### Related

P:[1,-5,2];

Q:[-1,3,1];

Calculate

##### apply-print-transpose

solnum : [[1,4,7],[2,...

solnum : apply(matrix...

solnum : transpose (s...

Calculate

##### apply-nary-numer-xthru

""/* SERIENSCHALTUNG */;

"~~"([x]):=xthru(appl...

nary("~~",110);

Calculate

##### apply-expand

expand( ( K * ( 1 + T...

apply (tex, [%i1]);

Calculate

matrix_element_mult:...

[a, b, c] . [x, y, z];

Calculate

##### apply-equal-lambda-notequal-numberp

list:[1, 2, false, 3,...

n:is(false);

n:2;

Calculate

##### apply-arraymake-do-false-if-kill-lambda-print

kill(all);

([t],t:false);

for i:0 thru 1 do(for...

Calculate

modulo(v):=sqrt(apply...

u:[-4,10,9,-15];

Calculate

##### apply-block-ceiling-cons-do-fpprec-rationalize-ratnump-reverse-sin

rationalize (0.5);

rationalize (0.1);

fpprec : 5;

Calculate

matrix_element_mult:...

[a, b, c] . [x, y, z];

Calculate

### apply

Run Example
```(%i1)load(draw);
(%o1)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i2) coord: setify(makelist(k,k,-4,4));
(%o2)                 {- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4}
(%i3) points2d: listify(cartesian_product (coord ,coord ));
(%o3) [[- 4, - 4], [- 4, - 3], [- 4, - 2], [- 4, - 1], [- 4, 0], [- 4, 1],
[- 4, 2], [- 4, 3], [- 4, 4], [- 3, - 4], [- 3, - 3], [- 3, - 2], [- 3, - 1],
[- 3, 0], [- 3, 1], [- 3, 2], [- 3, 3], [- 3, 4], [- 2, - 4], [- 2, - 3],
[- 2, - 2], [- 2, - 1], [- 2, 0], [- 2, 1], [- 2, 2], [- 2, 3], [- 2, 4],
[- 1, - 4], [- 1, - 3], [- 1, - 2], [- 1, - 1], [- 1, 0], [- 1, 1], [- 1, 2],
[- 1, 3], [- 1, 4], [0, - 4], [0, - 3], [0, - 2], [0, - 1], [0, 0], [0, 1],
[0, 2], [0, 3], [0, 4], [1, - 4], [1, - 3], [1, - 2], [1, - 1], [1, 0],
[1, 1], [1, 2], [1, 3], [1, 4], [2, - 4], [2, - 3], [2, - 2], [2, - 1],
[2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, - 4], [3, - 3], [3, - 2],
[3, - 1], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [4, - 4], [4, - 3],
[4, - 2], [4, - 1], [4, 0], [4, 1], [4, 2], [4, 3], [4, 4]]
(%i4) vf2d(x,y):=  vector ([x,y],[cos(y),x]/6);
[cos(y), x]
(%o4)              vf2d(x, y) := vector([x, y], -----------)
6
(%i5) vect2: makelist(vf2d(k[1],k[2]),k,points2d );
cos(4)    2                        cos(3)    2
(%o5) [vector([- 4, - 4], [------, - -]), vector([- 4, - 3], [------, - -]),
6       3                          6       3
cos(2)    2                        cos(1)    2
vector([- 4, - 2], [------, - -]), vector([- 4, - 1], [------, - -]),
6       3                          6       3
1    2                      cos(1)    2
vector([- 4, 0], [-, - -]), vector([- 4, 1], [------, - -]),
6    3                        6       3
cos(2)    2                      cos(3)    2
vector([- 4, 2], [------, - -]), vector([- 4, 3], [------, - -]),
6       3                        6       3
cos(4)    2                        cos(4)    1
vector([- 4, 4], [------, - -]), vector([- 3, - 4], [------, - -]),
6       3                          6       2
cos(3)    1                        cos(2)    1
vector([- 3, - 3], [------, - -]), vector([- 3, - 2], [------, - -]),
6       2                          6       2
cos(1)    1                      1    1
vector([- 3, - 1], [------, - -]), vector([- 3, 0], [-, - -]),
6       2                      6    2
cos(1)    1                      cos(2)    1
vector([- 3, 1], [------, - -]), vector([- 3, 2], [------, - -]),
6       2                        6       2
cos(3)    1                      cos(4)    1
vector([- 3, 3], [------, - -]), vector([- 3, 4], [------, - -]),
6       2                        6       2
