Tests do not pass

experimental/runge-kutta/aa-runge-kutta-4-4.jl

@@ -0,0 +1,12 @@
+R, (a_21, a_31, a_32, a_41, a_42, a_43, b_1, b_2, b_3, b_4) = PolynomialRing(QQ, ["a_21", "a_31", "a_32", "a_41", "a_42", "a_43", "b_1", "b_2", "b_3", "b_4"])
+
+system = [
+    b_1 + b_2 + b_3 + b_4 - 1,
+    2*a_21*b_2 + 2*a_31*b_3 + 2*a_32*b_3 + 2*a_41*b_4 + 2*a_42*b_4 + 2*a_43*b_4 - 1,
+    6*a_21*a_32*b_3 + 6*a_21*a_42*b_4 + 6*a_31*a_43*b_4 + 6*a_32*a_43*b_4 - 1,
+    3*a_21^2*b_2 + 3*a_31^2*b_3 + 6*a_31*a_32*b_3 + 3*a_32^2*b_3 + 3*a_41^2*b_4 + 6*a_41*a_42*b_4 + 6*a_41*a_43*b_4 + 3*a_42^2*b_4 + 6*a_42*a_43*b_4 + 3*a_43^2*b_4 - 1,
+    24*a_21*a_32*a_43*b_4 - 1,
+    12*a_21^2*a_32*b_3 + 12*a_21^2*a_42*b_4 + 12*a_31^2*a_43*b_4 + 24*a_31*a_32*a_43*b_4 + 12*a_32^2*a_43*b_4 - 1,
+    8*a_21*a_31*a_32*b_3 + 8*a_21*a_32^2*b_3 + 8*a_21*a_41*a_42*b_4 + 8*a_21*a_42^2*b_4 + 8*a_21*a_42*a_43*b_4 + 8*a_31*a_41*a_43*b_4 + 8*a_31*a_42*a_43*b_4 + 8*a_31*a_43^2*b_4 + 8*a_32*a_41*a_43*b_4 + 8*a_32*a_42*a_43*b_4 + 8*a_32*a_43^2*b_4 - 1,
+    4*a_21^3*b_2 + 4*a_31^3*b_3 + 12*a_31^2*a_32*b_3 + 12*a_31*a_32^2*b_3 + 4*a_32^3*b_3 + 4*a_41^3*b_4 + 12*a_41^2*a_42*b_4 + 12*a_41^2*a_43*b_4 + 12*a_41*a_42^2*b_4 + 24*a_41*a_42*a_43*b_4 + 12*a_41*a_43^2*b_4 + 4*a_42^3*b_4 + 12*a_42^2*a_43*b_4 + 12*a_42*a_43^2*b_4 + 4*a_43^3*b_4 - 1,
+]

experimental/runge-kutta/orderings.jl

@@ -0,0 +1,36 @@
+
+using AbstractAlgebra
+import Combinatorics
+using Plots
+using Random
+include("yang.jl")
+
+R = parent(polys[1])
+
+xs = gens(R)
+times = Dict()
+Groebner._perm[] = collect(1:length(xs))
+
+@profview Groebner.groebner(
+        polys, 
+        ordering=Groebner.DegRevLex(),
+        linalg=:prob
+    );
+
+times[Groebner._perm[]] = t.time
+
+i = 0
+for ord in Combinatorics.permutations(collect(1:length(xs)))
+    Groebner._perm[] = shuffle(collect(1:length(xs)))
+
+    t = @timed Groebner.groebner(
+        polys, 
+        ordering=Groebner.DegRevLex(),
+        linalg=:prob
+    );
+    times[Groebner._perm[]] = t.time
+    if i == 1
+        break
+    end
+    i += 1
+end

experimental/runge-kutta/run.jl

@@ -1,20 +1,56 @@
 using DynamicPolynomials
 using Groebner
 import Profile
+import Nemo
 
 macro pr(ex, args...)
     return quote
         Profile.clear()
-        Profile.init(n=10^7, delay=1e-5)
+        Profile.init(n=10^8, delay=1e-5)
         Profile.@profile $(esc(ex))
         view_profile(; $(esc.(args)...))
     end
 end
 
-include((@__DIR__)*"/runge-kutta-6-6.jl");
+using Nemo
+include((@__DIR__)*"/aa-runge-kutta-8-7.jl");
 
