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In [38]:
def HighestEntry(Matrix): List = sorted([Matrix[0,0],Matrix[0,1],Matrix[1,0],Matrix[1,1]]) return List[3] def LowestEntry(Matrix): List = sorted([Matrix[0,0],Matrix[0,1],Matrix[1,0],Matrix[1,1]]) return List[0]
In [46]:
count1 = 0 count2 = 0 for a in [-20..20]: A_1 = matrix(QQ,[[a+0,a+1],[a+2,a+3]]) A_2 = matrix(QQ,[[a+0,a+1],[a+3,a+2]]) A_3 = matrix(QQ,[[a+0,a+2],[a+1,a+3]]) A_4 = matrix(QQ,[[a+0,a+2],[a+3,a+1]]) A_5 = matrix(QQ,[[a+0,a+3],[a+1,a+2]]) A_6 = matrix(QQ,[[a+0,a+3],[a+2,a+1]]) A_7 = matrix(QQ,[[a+1,a+2],[a+3,a+0]]) A_8 = matrix(QQ,[[a+1,a+2],[a+0,a+3]]) A_9 = matrix(QQ,[[a+1,a+3],[a+2,a+0]]) A_10 = matrix(QQ,[[a+1,a+3],[a+0,a+2]]) A_11 = matrix(QQ,[[a+1,a+0],[a+2,a+3]]) A_12 = matrix(QQ,[[a+1,a+0],[a+3,a+2]]) A_13 = matrix(QQ,[[a+2,a+0],[a+1,a+3]]) A_14 = matrix(QQ,[[a+2,a+0],[a+3,a+1]]) A_15 = matrix(QQ,[[a+2,a+1],[a+0,a+3]]) A_16 = matrix(QQ,[[a+2,a+1],[a+3,a+0]]) A_17 = matrix(QQ,[[a+2,a+3],[a+1,a+0]]) A_18 = matrix(QQ,[[a+2,a+3],[a+0,a+1]]) A_19 = matrix(QQ,[[a+3,a+0],[a+2,a+1]]) A_20 = matrix(QQ,[[a+3,a+0],[a+1,a+2]]) A_21 = matrix(QQ,[[a+3,a+1],[a+2,a+0]]) A_22 = matrix(QQ,[[a+3,a+1],[a+0,a+2]]) A_23 = matrix(QQ,[[a+3,a+2],[a+1,a+0]]) A_24 = matrix(QQ,[[a+3,a+2],[a+0,a+1]]) A = [A_1,A_2,A_3,A_4,A_5,A_6,A_7,A_8,A_9,A_10,A_11,A_12,A_13,A_14,A_15,A_16,A_17,A_18,A_19,A_20,A_21,A_22,A_23,A_24] for b in [-20..20]: B_1 = matrix(QQ,[[b+0,b+1],[b+2,b+3]]) B_2 = matrix(QQ,[[b+0,b+1],[b+3,b+2]]) B_3 = matrix(QQ,[[b+0,b+2],[b+1,b+3]]) B_4 = matrix(QQ,[[b+0,b+2],[b+3,b+1]]) B_5 = matrix(QQ,[[b+0,b+3],[b+1,b+2]]) B_6 = matrix(QQ,[[b+0,b+3],[b+2,b+1]]) B_7 = matrix(QQ,[[b+1,b+2],[b+3,b+0]]) B_8 = matrix(QQ,[[b+1,b+2],[b+0,b+3]]) B_9 = matrix(QQ,[[b+1,b+3],[b+2,b+0]]) B_10 = matrix(QQ,[[b+1,b+3],[b+0,b+2]]) B_11 = matrix(QQ,[[b+1,b+0],[b+2,b+3]]) B_12 = matrix(QQ,[[b+1,b+0],[b+3,b+2]]) B_13 = matrix(QQ,[[b+2,b+0],[b+1,b+3]]) B_14 = matrix(QQ,[[b+2,b+0],[b+3,b+1]]) B_15 = matrix(QQ,[[b+2,b+1],[b+0,b+3]]) B_16 = matrix(QQ,[[b+2,b+1],[b+3,b+0]]) B_17 = matrix(QQ,[[b+2,b+3],[b+1,b+0]]) B_18 = matrix(QQ,[[b+2,b+3],[b+0,b+1]]) B_19 = matrix(QQ,[[b+3,b+0],[b+2,b+1]]) B_20 = matrix(QQ,[[b+3,b+0],[b+1,b+2]]) B_21 = matrix(QQ,[[b+3,b+1],[b+2,b+0]]) B_22 = matrix(QQ,[[b+3,b+1],[b+0,b+2]]) B_23 = matrix(QQ,[[b+3,b+2],[b+1,b+0]]) B_24 = matrix(QQ,[[b+3,b+2],[b+0,b+1]]) B=[B_1,B_2,B_3,B_4,B_5,B_6,B_7,B_8,B_9,B_10,B_11,B_12,B_13,B_14,B_15,B_16,B_17,B_18,B_19,B_20,B_21,B_22,B_23,B_24] for i in [0..23]: for j in [0..23]: C = A[i]*B[j] C_List = sorted([C[0,0], C[0,1], C[1,0], C[1,1]]) count1 = count1 + 1 if (C_List[0] +1 == C_List[1]) and (C_List[1] +1 == C_List[2]) and (C_List[2] +1 == C_List[3]): count2 = count2 + 1 show(count2,'.........',A[i],B[j],'=',C)
1.........(−20−17−18−19)(−2−3−1−4)=(94919293)
2.........(−20−17−18−19)(−1−4−2−3)=(92939491)
3.........(−19−18−17−20)(−4−1−3−2)=(93929194)
