CoCalc Shared FilesCounter example to LCFF.sagewsOpen in CoCalc with one click!
Author: Erez Nesharim
Views : 113
def Dragon(n): """ This function returns the nth element of the dragon sequence """ if n == 0: return 0 else: while Mod(n, 2) == 0: #while n%2 == 0: n = n / 2 return ((n-1)/2)%2 def Dragon2(n): """ This function returns the 2nth element of the dragon sequence """ return Dragon(2*n) def Pagoda(n): """ This function returns the nth element of the pagoda sequence """ return Dragon(n+1) - Dragon(n-1) def GoldenSection(n): """ This function returns the nth element of the golden section sequence It gol_{2n} = 0 and gol_{2n+1} = (-1)^{n+1} * catalan_number(n) """ if n%2==0: return 0 else: return catalan_number((n-1)/2)*(1 - (n-1)%4) def plot_labels(x_ticks,x_labels,y_ticks,y_labels,fontsize=12): import matplotlib.ticker def latex_ticklabels(lbls_x,lbls_y): return [matplotlib.ticker.FixedFormatter(lbls_x),matplotlib.ticker.FixedFormatter(lbls_y)] ft=fontsize return plot([],ticks=[x_ticks,y_ticks],tick_formatter=latex_ticklabels(x_labels,y_labels),fontsize=ft) def fibonaci_poly(n,k,char=0): """ This function returns the vector of coefficients of the kth coefficient of the nth fibonacci polynomial of degree n F(n,k) modulo char, which is set to be 0 by default. Fibonacci polynomials are defined recursively by q_n(t) = t*q_{n-1}(t) + q_{n-2}(t) and we use the formula F(n,k)=binomial((n+k-1)/2,k) """ if Mod(n,2)==Mod(k,2): return 0 else: return Mod(binomial((n+k-1)/2,k),char)
print([Mod(catalan_number(n),2) for n in range (1,300)]) print([Mod(catalan_number(n),3) for n in range (1,300)])
[1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
import time start = time.time() M = 170 leng = 2*M char = 3 pag = [Mod(Pagoda(n),char) for n in range (1,leng)] #rpf = [Dragon(n) for n in range (1,leng)] #gol = [Mod(GoldenSection(n),char) for n in range (1,leng)] par = [Mod(Pagoda(-n),char) for n in range (1,leng)] table = [[0 for j in range(0,m+1)] for m in range(1,M+1)] for m in range(1,M+1): tempMat = [[0 for j in range(0,m)] for n in range(0,m)] for h in range(0,m+1): for j in range(0,h): #print(j,h,m,"here") #tempMat[j] = [rpf[j + n] for n in range(0,m)] tempMat[j] = [pag[j + n] for n in range(0,m)] for j in range(h,m): #print(j,h,m,"there") tempMat[j] = [par[j - h - 1 + n] for n in range(0,m)] table[m-1][h] = Mod(matrix(tempMat).det(),char) end = time.time() print(end - start) P=plot_labels([],[],[],[]) for c in range(0,char): rgb=(char-1-c%char)/(char-1) P=P+points([(1+j,-m) for m in range(0,M) for j in range(0,m+1) if table[m][j]==mod(c,char)],color=Color(rgb,rgb,rgb),marker='s') P.axes_color('white') P.show() end = time.time() print(end - start)
Error in lines 9-16 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1191, in execute flags=compile_flags), namespace, locals) File "", line 7, in <module> File "src/cysignals/signals.pyx", line 320, in cysignals.signals.python_check_interrupt KeyboardInterrupt
import time start = time.time() M = 200 leng = 2*M char = 3 pag = [Mod(Pagoda(n),char) for n in range (1,leng)] #rpf = [Dragon(n) for n in range (1,leng)] #gol = [Mod(GoldenSection(n),char) for n in range (1,leng)] cat = [Mod(catalan_number(n),char) for n in range (1,leng)] table = [[0 for j in range(0,m+1)] for m in range(1,M+1)] for m in range(1,M+1): tempMat = [[0 for j in range(0,m)] for n in range(0,m)] for h in range(0,m+1): for j in range(0,h): #print(j,h,m,"here") #tempMat[j] = [rpf[j + n] for n in range(0,m)] tempMat[j] = [pag[j + n] for n in range(0,m)] for j in range(h,m): #print(j,h,m,"there") tempMat[j] = [cat[j - h + n] for n in range(0,m)] table[m-1][h] = Mod(matrix(tempMat).det(),char) end = time.time() print(end - start) #calculate defficiencies defs = [[0 for j in range(0,m+1)] for m in range(1,M+1)] for m in range (M,0,-1): #start counting from the bottom for j in range (0,m+1): if table[m-1][j] != 0: defs[m-1][j] = 0 else: if m == M: defs[m-1][j] = 1 else: defs[m-1][j] = max(defs[m][j],defs[m][j+1]) + 1 print([max(defs[m-1]) for m in range(1,M+1)]) P=plot_labels([],[],[],[]) for c in range(0,char): rgb=(char-1-c%char)/(char-1) P=P+points([(1+j,-m) for m in range(1,M+1) for j in range(0,m+1) if table[m-1][j]==mod(c,char)],color=Color(rgb,rgb,rgb),marker='s') P.axes_color('white') P.show() end = time.time() print(end - start)