-vs = split("a_21 a_31 a_32 a_41 a_42 a_43 a_51 a_52 a_53 a_54 a_61 a_62 a_63 a_64 a_65 b_1 b_2 b_3 b_4 b_5 b_6")
-length(vs)
+@time gb = Groebner.groebner(
+    system,
+    ordering=Groebner.DegRevLex(),
+    maxpairs=1000
+);
+
+vs = split("a_21 a_31 a_32 a_41 a_42 a_43 a_51 a_52 a_53 a_54 a_61 a_62 a_63 a_64 a_65 a_71 a_72 a_73 a_74 a_75 a_76 a_81 a_82 a_83 a_84 a_85 a_86 a_87 b_1 b_2 b_3 b_4 b_5 b_6 b_7 b_8")
+vs
+ord = Groebner.WeightedOrdering([[10 for i in 1:28]..., [1 for i in 1:8]...])
+
+gb = Groebner.groebner(
+    system,
+    linalg=:prob,
+    # ordering=ord
+);
+
+println(gb)
+
+using AbstractAlgebra
+include((@__DIR__)*"/aa-runge-kutta-6-6.jl");
 length(system)
+gens(parent(system[1]))
+
+system_autoreduced = deepcopy(system);
+for i in 1:length(system)
+    f = system_autoreduced[i]
+    I = system[i .!= 1:length(system)]
+    system_autoreduced[i] = AbstractAlgebra.normal_form(f, I)
+end;
+
+@pr gb = Groebner.groebner(
+    system,
+    linalg=:prob,
+    ordering=DegRevLex()
+);
 
-@time Groebner.groebner(system,linalg=:prob);
+@polyvar x y z a b c
+s = [y, x, z, a + b^2 + c^3]
+g = groebner(s, ordering=Groebner.WeightedOrdering([1,10,10,1,1,1]))

