committed to this course of action

.gitignore

@@ -22,7 +22,7 @@
 *.pdf
 
 ## Generated if empty string is given at "Please type another file name for output:"
-.pdf
+*.pdf
 
 ## Bibliography auxiliary files (bibtex/biblatex/biber):
 *.bbl
@@ -245,5 +245,10 @@ TSWLatexianTemp*
 # generated if using elsarticle.cls
 *.spl
 
+<<<<<<< HEAD
 #
 .ipynb_checkpoints/
+=======
+.ipynb_checkpoints/
+.vscode/
+>>>>>>> develop

ctnt2018/ECM.py

@@ -1,112 +1,56 @@
 # %load ec3.py
 from math import factorial, gcd, log
+import pickle
 import numpy as np
-P=np.zeros(1000)
-P[0]=1
-P[1]=1
-for i in range(2,100):
-    if P[i]==0:
-        j=2
-        while i*j<100:
-            P[i*j]=1
-            j=j+1
-Primes1000=[i for i,x in enumerate(P) if x==0 ]  
+import gmpy2
 
-
-def mexp(a,x,N):
-    m,s=1,a
-    while x>0:
-        if x % 2 ==1:
-            m=((m*s) % N)
-        s=((s*s) % N)
-        x=x//2
-    return m
-
-def euclid(u,v):
-    if v==0:
-        raise ArithmeticError('Division by Zero')
-    x0,x1=u,v
-    a0,a1=1,0
-    b0,b1=0,1
-    while x1!=0:
-        q=x0//x1
-        x2=x0-q*x1
-        a2=a0-q*a1
-        b2=b0-q*b1
-        x0,a0,b0=x1,a1,b1
-        x1,a1,b1=x2,a2,b2
-    if x0<0:
-        return -x0,-a0,-b0
-    else:
-        return x0,a0,b0
-
-def mod_inv(u,N):
-    d,a,b=euclid(u,N)
-    if d==1:
-        return a
-    else:
-        raise ArithmeticError('Common factor is '+str(d))
-
-def two_p(x,y,a,b,N):
-    Lu=(3*x**2+a) % N
-   # print(Lu)
-    Lb=mod_inv(2*y,N)
-  #  print(Lb)
-    L=Lu*Lb % N
-    x_two=(L*L-2*x) % N
-    y_two=(L*(x-x_two)-y) %N
-    return x_two,y_two
-
-def sum_p(x1,y1,x2,y2,a,b,N):
-    Lu=(y2-y1) % N
-    Lb=mod_inv(x2-x1,N)
-    L=(Lu*Lb) % N
-    x_sum=(L*L-x1-x2) %N
-    y_sum=(L*(x1-x_sum)-y1) %N
-    return x_sum,y_sum
-
-def exp_p(x,y,a,b,m,N):
-    sx,sy=x,y
-    first=True
-    while m>0:
-        if m%2==1:
-            if first:
-                xm,ym=sx,sy
-                first=False
-            else:
-                xm,ym=sum_p(xm,ym,sx,sy,a,b,N)
-        sx,sy=two_p(sx,sy,a,b,N)
-        m=m//2
-    return xm,ym
-
-#def mexp(a,x,N):
- #   m,s=1,a
- #   while x>0:
- #       if x % 2 ==1:
- #           m=((m*s) % N)
- #       s=((s*s) % N)
- #       x=x//2
- #   return m
-
-def ecm_trial(N,arange=50,krange=30):
+with open('primes10000.pickle','rb') as f:
+    Primes10000=pickle.load(f)
+
+def ecm(N,arange=100,krange=10000):
     for a in range(-arange,arange):
-        xm,ym=0,1
-        print(a) 
-        for k in range(2,krange):
-            try:
-                xm,ym=exp_p(xm,ym,a,1,k,N)
-            except ArithmeticError:
-                print('try the following: a=',a,' and k=',k)
-                break
+        x,y=0,1
+        for B in Primes10000:
+            k=B**(int(log(10000)/log(B)))
+            sx,sy,t=x,y,k
+            first=True
+            while t>0:
+                if t%2==1:
+                    if first:
+                        xm,ym=sx,sy
+                        first=False
+                    else:
+                        # x1=xm,y1=ym, x2=sx,y2=sy,a=a,b=1,N=N
+                        d,u,v=gmpy2.gcdext(sx-xm,N)
+                        if d>1:
+                            if d==N:
+                                break
+                            else:
+                                return d
+                        L=(u*(sy-ym)) % N
+                        x_sum=(L*L-xm-sx) % N
+                        ym=(L*(xm-x_sum)-ym) % N
+                        xm=x_sum
+                # sx=x,sy=y,a=a,b=1,N
+                d,u,v=gmpy2.gcdext(2*sy,N)
+                if d>1:
+                    if d==N:
+                        break
+                    else:
+                        return d
+                L=(u*(3*sx*sx+a)) % N
+                x2=(L*L-2*sx) % N
+                sy=(L*(sx-x2)-sy) %N
+                sx=x2
+                t=t//2
+            x,y=xm,ym
+    print('Failed')
+
+
+
+N=2**(128)+1
+print('answer is', ecm(N,arange=100,krange=10000),flush=True)
+
 
-
-
-#N=149185656432189838133
-#ecm_trial(N,arange=20,krange=10000)
-N=2**128+1
-#ecm_trial(N,arange=100,krange=10000)
-xm,ym=exp_p(0,1,-91,1,factorial(7883),N)
-
-
 
 

ctnt2018/MakePrimes10000.py

@@ -0,0 +1,18 @@
+import numpy as np
+import pickle
+
+
+
+P=np.zeros(10000)
+P[0]=1
+P[1]=1
+for i in range(2,10000):
+    if P[i]==0:
+        j=2
+        while i*j<1000:
+            P[i*j]=1
+            j=j+1
+
+Primes10000=[i for i,x in enumerate(P) if x==0]
+with open('primes10000.pickle','wb') as f:
+    pickle.dump(Primes10000,f)

ctnt2018/old_ecm.py

@@ -0,0 +1,94 @@
+def mexp(a,x,N):
+    m,s=1,a
+    while x>0:
+        if x % 2 ==1:
+            m=((m*s) % N)
+        s=((s*s) % N)
+        x=x//2
+    return m
+
+def euclid(u,v):
+    if v==0:
+        raise ArithmeticError('Division by Zero')
+    x0,x1=u,v
+    a0,a1=1,0
+    b0,b1=0,1
+    while x1!=0:
+        q=x0//x1
+        x2=x0-q*x1
+        a2=a0-q*a1
+        b2=b0-q*b1
+        x0,a0,b0=x1,a1,b1
+        x1,a1,b1=x2,a2,b2
+    if x0<0:
+        return -x0,-a0,-b0
+    else:
+        return x0,a0,b0
+
+def mod_inv(u,N):
+    d,a,b=euclid(u,N)
+    if d==1:
+        return a
+    else:
+        raise ArithmeticError('Common factor is '+str(d))
+
+def two_p(x,y,a,b,N):
+    Lu=(3*x**2+a) % N
+   # print(Lu)
+    Lb=mod_inv(2*y,N)
+  #  print(Lb)
+    L=Lu*Lb % N
+    x_two=(L*L-2*x) % N
+    y_two=(L*(x-x_two)-y) %N
+    return x_two,y_two
+
+def sum_p(x1,y1,x2,y2,a,b,N):
+    Lu=(y2-y1) % N
+    Lb=mod_inv(x2-x1,N)
+    L=(Lu*Lb) % N
+    x_sum=(L*L-x1-x2) %N
+    y_sum=(L*(x1-x_sum)-y1) %N
+    return x_sum,y_sum
+
+def exp_p(x,y,a,b,m,N):
+    sx,sy=x,y
+    first=True
+    while m>0:
+        if m%2==1:
+            if first:
+                xm,ym=sx,sy
+                first=False
+            else:
+                xm,ym=sum_p(xm,ym,sx,sy,a,b,N)
+        sx,sy=two_p(sx,sy,a,b,N)
+        m=m//2
+    return xm,ym
+
+#def mexp(a,x,N):
+ #   m,s=1,a
+ #   while x>0:
+ #       if x % 2 ==1:
+ #           m=((m*s) % N)
+ #       s=((s*s) % N)
+ #       x=x//2
+ #   return m
+
+def ecm_trial(N,arange=50,krange=30):
+    for a in range(-arange,arange):
+        xm,ym=0,1
+        print(a) 
+        for k in range(2,krange):
+            try:
+                xm,ym=exp_p(xm,ym,a,1,k,N)
+            except ArithmeticError:
+                print('try the following: a=',a,' and k=',k)
+                break
+
+
+
+#N=149185656432189838133
+#ecm_trial(N,arange=20,krange=10000)
+N=2**128+1
+#ecm_trial(N,arange=100,krange=10000)
+#xm,ym=exp_p(0,1,-91,1,factorial(7883),N)
+