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@@ -0,0 +1,80 @@
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+```python
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+sage: x
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+x
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+sage: l_2 = (x - 1)*(x - 3)*(x - 4)
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+sage: l_2
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+(x - 1)*(x - 3)*(x - 4)
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+sage: l_2(1)
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+0
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+sage: l_2(3)
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+0
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+sage: l_2(4)
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+0
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+sage: l_2(2)
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+2
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+sage: l_2
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+(x - 1)*(x - 3)*(x - 4)
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+sage: l_2 /= (2-1)*(2-3)*(2-4)
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+sage: l_2(2)
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+1
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+sage: l_3 = (x - 1)*(x - 2)*(x-4) / ((3-1)*(3-2)*(3-4))
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+sage: l_3(1)
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+0
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+sage: l_3(2)
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+0
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+sage: l_3(3)
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+1
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+sage: l_3(4)
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+0
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+sage: l_1 = (x - 2)*(x - 3)*(x - 4) / ((1 - 2)*(1 - 3)*(1
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+....: - 4))
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+sage: l_1(1)
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+1
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+sage: l_1(2)
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+0
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+sage: l_1(3)
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+0
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+sage: l_1(4)
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+0
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+sage: l_1
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+-1/6*(x - 2)*(x - 3)*(x - 4)
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+sage: l_2
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+1/2*(x - 1)*(x - 3)*(x - 4)
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+sage: l_3
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+-1/2*(x - 1)*(x - 2)*(x - 4)
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+sage: l_4
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+----------------------------------------------------------
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+NameError Traceback (most recent call last)
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+<ipython-input-24-cbdd82c87bb0> in <module>
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+----> 1 l_4
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+
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+NameError: name 'l_4' is not defined
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+sage: l_4 = (x - 1)*(x - 2)*(x - 3) / ((4 - 1)*(4 - 2)*(4
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+....: - 3))
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+sage: l_4(1)
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+0
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+sage: l_4(2)
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+0
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+sage: l_4(3)
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+0
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+sage: l_4(4)
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+1
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+sage: for i in range(1, 5):
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+....: print(i, l_1(i), l_2(i), l_3(i), l_4(i))
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+....:
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+1 1 0 0 0
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+2 0 1 0 0
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+3 0 0 1 0
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+4 0 0 0 1
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+sage: f = 6 * l_1 + 4 * l_2 + 3 * l_3 + 0 * l_4
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+sage: l_2(2)
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+1
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+sage: for i in range(1, 5):
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+....: print(i, f(i))
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+....:
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+1 6
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+2 4
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+3 3
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+4 0
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+```
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+
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narodnik