experimental/runge-kutta/yang.jl

@@ -0,0 +1,72 @@
+using AbstractAlgebra
+R1, (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V) =  PolynomialRing(GF(101), ["a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V"], ordering = :degrevlex);
+polys = [
+  d*g*j*m-c*h*j*m-d*f*k*m+b*h*k*m+c*f*l*m-b*g*l*m-d*g*i*n+c*h*i*n+d*e*k*n-a*h*k*n-c*e*l*n+a*g*l*n+d*f*i*o-b*h*i*o-d*e*j*o+a*h*j*o+b*e*l*o-a*f*l*o-c*f*i*p+b*g*i*p+c*e*j*p-a*g*j*p-b*e*k*p+a*f*k*p,
+  d*g*j*q-c*h*j*q-d*f*k*q+b*h*k*q+c*f*l*q-b*g*l*q-d*g*i*r+c*h*i*r+d*e*k*r-a*h*k*r-c*e*l*r+a*g*l*r+d*f*i*s-b*h*i*s-d*e*j*s+a*h*j*s+b*e*l*s-a*f*l*s-c*f*i*t+b*g*i*t+c*e*j*t-a*g*j*t-b*e*k*t+a*f*k*t,
+  d*g*n*q-c*h*n*q-d*f*o*q+b*h*o*q+c*f*p*q-b*g*p*q-d*g*m*r+c*h*m*r+d*e*o*r-a*h*o*r-c*e*p*r+a*g*p*r+d*f*m*s-b*h*m*s-d*e*n*s+a*h*n*s+b*e*p*s-a*f*p*s-c*f*m*t+b*g*m*t+c*e*n*t-a*g*n*t-b*e*o*t+a*f*o*t,
+  d*k*n*q-c*l*n*q-d*j*o*q+b*l*o*q+c*j*p*q-b*k*p*q-d*k*m*r+c*l*m*r+d*i*o*r-a*l*o*r-c*i*p*r+a*k*p*r+d*j*m*s-b*l*m*s-d*i*n*s+a*l*n*s+b*i*p*s-a*j*p*s-c*j*m*t+b*k*m*t+c*i*n*t-a*k*n*t-b*i*o*t+a*j*o*t,
+  h*k*n*q-g*l*n*q-h*j*o*q+f*l*o*q+g*j*p*q-f*k*p*q-h*k*m*r+g*l*m*r+h*i*o*r-e*l*o*r-g*i*p*r+e*k*p*r+h*j*m*s-f*l*m*s-h*i*n*s+e*l*n*s+f*i*p*s-e*j*p*s-g*j*m*t+f*k*m*t+g*i*n*t-e*k*n*t-f*i*o*t+e*j*o*t,
+  d*g*j*u-c*h*j*u-d*f*k*u+b*h*k*u+c*f*l*u-b*g*l*u-d*g*i*v+c*h*i*v+d*e*k*v-a*h*k*v-c*e*l*v+a*g*l*v+d*f*i*w-b*h*i*w-d*e*j*w+a*h*j*w+b*e*l*w-a*f*l*w-c*f*i*x+b*g*i*x+c*e*j*x-a*g*j*x-b*e*k*x+a*f*k*x,
+  d*g*n*u-c*h*n*u-d*f*o*u+b*h*o*u+c*f*p*u-b*g*p*u-d*g*m*v+c*h*m*v+d*e*o*v-a*h*o*v-c*e*p*v+a*g*p*v+d*f*m*w-b*h*m*w-d*e*n*w+a*h*n*w+b*e*p*w-a*f*p*w-c*f*m*x+b*g*m*x+c*e*n*x-a*g*n*x-b*e*o*x+a*f*o*x,
+  d*k*n*u-c*l*n*u-d*j*o*u+b*l*o*u+c*j*p*u-b*k*p*u-d*k*m*v+c*l*m*v+d*i*o*v-a*l*o*v-c*i*p*v+a*k*p*v+d*j*m*w-b*l*m*w-d*i*n*w+a*l*n*w+b*i*p*w-a*j*p*w-c*j*m*x+b*k*m*x+c*i*n*x-a*k*n*x-b*i*o*x+a*j*o*x,
+  h*k*n*u-g*l*n*u-h*j*o*u+f*l*o*u+g*j*p*u-f*k*p*u-h*k*m*v+g*l*m*v+h*i*o*v-e*l*o*v-g*i*p*v+e*k*p*v+h*j*m*w-f*l*m*w-h*i*n*w+e*l*n*w+f*i*p*w-e*j*p*w-g*j*m*x+f*k*m*x+g*i*n*x-e*k*n*x-f*i*o*x+e*j*o*x,
+  d*g*r*u-c*h*r*u-d*f*s*u+b*h*s*u+c*f*t*u-b*g*t*u-d*g*q*v+c*h*q*v+d*e*s*v-a*h*s*v-c*e*t*v+a*g*t*v+d*f*q*w-b*h*q*w-d*e*r*w+a*h*r*w+b*e*t*w-a*f*t*w-c*f*q*x+b*g*q*x+c*e*r*x-a*g*r*x-b*e*s*x+a*f*s*x,