1145.0585959 [1, 0, 4, 3, 2, 1, 1, 1, 7, 6, 5, 4, 3, 2, 4, 3, 2, 7, 9, 8, 7, 6, 5, 4, 4, 4, 5, 4, 3, 2, 3, 13, 12, 11, 10, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 10, 9, 8, 7, 6, 5, 9, 8, 7, 11, 10, 9, 8, 7, 6, 8, 7, 6, 5, 5, 4, 5, 8, 9, 16, 15, 14, 13, 12, 11, 10, 9, 8, 10, 9, 8, 7, 6, 5, 4, 4, 4, 3, 10, 9, 8, 7, 6, 5, 6, 12, 11, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 7, 6, 7, 6, 7, 10, 9, 8, 12, 11, 10, 9, 8, 9, 8, 22, 21, 20, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 13, 12, 11, 14, 13, 12, 11, 10, 9, 8, 7, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 12, 11, 10, 9, 10, 9, 8, 9, 8, 7, 6, 5, 12, 11, 12, 11, 10, 9, 11, 10, 9, 8, 7, 6, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1150.42876387
import time start = time.time() M = 600 leng = 2*M char = 3 weight = 1/2 pag = [Mod(Pagoda(n),char) for n in range (1,leng)] #rpf = [Dragon(n) for n in range (1,leng)] #gol = [Mod(GoldenSection(n),char) for n in range (1,leng)] cat = [Mod(catalan_number(n),char) for n in range (1,leng)] end = time.time() print(end - start) dets = [0 for m in range(1,M+1)] for m in range(1,M+1): tempMat = [[0 for j in range(0,m)] for n in range(0,m)] h = round(weight*m) for j in range(0,h): tempMat[j] = [pag[j + n] for n in range(0,m)] for j in range(h,m): tempMat[j] = [cat[j - h + n] for n in range(0,m)] dets[m-1] = Mod(matrix(tempMat).det(),char) print(dets) defs = [0 for m in range(1,M+1)] for m in range (M,0,-1): #start counting from the bottom if dets[m-1] != 0: defs[m-1] = 0 else: if m == M: defs[m-1] = 1 else: defs[m-1] = defs[m] + 1 print(defs) print(max(defs)) end = time.time() print(end - start)
0.205230951309 [0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 0, 2, 2, 0, 0, 2, 0, 2, 1, 1, 2, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 1, 1, 2, 0, 2, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 2, 0, 2, 0, 0, 1, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 1, 2, 1, 0, 0, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 1, 2, 1, 1, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 2, 2, 1, 1, 0, 2, 0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 0, 0, 2, 0, 0, 0, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 2, 2, 1, 0, 1, 1, 1, 2, 2, 2, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 0, 0, 2, 2, 1, 0, 1, 2, 1, 2, 0, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 1, 0, 1, 0, 2, 2, 0, 1, 1, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 2, 1, 1, 0, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0] [1, 0, 4, 3, 2, 1, 0, 1, 0, 0, 3, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 3, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 4, 3, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 3, 2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 2, 1, 0, 0, 0, 0, 3, 2, 1, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 1, 0, 0, 3, 2, 1, 0, 0, 0, 1, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1] 8 654.19997406
m)] tempMat[j] = [pag[j + n] for n in range(0,m)] for j in range(h,m): #print(j,h,m,"there") tempMat[j] = [cat[j - h + n] for n in range(0,m)] table[m-1][h] = Mod(matrix(tempMat).det(),char) end = time.time() print(end - start) #calculate defficiencies defs = [[0 for j in range(0,m+1)] for m in range(1,M+1)] for m in range (M,0,-1): #start counting from the bottom for j in range (0,m+1): if table[m-1][j] != 0: defs[m-1][j] = 0 else: if m == M: defs[m-1][j] = 1 else: defs[m-1][j] = max(defs[m][j],defs[m][j+1]) + 1 print([max(defs[m-1]) for m in range(1,M+1)]) P=plot_labels([],[],[],[]) for c in range(0,char): rgb=(char-1-c%char)/(char-1) P=P+points([(1+j,-m) for m in range(1,M+1) for j in range(0,m+1) if table[m-1][j]==mod(c,char)],color=Color(rgb,rgb,rgb),marker='s') P.axes_color('white') P.show() end = time.time() print(end - start)
1145.0585959 [1, 0, 4, 3, 2, 1, 1, 1, 7, 6, 5, 4, 3, 2, 4, 3, 2, 7, 9, 8, 7, 6, 5, 4, 4, 4, 5, 4, 3, 2, 3, 13, 12, 11, 10, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 10, 9, 8, 7, 6, 5, 9, 8, 7, 11, 10, 9, 8, 7, 6, 8, 7, 6, 5, 5, 4, 5, 8, 9, 16, 15, 14, 13, 12, 11, 10, 9, 8, 10, 9, 8, 7, 6, 5, 4, 4, 4, 3, 10, 9, 8, 7, 6, 5, 6, 12, 11, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 7, 6, 7, 6, 7, 10, 9, 8, 12, 11, 10, 9, 8, 9, 8, 22, 21, 20, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 13, 12, 11, 14, 13, 12, 11, 10, 9, 8, 7, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 12, 11, 10, 9, 10, 9, 8, 9, 8, 7, 6, 5, 12, 11, 12, 11, 10, 9, 11, 10, 9, 8, 7, 6, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1150.42876387
