HF6_megoldas

1579 days ago by ballar

X = matrix([[x,1],[1,x]]); Y = matrix([[2,x],[-1,-1]]); Z = matrix([[-1,2],[x,2]]); A = block_matrix([[X,X],[X,X]]); B = block_matrix([[X,Y],[Y,X]]); C = block_matrix([[X,Z],[Y,Z]]); xa = Set(RR).difference(Set(solve(det(A) == 0, x))); xb = Set(RR).difference(Set(solve(det(B) == 0, x))); xc = Set(RR).difference(Set(solve(det(C) == 0, x))); 
       
xa 
       
Set-theoretic difference of Set of elements of Real Field with 53 bits
of precision and {x == r1}
Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == r1}
xb 
       
Set-theoretic difference of Set of elements of Real Field with 53 bits
of precision and {x == -2, x == 1, x == -1/2*sqrt(17) - 1/2, x ==
1/2*sqrt(17) - 1/2}
Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == -2, x == 1, x == -1/2*sqrt(17) - 1/2, x == 1/2*sqrt(17) - 1/2}
xc 
       
Set-theoretic difference of Set of elements of Real Field with 53 bits
of precision and {x == 1/2*sqrt(17) - 1/2, x == -1/2*sqrt(17) - 1/2, x
== -1}
Set-theoretic difference of Set of elements of Real Field with 53 bits of precision and {x == 1/2*sqrt(17) - 1/2, x == -1/2*sqrt(17) - 1/2, x == -1}
plot(det(C),(x,-3,2)) 
       
[(a,b,c) for a in range(1,100) for b in range(a,100) for c in range(b,100) if a^2 + b^2 == c^2 and (is_prime(a) or is_prime(b) or is_prime(c))] 
       
[(3, 4, 5),
 (5, 12, 13),
 (7, 24, 25),
 (8, 15, 17),
 (9, 40, 41),
 (11, 60, 61),
 (12, 35, 37),
 (13, 84, 85),
 (20, 21, 29),
 (28, 45, 53),
 (39, 80, 89),
 (48, 55, 73),
 (65, 72, 97)]
[(3, 4, 5),
 (5, 12, 13),
 (7, 24, 25),
 (8, 15, 17),
 (9, 40, 41),
 (11, 60, 61),
 (12, 35, 37),
 (13, 84, 85),
 (20, 21, 29),
 (28, 45, 53),
 (39, 80, 89),
 (48, 55, 73),
 (65, 72, 97)]