl2(coxgroup(:A,4))
 #1.10.3  4.526 ms (87990 allocs: 7.199 MiB)
-#1.11.α2 3.689 ms (164592 allocs: 6.844 MiB)
+#1.11.rc 3.689 ms (164568 allocs: 6.847 MiB)
 function test_kl2(W)
   el=elements(W)
   maximum(degree(KLPol(W,x,y)) for x in el, y in el)
@@ -100,7 +100,7 @@ end;
 #1.8.5  248.055 μs (6433 allocations: 502.81 KiB)
 #1.9.0  250.546 μs (6254 allocations: 517.97 KiB)
 #1.10.3 264.118 μs (6200 allocs: 517.859 KiB)
-#1.11.α2 230.321 μs (10200 allocs: 576.328 KiB)
+#1.11.rc 230.321 μs (10200 allocs: 576.328 KiB)
 function test_b(W)
   B=BraidMonoid(W)
   b=B(-4,-3,-2,-15,-14,-13,-10,-11,-12,-7,-2,-12,-11,-10,-7,-8,-9,-6,-7,-8,-2,
@@ -121,7 +121,7 @@ end;
 # for r>13 needs BigInt
 #julia> @b test_hm(BigInt,35) seconds=1
 #1.10.3  42.886 ms (1795660 allocs: 57.618 MiB)
-#1.11.α2 48.393 ms (1795664 allocs: 57.618 MiB)
+#1.11.rc 48.393 ms (1795664 allocs: 57.618 MiB)
 function test_hm(rtype,rank)
   m=[rtype(1)//(n+m) for n in 1:rank, m in 1:rank]
   one(m)==m*inv(m)
@@ -136,7 +136,7 @@ end;
 
 #julia> @b PuiseuxPolynomials.fateman(7)
 #1.10.3  15.031 ms (112807 allocs: 29.657 MiB)
-#1.11.β1 14.864 ms (225638 allocs: 29.637 MiB)
+#1.11.rc 14.864 ms (225638 allocs: 29.637 MiB)
 # GAP3: fateman(7) takes 722ms
 """
 fateman:=function(n)local p;
@@ -152,33 +152,32 @@ end;
 #1.8    23.273 μs (621 allocations: 43.44 KiB)
 #1.9.3  25.877 μs (662 allocations: 46.00 KiB)
 #1.10.3 19.070 μs (429 allocs: 28.953 KiB)
-#1.11.α2 15.460 μs (819 allocs: 29.016 KiB)
+#1.11.rc 15.460 μs (819 allocs: 29.016 KiB)
 
 # @b ((x,y)=Mvp.(:x,:y);inv(Frac.([x+y x-y;x+1 y+1])))
 #1.6.3 187.233 μs (3941 allocations: 291.50 KiB)
 #1.7.2 139.797 μs (3418 allocations: 236.66 KiB)
 #1.8.5 137.125 μs (3102 allocations: 216.19 KiB)
 #1.9.0 128.179 μs (2937 allocations: 210.86 KiB)
 #1.10.3 153.370 μs (3631 allocs: 243.969 KiB)
-#1.11.α2 122.602 μs (4994 allocs: 223.609 KiB)
-# GAP3 invert Mvp matrix 3.9ms
-# [[x+y,x-y],[x+1,y+1]]^-1;
+#1.11.rc 122.602 μs (4994 allocs: 223.609 KiB)
+# [[x+y,x-y],[x+1,y+1]]^-1; # GAP3 3.9ms
 
 # @b CycPols.p(Pol()) #GAP3 1.25 ms
 #1.8.5   254.158 μs (5626 allocations: 416.19 KiB)
 #1.10.3  261.749 μs (5240 allocs: 394.188 KiB)
-#1.11.α2 224.240 μs (7381 allocs: 379.156 KiB)
+#1.11.rc 224.240 μs (7381 allocs: 379.156 KiB)
 
 # @b CycPols.p(1) #GAP3 142μs
 #1.8.5   5.140 μs (101 allocations: 19.88 KiB)
 #1.10.3  6.162 μs (101.75 allocs: 21.152 KiB)
-#1.11.α2 5.819 μs (151 allocs: 21.012 KiB)
+#1.11.rc 5.819 μs (151 allocs: 21.012 KiB)
 u=CycPols.p(Pol());
 # @b u _(1) #GAP3 40μs
 #1.8.5   24.669 μs (553 allocations: 41.91 KiB)
 #1.10.3  27.458 μs (553 allocs: 41.906 KiB)
-#1.11.α2 23.535 μs (828 allocs: 41.375 KiB)
+#1.11.rc 23.535 μs (828 allocs: 41.375 KiB)
 # @b u CycPol(_) #GAP3 8.2ms
 #1.8.5   4.749 ms (92895 allocations: 7.35 MiB)
 #1.10.3  4.906 ms (87044 allocs: 6.861 MiB)
-#1.11.β1 3.931 ms (114898 allocs: 6.529 MiB)
+#1.11.rc 3.931 ms (114917 allocs: 6.631 MiB)