+  d*k*r*u-c*l*r*u-d*j*s*u+b*l*s*u+c*j*t*u-b*k*t*u-d*k*q*v+c*l*q*v+d*i*s*v-a*l*s*v-c*i*t*v+a*k*t*v+d*j*q*w-b*l*q*w-d*i*r*w+a*l*r*w+b*i*t*w-a*j*t*w-c*j*q*x+b*k*q*x+c*i*r*x-a*k*r*x-b*i*s*x+a*j*s*x,
+  h*k*r*u-g*l*r*u-h*j*s*u+f*l*s*u+g*j*t*u-f*k*t*u-h*k*q*v+g*l*q*v+h*i*s*v-e*l*s*v-g*i*t*v+e*k*t*v+h*j*q*w-f*l*q*w-h*i*r*w+e*l*r*w+f*i*t*w-e*j*t*w-g*j*q*x+f*k*q*x+g*i*r*x-e*k*r*x-f*i*s*x+e*j*s*x,
+  d*o*r*u-c*p*r*u-d*n*s*u+b*p*s*u+c*n*t*u-b*o*t*u-d*o*q*v+c*p*q*v+d*m*s*v-a*p*s*v-c*m*t*v+a*o*t*v+d*n*q*w-b*p*q*w-d*m*r*w+a*p*r*w+b*m*t*w-a*n*t*w-c*n*q*x+b*o*q*x+c*m*r*x-a*o*r*x-b*m*s*x+a*n*s*x,
+  h*o*r*u-g*p*r*u-h*n*s*u+f*p*s*u+g*n*t*u-f*o*t*u-h*o*q*v+g*p*q*v+h*m*s*v-e*p*s*v-g*m*t*v+e*o*t*v+h*n*q*w-f*p*q*w-h*m*r*w+e*p*r*w+f*m*t*w-e*n*t*w-g*n*q*x+f*o*q*x+g*m*r*x-e*o*r*x-f*m*s*x+e*n*s*x,
+  l*o*r*u-k*p*r*u-l*n*s*u+j*p*s*u+k*n*t*u-j*o*t*u-l*o*q*v+k*p*q*v+l*m*s*v-i*p*s*v-k*m*t*v+i*o*t*v+l*n*q*w-j*p*q*w-l*m*r*w+i*p*r*w+j*m*t*w-i*n*t*w-k*n*q*x+j*o*q*x+k*m*r*x-i*o*r*x-j*m*s*x+i*n*s*x,
+  a*y+b*z+c*A+d*B,
+  e*y+f*z+g*A+h*B,
+  i*y+j*z+k*A+l*B,
+  m*y+n*z+o*A+p*B,
+  q*y+r*z+s*A+t*B,
+  u*y+v*z+w*A+x*B,
+  a*C+b*D+c*E+d*F,
+  e*C+f*D+g*E+h*F,
+  i*C+j*D+k*E+l*F,
+  m*C+n*D+o*E+p*F,
+  q*C+r*D+s*E+t*F,
+  u*C+v*D+w*E+x*F,
+  a*G+b*H+c*I+d*J,
+  e*G+f*H+g*I+h*J,
+  i*G+j*H+k*I+l*J,
+  m*G+n*H+o*I+p*J,
+  q*G+r*H+s*I+t*J,
+  u*G+v*H+w*I+x*J,
+  a*K+b*L+c*M+d*N,
+  e*K+f*L+g*M+h*N,
+  i*K+j*L+k*M+l*N,
+  m*K+n*L+o*M+p*N,
+  q*K+r*L+s*M+t*N,
+  u*K+v*L+w*M+x*N,
+  B*E*H*K-A*F*H*K-B*D*I*K+z*F*I*K+A*D*J*K-z*E*J*K-B*E*G*L+A*F*G*L+B*C*I*L-y*F*I*L-A*C*J*L+y*E*J*L+B*D*G*M-z*F*G*M-B*C*H*M+y*F*H*M+z*C*J*M-y*D*J*M-A*D*G*N+z*E*G*N+A*C*H*N-y*E*H*N-z*C*I*N+y*D*I*N,
+  a*O+b*P+c*Q+d*R,
+  e*O+f*P+g*Q+h*R,
+  i*O+j*P+k*Q+l*R,
+  m*O+n*P+o*Q+p*R,
+  q*O+r*P+s*Q+t*R,
+  u*O+v*P+w*Q+x*R,
+  B*E*H*O-A*F*H*O-B*D*I*O+z*F*I*O+A*D*J*O-z*E*J*O-B*E*G*P+A*F*G*P+B*C*I*P-y*F*I*P-A*C*J*P+y*E*J*P+B*D*G*Q-z*F*G*Q-B*C*H*Q+y*F*H*Q+z*C*J*Q-y*D*J*Q-A*D*G*R+z*E*G*R+A*C*H*R-y*E*H*R-z*C*I*R+y*D*I*R,
+  B*E*L*O-A*F*L*O-B*D*M*O+z*F*M*O+A*D*N*O-z*E*N*O-B*E*K*P+A*F*K*P+B*C*M*P-y*F*M*P-A*C*N*P+y*E*N*P+B*D*K*Q-z*F*K*Q-B*C*L*Q+y*F*L*Q+z*C*N*Q-y*D*N*Q-A*D*K*R+z*E*K*R+A*C*L*R-y*E*L*R-z*C*M*R+y*D*M*R,
+  B*I*L*O-A*J*L*O-B*H*M*O+z*J*M*O+A*H*N*O-z*I*N*O-B*I*K*P+A*J*K*P+B*G*M*P-y*J*M*P-A*G*N*P+y*I*N*P+B*H*K*Q-z*J*K*Q-B*G*L*Q+y*J*L*Q+z*G*N*Q-y*H*N*Q-A*H*K*R+z*I*K*R+A*G*L*R-y*I*L*R-z*G*M*R+y*H*M*R,