import time start = time.time() M = 600 leng = 2*M char = 3 pag = [Mod(Pagoda(n),char) for n in range (1,leng)] #rpf = [Dragon(n) for n in range (1,leng)] #gol = [Mod(GoldenSection(n),char) for n in range (1,leng)] cat = [Mod(catalan_number(n),char) for n in range (1,leng)] end = time.time() print(end - start) dets = [0 for m in range(1,M+1)] for m in range(1,M+1): tempMat = [[0 for j in range(0,m)] for n in range(0,m)] h = round(weight*m) for j in range(0,h): tempMat[j] = [pag[j + n] for n in range(0,m)] for j in range(h,m): tempMat[j] = [cat[j - h + n] for n in range(0,m)] dets[m-1] = Mod(matrix(tempMat).det(),char) print(dets) defs = [0 for m in range(1,M+1)] for m in range (M,0,-1): #start counting from the bottom if dets[m-1] != 0: defs[m-1] = 0 else: if m == M: defs[m-1] = 1 else: defs[m-1] = defs[m] + 1 print(defs) print(max(defs)) end = time.time() print(end - start)
0.205230951309 [0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 0, 2, 2, 0, 0, 2, 0, 2, 1, 1, 2, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 1, 1, 2, 0, 2, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 2, 0, 2, 0, 0, 1, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 1, 2, 1, 0, 0, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 1, 2, 1, 1, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 2, 2, 1, 1, 0, 2, 0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 0, 0, 2, 0, 0, 0, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 2, 2, 1, 0, 1, 1, 1, 2, 2, 2, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 0, 0, 2, 2, 1, 0, 1, 2, 1, 2, 0, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 1, 0, 1, 0, 2, 2, 0, 1, 1, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 2, 1, 1, 0, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0] [1, 0, 4, 3, 2, 1, 0, 1, 0, 0, 3, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 3, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 4, 3, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 3, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 3, 2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 2, 1, 0, 0, 0, 0, 3, 2, 1, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 1, 0, 0, 3, 2, 1, 0, 0, 0, 1, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1] 8 654.19997406
import time start = time.time() M = 1000 leng = 2*M char = 3 pag = [Pagoda(n) for n in range (1,leng)] pag_def = 1 defs_along_convergents = [0 for m in range(1,M+1)] for m in range(1,M+1): i=0 fib_m = [fibonaci_poly(m,n,char) for n in range(0,m)] while i < m + pag_def and sum([pag[i + n]*fib_m[n] for n in range(0,m)])%char==0: i += 1 defs_along_convergents[m-1] = i print(defs_along_convergents) print(max(defs_along_convergents)) end = time.time() print(end - start)
[1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 2, 0, 1, 3, 1, 0, 0, 0, 1, 7, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 4, 0, 1, 5, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 3, 1, 0, 6, 0, 1, 3, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 1, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 3, 1, 0, 4, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 4, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 1, 1, 0, 0, 6, 0, 0, 1, 1, 0, 0, 0, 0, 3, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 6, 0, 1, 1, 0, 0, 2, 0, 0, 7, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 3, 1, 0, 2, 0, 0, 5, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 3, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 7, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 3, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 5, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 6, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 1, 0, 0, 4, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 4, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 11, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0] 11 25.9435641766
import time start = time.time() M = 100 leng = 2*M char = 3 rpf = [Mod(Dragon(n),char) for n in range (1,leng)] rpf2 = [Mod(Dragon(2*n-1),char) for n in range (1,leng)] table = [[0 for j in range(0,m+1)] for m in range(1,M+1)] for m in range(1,M+1): tempMat = [[0 for j in range(0,m)] for n in range(0,m)] for h in range(0,m+1): for j in range(0,h): #print(j,h,m,"here") #tempMat[j] = [rpf[j + n] for n in range(0,m)] tempMat[j] = [rpf[j + n] for n in range(0,m)] for j in range(h,m): #print(j,h,m,"there") tempMat[j] = [rpf2[j - h - 1 + n] for n in range(0,m)] table[m-1][h] = Mod(matrix(tempMat).det(),char) end = time.time() print(end - start) P=plot_labels([],[],[],[]) for c in range(0,char): rgb=(char-1-c%char)/(char-1) P=P+points([(1+j,-m) for m in range(0,M) for j in range(0,m+1) if table[m][j]==mod(c,char)],color=Color(rgb,rgb,rgb),marker='s') P.axes_color('white') P.show() end = time.time() print(end - start)
67.6483972073
69.0173401833
rpf2 = [Mod(Dragon(2*n),char) for n in range (1,leng)] print(rpf2)
[0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]