4.........(−19−18−17−20)(−3−2−4−1)=(91949392)
5.........(−18−19−20−17)(−4−1−3−2)=(92939491)
6.........(−18−19−20−17)(−3−2−4−1)=(94919293)
7.........(−17−20−19−18)(−2−3−1−4)=(91949392)
8.........(−17−20−19−18)(−1−4−2−3)=(93929194)
9.........(−20−17−18−19)(−1−20−3)=(56555457)
10.........(−20−17−18−19)(0−3−1−2)=(54575655)
11.........(−19−18−17−20)(−30−2−1)=(57545556)
12.........(−19−18−17−20)(−2−1−30)=(55565754)
13.........(−18−19−20−17)(−30−2−1)=(54575655)
14.........(−18−19−20−17)(−2−1−30)=(56555457)
15.........(−17−20−19−18)(−1−20−3)=(55565754)
16.........(−17−20−19−18)(0−3−1−2)=(57545556)
17.........(−20−18−19−17)(−21−10)=(21192018)
18.........(−20−18−19−17)(−10−21)=(20182119)
19.........(−20−18−19−17)(0−11−2)=(19171816)
20.........(−20−18−19−17)(1−20−1)=(18161917)
21.........(−20−17−19−18)(−101−2)=(20171819)
22.........(−20−17−19−18)(1−2−10)=(18192017)
23.........(−20−19−18−17)(−21−10)=(22212019)
24.........(−20−19−18−17)(−10−21)=(20192221)
25.........(−20−19−18−17)(0−11−2)=(18171615)
26.........(−20−19−18−17)(1−20−1)=(16151817)
27.........(−19−20−17−18)(−21−10)=(21221920)
28.........(−19−20−17−18)(−10−21)=(19202122)
29.........(−19−20−17−18)(0−11−2)=(17181516)
30.........(−19−20−17−18)(1−20−1)=(15161718)
31.........(−19−18−20−17)(−210−1)=(18192017)
32.........(−19−18−20−17)(0−1−21)=(20171819)
33.........(−19−17−20−18)(−21−10)=(18161917)
34.........(−19−17−20−18)(−10−21)=(19171816)
35.........(−19−17−20−18)(0−11−2)=(20182119)
36.........(−19−17−20−18)(1−20−1)=(21192018)
37.........(−18−17−20−19)(−21−10)=(16151817)
38.........(−18−17−20−19)(−10−21)=(18171615)
39.........(−18−17−20−19)(0−11−2)=(20192221)
40.........(−18−17−20−19)(1−20−1)=(22212019)
41.........(−18−19−17−20)(−210−1)=(19181720)
42.........(−18−19−17−20)(0−1−21)=(17201918)
43.........(−18−20−17−19)(−21−10)=(19211820)
44.........(−18−20−17−19)(−10−21)=(18201921)
45.........(−18−20−17−19)(0−11−2)=(17191618)
46.........(−18−20−17−19)(1−20−1)=(16181719)
47.........(−17−18−19−20)(−21−10)=(15161718)
48.........(−17−18−19−20)(−10−21)=(17181516)
49.........(−17−18−19−20)(0−11−2)=(19202122)
50.........(−17−18−19−20)(1−20−1)=(21221920)
51.........(−17−19−18−20)(−21−10)=(16181719)
52.........(−17−19−18−20)(−10−21)=(17191618)
53.........(−17−19−18−20)(0−11−2)=(18201921)
54.........(−17−19−18−20)(1−20−1)=(19211820)
WARNING: Some output was deleted.
In [40]:
show(count1) show(count2) show(RR(count2/count1))
3545
1
0.000282087447108604
In [0]:
lowestInA = LowestEntry(A[i]) lowestInB = LowestEntry(B[j]) highestInA = HighestEntry(A[i]) highestInB = HighestEntry(B[j]) if Alowest > lowestInA: count2 = count2 + 1 show(count2,'.........',A[i],B[j],'=',C) Alowest = lowestInA if Blowest > lowestInB: count2 = count2 + 1 show(count2,'.........',A[i],B[j],'=',C) Blowest = lowestInB if Ahighest < highestInA: count2 = count2 + 1 show(count2,'.........',A[i],B[j],'=',C) Alowest = lowestInA if Bhighest < lowestInB:
In [0]: