기초수학 실습 1월14일 김동민

1978 days 전, khk1741 작성

[-9,-7..30] 
       
[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27,
29]
[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
[-18,-15..100] 
       
[-18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33,
36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87,
90, 93, 96, 99]
[-18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99]
[a.is_prime() for a in [1..100]] 
       
[False, True, True, False, True, False, True, False, False, False, True,
False, True, False, False, False, True, False, True, False, False,
False, True, False, False, False, False, False, True, False, True,
False, False, False, False, False, True, False, False, False, True,
False, True, False, False, False, True, False, False, False, False,
False, True, False, False, False, False, False, True, False, True,
False, False, False, False, False, True, False, False, False, True,
False, True, False, False, False, False, False, True, False, False,
False, True, False, False, False, False, False, True, False, False,
False, False, False, False, False, True, False, False, False]
[False, True, True, False, True, False, True, False, False, False, True, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, True, False, False, False, False, False, True, False, False, False, True, False, False, False, False, False, True, False, False, False, False, False, False, False, True, False, False, False]
b=[] for a in [1..100]: if a.is_prime(): b.append(a) print b 
       
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97]
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
p(x)=(x-2)^3*(x^2-4*x+3)*2 p(x) 
       
2*(x^2 - 4*x + 3)*(x - 2)^3
2*(x^2 - 4*x + 3)*(x - 2)^3
show (expand(p(x))) 
       
factor( 2*(x^2 - 4*x + 3)*(x - 2)^3) 
       
2*(x - 1)*(x - 2)^3*(x - 3)
2*(x - 1)*(x - 2)^3*(x - 3)
(p(x)/(x-1)).simplify_full() 
       
2*x^4 - 18*x^3 + 60*x^2 - 88*x + 48
2*x^4 - 18*x^3 + 60*x^2 - 88*x + 48
W.<x>=QQ[] W(p(x)).quo_rem(x-5) 
       
(2*x^4 - 10*x^3 + 28*x^2 - 8*x + 96, 432)
(2*x^4 - 10*x^3 + 28*x^2 - 8*x + 96, 432)
W.<x>=QQ[] W(P(x)).quo_rem(x^2-5*x+1) 
       
(2*x^3 - 10*x^2 + 26*x - 8, 70*x - 40)
(2*x^3 - 10*x^2 + 26*x - 8, 70*x - 40)
(2*x^3 - 10*x^2 + 26*x - 8)*(x^2-5*x+1)+70*x-40 
       
2*x^5 - 20*x^4 + 78*x^3 - 148*x^2 + 136*x - 48
2*x^5 - 20*x^4 + 78*x^3 - 148*x^2 + 136*x - 48
var('x,y') solve( [3*x - y == 2, -2*x -y == 1 ], x,y) 
       
[[x == (1/5), y == (-7/5)]]
[[x == (1/5), y == (-7/5)]]
solve( [ 2*x + y == -1 , -4*x - 2*y == 2],x,y) 
       
[[x == -1/2*r1 - 1/2, y == r1]]
[[x == -1/2*r1 - 1/2, y == r1]]
solve( [ 2*x - y == -1 , 2*x - y == 2],x,y) 
       
[]
[]
var('z') solve([ 2*x + 3*y + 5*z == 1, 4*x + 6*y + 10*z == 2, 6*x + 9*y + 15*z == 3], x,y,z) 
       
[[x == -5/2*r4 - 3/2*r5 + 1/2, y == r5, z == r4]]
[[x == -5/2*r4 - 3/2*r5 + 1/2, y == r5, z == r4]]
var('x') solve([x^3-x==7*x^2-7],x) 
       
[x == 7, x == -1, x == 1]
[x == 7, x == -1, x == 1]
var('t') solve(abs(t-7)>=3,t) 
       
#0: solve_rat_ineq(ineq=abs(t-7) >= 3)
[[t == 10], [t == 4], [t < 4], [10 < t]]
#0: solve_rat_ineq(ineq=abs(t-7) >= 3)
[[t == 10], [t == 4], [t < 4], [10 < t]]
var('x','y') solve([2*x+y==17,x-3*y==-16],x,y) 
       
[[x == 5, y == 7]]
[[x == 5, y == 7]]
f(x) = cos(x) p = plot(f(x), (x, 0, pi/2),color='gold')+plot(sin(x),(x,0,2*pi),color='red') p 
       
plot(f(x), (x,-pi/2, pi/2), linestyle='--', thickness=3,color='red') 
       
f(x) = (x^3 + x^2 + x)/(x^2 - x -2 ) p = plot(f(x), (x, -5,5)) p.show(xmin=-2, xmax=4, ymin=-20, ymax=20) 
       
p=plot(sin(pi*x-pi), (x,-1,1), thickness=3, color='red') q=plot(cos(pi*x-pi), (x,-1,1), thickness=3, color='gold') 
       
p+q 
       
plot(1/x,(x,-1,1),ymin=-10,ymax=10,xmax=1,xmin=-1) 
       
p(x)=2*x^3+3*x^2-5*x-6 solve(P(x)==0, x) 
       
[x == 3, x == 1, x == 2]
[x == 3, x == 1, x == 2]
plot(P(x), (x, -4, 4), ymax=20, ymin=-20) 
       
f(x)=2/(x-5) plot(f(x),(x,2,7),ymax=10,ymin=-10) 
       
f(x)=(2*x^2+1)/(x^2-4*x+3) plot(f(x), (x, -2, 6), ymax=20, ymin=-20) 
       
f(x)=(x+2)/(x^2-x-6) plot(f(x), (x, -4, 6), ymax=20, ymin=-20) 
       
x,y = var("x y") f(x,y) = x^2 - y^2 p = plot3d(f(x,y), (x,-10,10), (y,-10,10)) p.show() 
       
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