First pull request

precomp.py

@@ -0,0 +1,105 @@
+"""
+This generates bounds for products of coefficients of points in our fundamental domain.
+
+Pypy to be used. 
+"""
+import sys
+sys.setrecursionlimit(2000)
+import itertools
+subsets = []
+def findsubsets(S):
+  A = []
+  m = 0
+  while(m <= len(S)):
+    A.append(itertools.combinations(S,m))
+    m+=1
+  for k in A:
+    for l in k:
+       l = list(l)
+       subsets.append(l)
+findsubsets([0,1,2,3,4,5,6,7,8,9,10,11])
+gamma = [[0,1,1,1],[0,1,2,1],[0,1,3,1],[0,2,2,1],[0,2,3,1],[0,3,3,1],[0,1,1,-1],[0,1,2,-1],[0,1,3,-1],[0,2,2,-1],[0,2,3,-1],[0,3,3,-1]]
+print len(subsets)
+def check(list):
+  I = 0
+  J = 0
+  K = 0
+  AB = 0
+  i = 0
+  while(i < len(list)):
+    if(gamma[list[i]][1] == 1):
+      I+=1
+    if(gamma[list[i]][2] == 1):
+      I+=1
+    if(gamma[list[i]][1] == 2):
+      J+=1
+    if(gamma[list[i]][2] == 2):
+      J+=1
+    if(gamma[list[i]][1] == 3):
+      K+=1
+    if(gamma[list[i]][2] == 3):
+      K+=1
+    AB += gamma[list[i]][3]
+  if(I+J >=2*K and 2*I>=J+K and AB>=0):
+    return 0
+  change=0
+  while(I+J < 2*K or 2*I < J+K or AB < 0):
+      I+=2
+      AB+=1
+      change+=1
+  return change
+
+abval = [[0,0,0,0,0,0,0,0,0,0,0,0],[0.5,0,0,0,0,0,0,0,0,0,0,0],[0.75,0.5,0,0,0,0,0,0,0,0,0,0],[0.25,1,0,0,0,0,0,0,0,0,0,0],[0.625,2.125,0.5,0.5,0,0,0,0,0,0,0,0],[23.0/16.0,3.625,1.5,0.25,1,0,0,0,0,0,0,0],[0.5,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0.5,0,0,0,0,0],[0,0,0,0,0,0,0.75,0.5,0,0,0,0],[0,0,0,0,0,0,0.25,1,0,0,0,0],[0,0,0,0,0,0,0.625,2.125,0.5,0.5,0,0],[0,0,0,0,0,0,23.0/16.0,3.625,1.5,0.25,1,0]]
+
+cdval = [[1,0,0,0,0,0,0,0,0,0,0,0],[0.5,1,0,0,0,0,0,0,0,0,0,0],[0.5,0.5,1,0,0,0,0,0,0,0,0,0],[0.25,1,0,1,0,0,0,0,0,0,0,0],[0.25,1,0.5,0.5,1,0,0,0,0,0,0,0],[0.25,0.25,1,0.25,1,1,0,0,0,0,0,0],[0.5,0,0,0,0,0,1,0,0,0,0,0],[0.25,0.5,0,0,0,0,0.5,1,0,0,0,0],[0.25,0.25,0.5,0,0,0,0.5,0.5,1,0,0,0],[0.125,0.5,0,0.5,0,0,0.25,1,0,1,0,0],[0.125,0.5,0.25,0.25,0.5,0,0.25,0.5,0.5,1,0,0],[0.125,0.125,0.5,0.125,0.5,0.5,0.25,0.25,1,0.25,1,1]]
+
+R = range(0,12)
+def loop_product(current, array, S,t1,t2,t3,t):
+  answer = 0
+  if(current == len(array) - 1):   
+    for j in R:
+      S1=S
+      if(gamma[j][1] == 1):
+        t1+=1
+      if(gamma[j][2] == 1):
+        t1+=1
+      if(gamma[j][1] == 2):
+        t2+=1
+      if(gamma[j][2] == 2):
+        t2+=1
+      if(gamma[j][1] == 3):
+        t3+=1
+      if(gamma[j][2] == 3):
+        t3+=1
+      t+= gamma[j][3]
+      S1*=cdval[array[current]][j]
+      l = min(min(t1,t2),t3)
+      if(l!=0):
+        t1=t1%l
+        t2=t2%l
+        t3=t3%l
+      S1*= 1.07457**t
+      S1*= 1.54701**(t1-t3)
+      S1*= 0.895503**len(array)
+      if(S1!=0):
+        answer+=S1
+  if(current < len(array) - 1):
+    for j in R:
+      if(gamma[j][1] == 1):
+        t1+=1
+      if(gamma[j][2] == 1):
+        t1+=1
+      if(gamma[j][1] == 2):
+        t2+=1
+      if(gamma[j][2] == 2):
+        t2+=1
+      if(gamma[j][1] == 3):
+        t3+=1
+      if(gamma[j][2] == 3):
+        t3+=1
+      t+= gamma[j][3]
+      S*=cdval[array[current]][j]
+      answer += loop_product(current+1, array, S,t1,t2,t3,t)
+  return answer
+for k in range(0, 4096):
+  print k, loop_product(1,subsets[k],1,0,0,0,0)

todo.txt

@@ -0,0 +1,15 @@
+1. Send Kevin the code/GIT. [Today]
+
+2. Check random pts outside the domain. (~10^6) [2nd]
+
+3. Run races on bounds and see which ones run fastest. [For b_{ij}, where {ij} are large, especially] [4th]
+
+4. See if decision tree is better than linear checks (flattening the decision tree) [3rd]
+
+5. PyPy [Today]
+
+6. Write reduction code in Cython. [Step 1, Section 4, jpv3.pdf] [1st]
+
+7. Compute splitting types. [Given (A,B) and prime p, compute the splitting type of Q(A,B), precompute the sieve] [Soon]
+
+8.