+  F*I*L*O-E*J*L*O-F*H*M*O+D*J*M*O+E*H*N*O-D*I*N*O-F*I*K*P+E*J*K*P+F*G*M*P-C*J*M*P-E*G*N*P+C*I*N*P+F*H*K*Q-D*J*K*Q-F*G*L*Q+C*J*L*Q+D*G*N*Q-C*H*N*Q-E*H*K*R+D*I*K*R+E*G*L*R-C*I*L*R-D*G*M*R+C*H*M*R,
+  a*S+b*T+c*U+d*V,
+  e*S+f*T+g*U+h*V,
+  i*S+j*T+k*U+l*V,
+  m*S+n*T+o*U+p*V,
+  q*S+r*T+s*U+t*V,
+  u*S+v*T+w*U+x*V,
+  B*E*H*S-A*F*H*S-B*D*I*S+z*F*I*S+A*D*J*S-z*E*J*S-B*E*G*T+A*F*G*T+B*C*I*T-y*F*I*T-A*C*J*T+y*E*J*T+B*D*G*U-z*F*G*U-B*C*H*U+y*F*H*U+z*C*J*U-y*D*J*U-A*D*G*V+z*E*G*V+A*C*H*V-y*E*H*V-z*C*I*V+y*D*I*V,
+  B*E*L*S-A*F*L*S-B*D*M*S+z*F*M*S+A*D*N*S-z*E*N*S-B*E*K*T+A*F*K*T+B*C*M*T-y*F*M*T-A*C*N*T+y*E*N*T+B*D*K*U-z*F*K*U-B*C*L*U+y*F*L*U+z*C*N*U-y*D*N*U-A*D*K*V+z*E*K*V+A*C*L*V-y*E*L*V-z*C*M*V+y*D*M*V,
+  B*I*L*S-A*J*L*S-B*H*M*S+z*J*M*S+A*H*N*S-z*I*N*S-B*I*K*T+A*J*K*T+B*G*M*T-y*J*M*T-A*G*N*T+y*I*N*T+B*H*K*U-z*J*K*U-B*G*L*U+y*J*L*U+z*G*N*U-y*H*N*U-A*H*K*V+z*I*K*V+A*G*L*V-y*I*L*V-z*G*M*V+y*H*M*V,
+  F*I*L*S-E*J*L*S-F*H*M*S+D*J*M*S+E*H*N*S-D*I*N*S-F*I*K*T+E*J*K*T+F*G*M*T-C*J*M*T-E*G*N*T+C*I*N*T+F*H*K*U-D*J*K*U-F*G*L*U+C*J*L*U+D*G*N*U-C*H*N*U-E*H*K*V+D*I*K*V+E*G*L*V-C*I*L*V-D*G*M*V+C*H*M*V,
+  B*E*P*S-A*F*P*S-B*D*Q*S+z*F*Q*S+A*D*R*S-z*E*R*S-B*E*O*T+A*F*O*T+B*C*Q*T-y*F*Q*T-A*C*R*T+y*E*R*T+B*D*O*U-z*F*O*U-B*C*P*U+y*F*P*U+z*C*R*U-y*D*R*U-A*D*O*V+z*E*O*V+A*C*P*V-y*E*P*V-z*C*Q*V+y*D*Q*V,
+  B*I*P*S-A*J*P*S-B*H*Q*S+z*J*Q*S+A*H*R*S-z*I*R*S-B*I*O*T+A*J*O*T+B*G*Q*T-y*J*Q*T-A*G*R*T+y*I*R*T+B*H*O*U-z*J*O*U-B*G*P*U+y*J*P*U+z*G*R*U-y*H*R*U-A*H*O*V+z*I*O*V+A*G*P*V-y*I*P*V-z*G*Q*V+y*H*Q*V,
+  F*I*P*S-E*J*P*S-F*H*Q*S+D*J*Q*S+E*H*R*S-D*I*R*S-F*I*O*T+E*J*O*T+F*G*Q*T-C*J*Q*T-E*G*R*T+C*I*R*T+F*H*O*U-D*J*O*U-F*G*P*U+C*J*P*U+D*G*R*U-C*H*R*U-E*H*O*V+D*I*O*V+E*G*P*V-C*I*P*V-D*G*Q*V+C*H*Q*V,
+  B*M*P*S-A*N*P*S-B*L*Q*S+z*N*Q*S+A*L*R*S-z*M*R*S-B*M*O*T+A*N*O*T+B*K*Q*T-y*N*Q*T-A*K*R*T+y*M*R*T+B*L*O*U-z*N*O*U-B*K*P*U+y*N*P*U+z*K*R*U-y*L*R*U-A*L*O*V+z*M*O*V+A*K*P*V-y*M*P*V-z*K*Q*V+y*L*Q*V,
+  F*M*P*S-E*N*P*S-F*L*Q*S+D*N*Q*S+E*L*R*S-D*M*R*S-F*M*O*T+E*N*O*T+F*K*Q*T-C*N*Q*T-E*K*R*T+C*M*R*T+F*L*O*U-D*N*O*U-F*K*P*U+C*N*P*U+D*K*R*U-C*L*R*U-E*L*O*V+D*M*O*V+E*K*P*V-C*M*P*V-D*K*Q*V+C*L*Q*V,
+  J*M*P*S-I*N*P*S-J*L*Q*S+H*N*Q*S+I*L*R*S-H*M*R*S-J*M*O*T+I*N*O*T+J*K*Q*T-G*N*Q*T-I*K*R*T+G*M*R*T+J*L*O*U-H*N*O*U-J*K*P*U+G*N*P*U+H*K*R*U-G*L*R*U-I*L*O*V+H*M*O*V+I*K*P*V-G*M*P*V-H*K*Q*V+G*L*Q*V
+  ];
+# @time G = groebner(polys)
+