1.14 기초수학실습 방승원 젠틀하신 교수님과

1979 days 전, tmddnjs513 작성

[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 
       
expand(P(x)) 
       
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
show (factor(P(x))) 
       
(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^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)
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]]
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*r2 - 3/2*r3 + 1/2, y == r3, z == r2]]
[[x == -5/2*r2 - 3/2*r3 + 1/2, y == r3, z == r2]]
solve([x^3) 
       
[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]]
solve([2*x+y==17,x-3*y==16],x,y) 
       
[[x == (67/7), y == (-15/7)]]
[[x == (67/7), y == (-15/7)]]
f(x) = sin(x) p = plot(f(x), (x, -pi/2, pi/2)) p.show() 
       
p = plot(f(x), (x,-pi/2, pi/2), axes_labels=['x','sin(x)'], color='darkgreen'+plot(sin(x),(x,0,2*pi),color='red') p.show() 
       
Traceback (click to the left of this block for traceback)
...
SyntaxError: invalid syntax
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_57.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cCA9IHBsb3QoZih4KSwgKHgsLXBpLzIsIHBpLzIpLCBheGVzX2xhYmVscz1bJ3gnLCdzaW4oeCknXSwgY29sb3I9J2RhcmtncmVlbicrcGxvdChzaW4oeCksKHgsMCwyKnBpKSxjb2xvcj0ncmVkJykKcC5zaG93KCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpzuy2K1/___code___.py", line 4
    exec compile(u'p.show()
       ^
SyntaxError: invalid syntax
f(x) = (x^3 + x^2 + x)/(x^2 - x -2 ) p = plot(f(x), (x, -5,5)) p.show() p.show(xmin=-2, xmax=4, ymin=-20, 
       
Traceback (click to the left of this block for traceback)
...
SyntaxError: invalid syntax
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_60.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Zih4KSA9ICh4XjMgKyB4XjIgKyB4KS8oeF4yIC0geCAtMiApCnAgPSBwbG90KGYoeCksICh4LCAtNSw1KSkKcC5zaG93KCkKcC5zaG93KHhtaW49LTIsIHhtYXg9NCwgeW1pbj0tMjAs"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpcnzf9T/___code___.py", line 7
    
                                                                            ^
SyntaxError: invalid syntax
f(x)=sin(pi*x-pi) g(x)=cos(pi*x-pi) 
       
p=plot(f(x),(x,-1,1),thickness=3,color='red') q=plot(g(x),(x,-1,1),thickness=3,color='darkblue') 
       
r=p+q 
       
r.show() 
       
plot(1/x,(x,-1,1),ymin=-10,ymax=10) 
       
P(x)=2*x^3+3*x^2-5*x-6 solve(P(x)==0, x) 
       
[x == -2, x == -1, x == (3/2)]
[x == -2, x == -1, x == (3/2)]
plot(P(x), (x, -4, 4), ymax=20, ymin=-20) 
       
P(x)=4*x^4++4*x^3-9*x^2-x+2 solve(P(x)==0, x) 
       
[x == (1/2), x == -2, x == 1, x == (-1/2)]
[x == (1/2), x == -2, x == 1, x == (-1/2)]
 
       
plot(P(x), (x, -3, 3), ymax=20, ymin=-20) 
       
f(x)=2/(x-5) plot(f(x), (x, 2, 7), ymax=10, ymin=-10) 
       
f(x)=-4/((x-4)^2) plot(f(x), (x, 2, 7), ymax=10, ymin=-20) 
       
f(x)=(2*x^2+1)/(x^2-4*x+3) plot(f(x), (x, -2, 6), ymax=20, ymin=-20) 
       
x,y = var("x y") f(x,y) = x^2 - y^2 p = plot3d(f(x,y), (x,-1,400), (y,-400,1)) p.show() 
       
Sleeping...
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