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approx
last edited on December 03, 2008 07:07 AM by jachter
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a = approx(sin(pi*x))  # What happens if we approximate this function?
for i in range(0,n):
 a[i] 
evaluate
        
[1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9]
[1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9]
evaluate
       
evaluate
       
evaluate
       
evaluate
        
0.707106781186548
1.224744871391589*x
2.371708245126284*(x^2 - 0.333333333333333)
4.67707173346743*(x^3 - 0.600000000000000*x)
9.280776503073419*(x^4 - 0.857142857142857*(x^2 - 0.333333333333333) -
0.200000000000000)
18.46851205430498*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) -
0.428571428571428*x)
36.80854711374455*(x^6 - 1.363636363636358*(x^4 - 0.857142857142857*(x^2
- 0.333333333333333) - 0.200000000000000) - 0.714285714285714*(x^2 -
0.333333333333333) - 0.142857142857143)
73.42905536558702*(x^7 - 1.615384615384656*(x^5 - 1.111111111111112*(x^3
- 0.600000000000000*x) - 0.428571428571428*x) - 1.060606060606062*(x^3 -
0.600000000000000*x) - 0.333333333333333*x)
146.5709978245593*(x^8 - 1.866666666666325*(x^6 - 1.363636363636358*(x^4
- 0.857142857142857*(x^2 - 0.333333333333333) - 0.200000000000000) -
0.714285714285714*(x^2 - 0.333333333333333) - 0.142857142857143) -
1.468531468531463*(x^4 - 0.857142857142857*(x^2 - 0.333333333333333) -
0.200000000000000) - 0.606060606060606*(x^2 - 0.333333333333333) -
0.111111111111111)
0.707106781186548
1.224744871391589*x
2.371708245126284*(x^2 - 0.333333333333333)
4.67707173346743*(x^3 - 0.600000000000000*x)
9.280776503073419*(x^4 - 0.857142857142857*(x^2 - 0.333333333333333) - 0.200000000000000)
18.46851205430498*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x)
36.80854711374455*(x^6 - 1.363636363636358*(x^4 - 0.857142857142857*(x^2 - 0.333333333333333) - 0.200000000000000) - 0.714285714285714*(x^2 - 0.333333333333333) - 0.142857142857143)
73.42905536558702*(x^7 - 1.615384615384656*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 1.060606060606062*(x^3 - 0.600000000000000*x) - 0.333333333333333*x)
146.5709978245593*(x^8 - 1.866666666666325*(x^6 - 1.363636363636358*(x^4 - 0.857142857142857*(x^2 - 0.333333333333333) - 0.200000000000000) - 0.714285714285714*(x^2 - 0.333333333333333) - 0.142857142857143) - 1.468531468531463*(x^4 - 0.857142857142857*(x^2 - 0.333333333333333) - 0.200000000000000) - 0.606060606060606*(x^2 - 0.333333333333333) - 0.111111111111111)
evaluate
       
evaluate
        
0.000000000000000
0.954929658551372*x
0.954929658551372*x
0.954929658551372*x - 2.895604780498532*(x^3 - 0.600000000000000*x)
0.954929658551372*x - 2.895604780498532*(x^3 - 0.600000000000000*x)
1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) -
0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) +
0.954929658551372*x
1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) -
0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) +
0.954929658551372*x
-0.446220781740244*(x^7 - 1.615384615384656*(x^5 -
1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) -
1.060606060606062*(x^3 - 0.600000000000000*x) - 0.333333333333333*x) +
1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) -
0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) +
0.954929658551372*x
-0.446220781740244*(x^7 - 1.615384615384656*(x^5 -
1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) -
1.060606060606062*(x^3 - 0.600000000000000*x) - 0.333333333333333*x) +
1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) -
0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) +
0.954929658551372*x
0.000000000000000
0.954929658551372*x
0.954929658551372*x
0.954929658551372*x - 2.895604780498532*(x^3 - 0.600000000000000*x)
0.954929658551372*x - 2.895604780498532*(x^3 - 0.600000000000000*x)
1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) + 0.954929658551372*x
1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) + 0.954929658551372*x
-0.446220781740244*(x^7 - 1.615384615384656*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 1.060606060606062*(x^3 - 0.600000000000000*x) - 0.333333333333333*x) + 1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) + 0.954929658551372*x
-0.446220781740244*(x^7 - 1.615384615384656*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 1.060606060606062*(x^3 - 0.600000000000000*x) - 0.333333333333333*x) + 1.726905184327746*(x^5 - 1.111111111111112*(x^3 - 0.600000000000000*x) - 0.428571428571428*x) - 2.895604780498532*(x^3 - 0.600000000000000*x) + 0.954929658551372*x
evaluate
       
evaluate
       
evaluate
       
evaluate
       
evaluate
        
1.103638323514327*x + 1.175201193643801
1.103638323514327*x + 1.175201193643801