The function minimax is called by entering :

minimax(expr,var=a..b,n,[limit=m])

where expr is an univariate expression (e.g. f(x) ) to approximate, var is a variable (e.g. x ), [a,b]⊂ℝ and n∈ℕ . Expression expr must be continuous on [a,b] . The function returns minimax polynomial (e.g. p(x) ) of degree n or lower that approximates expr on [a,b] . The approximation is found by applying Remez algorithm.

If the fourth argument is specified, m is used to limit the number of iterations of the algorithm. It is unlimited by default.

The largest absolute error of the approximation p(x) , i.e. max_{a≤ x≤ b}|f(x)−p(x)| , is printed in the message area.

Since the coefficients of p are computed numerically, one should avoid setting n unnecessary high as it may result in a poor approximation due to the roundoff errors.

Input :

minimax(sin(x),x=0..2*pi,10)

Output :

5.8514210172e-06+0.999777263385*x+0.00140015265723*x

-0.170089663733*x

0.00525794766407*x

-0.000570502074548*x

-2.14787414001e-06*x

`^`

2-0.170089663733*x

`^`

3+0.0042684304696*x`^`

4+0.00525794766407*x

`^`

5+0.00135760214958*x`^`

6-0.000570502074548*x

`^`

7+6.07297119422e-05*x`^`

8-2.14787414001e-06*x

`^`

9-2.97767481643e-15*x`^`

10
The largest absolute error of this approximation is 5.85234008632× 10^{−6} .