### Related

##### horner-keepfloat-true

expr: 1 * x^4 +2 *x^2...

expr2: horner (%, x),...

Calculate

##### horner-jacobi_p

jacobi_p(0,1,1,x);

horner(jacobi_p(1,a,0...

horner(jacobi_p(2,a,0...

Calculate

##### horner-jacobi_p

jacobi_p(0,1,1,x);

horner(jacobi_p(1,1,1...

horner(jacobi_p(2,1,1...

Calculate

##### horner-jacobi_p

jacobi_p(0,1,1,x);

horner(jacobi_p(1,a,0...

horner(jacobi_p(2,a,0...

Calculate

##### horner

eq1:horner((x^3 - (2 ...

Calculate

##### horner

a00:(x2-x1)*(x2-x1)+(...

a11:(x3-x4)*(x3-x4)+(...

a01:(x2-x1)*(x3-x4)+(...

Calculate

##### horner-keepfloat-true

expr: 4-x^2+x^4;

expr2: horner (%, x)...

Calculate

##### horner-keepfloat-true

expr: 5 * x^2 - 3 * x...

expr2: horner (%, x+2...

Calculate

##### horner-keepfloat-true

expr: 5 * x^2 - 3 * x...

expr2: horner (%, x),...

Calculate

##### horner-taylor

f(x) := x^(1/12);

g(x) := taylor(f(x), ...

g(x);

Calculate

### horner

Run Example
```(%i1)x1:-3;
(%o1)                                 - 3
(%i2) x2:-2;
(%o2)                                 - 2
(%i3) x3:-1;
(%o3)                                 - 1
(%i4) x4:0;
(%o4)                                  0
(%i5) x5:1;
(%o5)                                  1
(%i6) x6:2;
(%o6)                                  2
(%i7) x7:3;
(%o7)                                  3
(%i8) eq2:horner(expand(((x-x1)*(x-x2)*(x-x3)*(x-x5)*(x-x6)*(x-x7))/((x4-x1)*(x4-x2)*(x4-x3)*(x4-x5)*(x4-x6)*(x4-x7))));
2   2        2
x  (x  (14 - x ) - 49) + 36
(%o8)                     ---------------------------
36
(%i9) ```
Run Example
```f(x) := x^(1/12);
1/12
(%o1)                            f(x) := x
(%i2) k : 5;
(%o2)                                  5
(%i3) n : 2*k;
(%o3)                                 10
(%i4) g(x) := taylor(f(x), x, 1, n);
(%o4)                    g(x) := taylor(f(x), x, 1, n)
(%i5) g(x);
2              3               4
x - 1   11 (x - 1)    253 (x - 1)    8855 (x - 1)
(%o5)/T/ 1 + ----- - ----------- + ------------ - -------------
12         288          10368          497664
5                  6                   7                     8
83237 (x - 1)    4910983 (x - 1)    49811399 (x - 1)    4134346117 (x - 1)
+ -------------- - ---------------- + ----------------- - -------------------
5971968          429981696          5159780352          495338913792
9                        10
392762881115 (x - 1)    8405125655861 (x - 1)
+ --------------------- - ----------------------- + . . .
53496602689536          1283918464548864
(%i6) bfloat(g(x));
10                                   9
(%o6) - 6.546463726428567b-3 (x - 1.0b0)   + 7.341828478237645b-3 (x - 1.0b0)
8                                   7
- 8.346499743680691b-3 (x - 1.0b0)  + 9.653782836064414b-3 (x - 1.0b0)
6                                   5
- 1.142137687647057b-2 (x - 1.0b0)  + 1.393795144247257b-2 (x - 1.0b0)
4                                   3
- 1.779312950102881b-2 (x - 1.0b0)  + 2.440200617283951b-2 (x - 1.0b0)
2
- 3.819444444444444b-2 (x - 1.0b0)  + 8.333333333333333b-2 (x - 1.0b0) + 1.0b0
(%i7) p(x) := pade(g(x), n/2, n/2)[1];
n  n
(%o7)                      p(x) := pade(g(x), -, -)
2  2
1
(%i8) horner(p(x));
(%o8)
x (x (x (x (1026935 x + 23303525) + 87621254) + 82884970) + 19452595) + 701569
------------------------------------------------------------------------------
x (x (x (x (701569 x + 19452595) + 82884970) + 87621254) + 23303525) + 1026935
(%i9) l : 1-1/8;
7
(%o9)                                  -
8
(%i10) r : 1+1/8;
9
(%o10)                                 -
8
(%i11) plot2d([(f(x) - bfloat(g(x)))/f(x)], [x, l, r]);
plotplot2d([(f(x) - bfloat(p(x)))/f(x)], [x, l, r]);
plotplot2d([f(x), bfloat(g(x))], [x, l, r]);
plot```
Run Example
```eq1:horner((x^3-x^2-2*x)/-2);
x ((1 - x) x + 2)
(%o1)                          -----------------
2
(%i2) ```

Help for Horner