# Kratki osvrt na liste
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t1 = [0,1,2,3,4];
t2 = [5,6,7,8,6];
z=zip(t1,t2); z
[(0, 5), (1, 6), (2, 7), (3, 8), (4, 6)] |
mul(t2); add(t1); print 22 not in t1
10080 10 True |
[i^2 for i in t1 if 0<i<4]
[1, 4, 9] |
for (a,b) in zip(t1,t2): print a,"...",b+1 # forall
0 ... 6 1 ... 7 2 ... 8 3 ... 9 4 ... 7 |
# Funkcije
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f(x)=x^2; type(f)
<type 'sage.symbolic.expression.Expression'> |
f1=diff(f); f1(3)
6 |
diff(f)(3) # diff(f,x)
6 |
plot(f1,0,1)
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f1=f.derivative(); f1(3)
6 |
type(f1)
<type 'sage.symbolic.expression.Expression'> |
def g(x): return x^2
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g(2)
4 |
type(g)
<type 'function'> |
g1=g.derivative()
Traceback (click to the left of this block for traceback) ... AttributeError: 'function' object has no attribute 'derivative' |
var("y"); plot(g(y),y,0,1)
y |
.png)
clear_vars(y); plot(g(y),y,0,1)
Traceback (click to the left of this block for traceback) ... TypeError: clear_vars() takes no arguments (1 given) |
f(x)=x;
g=f.derivative();
g
x |--> 1 |
g(3)
1 |
f=x; #x^3
g=f.derivative();
g
1 |
g(3)
Traceback (click to the left of this block for traceback) ... ValueError: the number of arguments must be less than or equal to 0 |
g(x=3)
1 |
# http://www.sagemath.org/doc/tutorial/tour_functions.html
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def h(x):
if x<2:
return x^2
else:
return x
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plot(h,x,1,3,exclude=[2])
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.png)
plot(h(x),x,1,3)
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.png)
type(x<2)
<type 'sage.symbolic.expression.Expression'> |
# Primjer
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def f(n): p=list_plot([[i,primes_first_n(i)[-1]/i] for i in range(1,n)]); return p
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f(20)
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.png)
def g(n): p=list_plot([[i,primes_first_n(i)[-1]/i] for i in range(1,n)]); show(p); return
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g(20)
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.png)
# Rekurzivne funkcije
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def fr(n):
if n==0:
return 1
else:
return n*fr(n-1);
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fr(5)
120 |
def tt1(k): t=cputime(); [fr(500) for i in range(1,k)]; return cputime(t)
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tt1(1000)
0.46402800000000011 |
def tt2(k): t=cputime(); [factorial(500) for i in range(1,k)]; return cputime(t)
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tt2(1000)
0.0080009999999997028 |