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Er N0 F1 Ce

The document defines a Lagrange polynomial that fits 16 data points exactly. It lists the polynomial, which is a 15th degree polynomial in x with rational coefficients. It then evaluates the polynomial at integers from 0 to 16, printing the results. The last value is -1514935, showing the polynomial does not match the (nonexistent) 17th data point.

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ram4a5
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849 views1 page

Er N0 F1 Ce

The document defines a Lagrange polynomial that fits 16 data points exactly. It lists the polynomial, which is a 15th degree polynomial in x with rational coefficients. It then evaluates the polynomial at integers from 0 to 16, printing the results. The last value is -1514935, showing the polynomial does not match the (nonexistent) 17th data point.

Uploaded by

ram4a5
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as TXT, PDF, TXT or read online on Scribd
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R=PolynomialRing(QQ,'x')

sage: f = R.lagrange_polynomial([(0,1),(1,3),(2,7),(3,8),(4,21),(5,49),(6,76),
(7,224),(8,467),(9,514),(10,1155),(11,2683),(12,5216),(13,10544),(14,26867),
(15,51510)]); f
-673909/1307674368000*x^15 + 5004253/87178291200*x^14 - 151337/52254720*x^13 +
9320029/106444800*x^12 - 25409989753/14370048000*x^11 + 2192506957/87091200*x^10 -
19011117413/73156608*x^9 + 1200887962891/609638400*x^8 -
3585932821063/326592000*x^7 + 647416874047/14515200*x^6 -
18586394742863/143700480*x^5 + 30899291755337/119750400*x^4 -
274137631043849/825552000*x^3 + 36933161067083/151351200*x^2 - 87781079/1155*x + 1
sage: for i in range(0,17):
print f(i)
....:
1
3
7
8
21
49
76
224
467
514
1155
2683
5216
10544
26867
51510
-1514935
sage:

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