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chebyshev_t-do

/* input numbers b,k,...

k:1;

n:19;

Calculate

chebyshev_t-plot2d
plot2d([(chebyshev_t(6,x))/2^5,x^6,x^6-(chebyshev_t(6,x))/2^5],[x,-1,1]);

plot2d([(chebyshev_t(...

Calculate

chebyshev_t-do-mod

/* input numbers b an...

n:4;

(s:2*chebyshev_t(b/2,...

Calculate

chebyshev_t-do

/* b=4,6 (mod 8) , n&...

n:19;

a:6;

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:1999;

(s:2*chebyshev_t(k,3)...

Calculate

chebyshev_t-do

/* b=0,6 (mod 8) , n&...

n:31;

a:6;

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:13;

(s:2*chebyshev_t(k,3)...

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:248;

(s:2*chebyshev_t(k,3)...

Calculate

chebyshev_t-taylor

taylor(chebyshev_t(13...

Calculate

chebyshev_t-do-mod

/* input numbers b,k,...

b:10;

n:3;

Calculate

chebyshev_t

Run Example
(%i1)/* b=0,6 (mod 8) , n>
2 *//* input numbers b and n */b:6;
(%o1)                                  6
(%i2)  n:31;
(%o2)                                 31
(%i3)  a:6;
(%o3)                                  6
(%i4) (s:2*chebyshev_t(b/2,a/2),N:(b^n+1)/(b+1),for i from 1 thru n-1 do (s:mod(2*chebyshev_t(b,s/2),N)));
(%o4)                                done
(%i5) (if(s=2*chebyshev_t(b/2,a/2)) then print("prime") else print("composite"));
prime 
(%o5)                                prime
(%i6) 
Run Example
ratsimp(chebyshev_t(6,x)/2^5);
                               6       4       2
                           32 x  - 48 x  + 18 x  - 1
(%o1)                      -------------------------
                                      32
(%i2) ratsimp(x^6-(chebyshev_t(6,x))/2^5);
                                   4       2
                               48 x  - 18 x  + 1
(%o2)                          -----------------
                                      32
(%i3) plot2d([(chebyshev_t(6,x))/2^5,x^6,x^6-(chebyshev_t(6,x))/2^5],[x,-1,1],[y,-0.2,0.2],[legend,Tst,p(x),q(x)]);
plotplot2d([(chebyshev_t(6,x))/2^5,x^6,x^6-(chebyshev_t(6,x))/2^5],[x,-1,1],[y,-0.2,0.2],[legend,Tst,p(x),q(x)]);
Run Example
g(x):= 0.11* chebyshev_t (2, x) + 0.11*chebyshev_t(6, x);
(%o1)       g(x) := 0.11 chebyshev_t(2, x) + 0.11 chebyshev_t(6, x)
(%i2) horner(g(x), x);

rat: replaced 0.11 by 11/100 = 0.11

rat: replaced 0.11 by 11/100 = 0.11
                        2   2       2
                       x  (x  (176 x  - 264) + 110) - 11
(%o2)                  ---------------------------------
                                      50
(%i3) expand(g(x));
                             6         4        2
(%o3)                  3.52 x  - 5.28 x  + 2.2 x  - 0.22
(%i4) 

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