cos(4)    1                        cos(3)    1
vector([- 2, - 4], [------, - -]), vector([- 2, - 3], [------, - -]),
6       3                          6       3
cos(2)    1                        cos(1)    1
vector([- 2, - 2], [------, - -]), vector([- 2, - 1], [------, - -]),
6       3                          6       3
1    1                      cos(1)    1
vector([- 2, 0], [-, - -]), vector([- 2, 1], [------, - -]),
6    3                        6       3
cos(2)    1                      cos(3)    1
vector([- 2, 2], [------, - -]), vector([- 2, 3], [------, - -]),
6       3                        6       3
cos(4)    1                        cos(4)    1
vector([- 2, 4], [------, - -]), vector([- 1, - 4], [------, - -]),
6       3                          6       6
cos(3)    1                        cos(2)    1
vector([- 1, - 3], [------, - -]), vector([- 1, - 2], [------, - -]),
6       6                          6       6
cos(1)    1                      1    1
vector([- 1, - 1], [------, - -]), vector([- 1, 0], [-, - -]),
6       6                      6    6
cos(1)    1                      cos(2)    1
vector([- 1, 1], [------, - -]), vector([- 1, 2], [------, - -]),
6       6                        6       6
cos(3)    1                      cos(4)    1
vector([- 1, 3], [------, - -]), vector([- 1, 4], [------, - -]),
6       6                        6       6
cos(4)                         cos(3)
vector([0, - 4], [------, 0]), vector([0, - 3], [------, 0]),
6                              6
cos(2)                         cos(1)
vector([0, - 2], [------, 0]), vector([0, - 1], [------, 0]),
6                              6
1                       cos(1)
vector([0, 0], [-, 0]), vector([0, 1], [------, 0]),
6                         6
cos(2)                       cos(3)
vector([0, 2], [------, 0]), vector([0, 3], [------, 0]),
6                            6
cos(4)                         cos(4)  1
vector([0, 4], [------, 0]), vector([1, - 4], [------, -]),
6                              6     6
cos(3)  1                      cos(2)  1
vector([1, - 3], [------, -]), vector([1, - 2], [------, -]),
6     6                        6     6
cos(1)  1                    1  1
vector([1, - 1], [------, -]), vector([1, 0], [-, -]),
6     6                    6  6
cos(1)  1                    cos(2)  1
vector([1, 1], [------, -]), vector([1, 2], [------, -]),
6     6                      6     6
cos(3)  1                    cos(4)  1
vector([1, 3], [------, -]), vector([1, 4], [------, -]),
6     6                      6     6
cos(4)  1                      cos(3)  1
vector([2, - 4], [------, -]), vector([2, - 3], [------, -]),
6     3                        6     3
cos(2)  1                      cos(1)  1
vector([2, - 2], [------, -]), vector([2, - 1], [------, -]),
6     3                        6     3
1  1                    cos(1)  1
vector([2, 0], [-, -]), vector([2, 1], [------, -]),
6  3                      6     3
cos(2)  1                    cos(3)  1
vector([2, 2], [------, -]), vector([2, 3], [------, -]),
6     3                      6     3
cos(4)  1                      cos(4)  1
vector([2, 4], [------, -]), vector([3, - 4], [------, -]),
6     3                        6     2
cos(3)  1                      cos(2)  1
vector([3, - 3], [------, -]), vector([3, - 2], [------, -]),
6     2                        6     2
cos(1)  1                    1  1
vector([3, - 1], [------, -]), vector([3, 0], [-, -]),
6     2                    6  2
cos(1)  1                    cos(2)  1
vector([3, 1], [------, -]), vector([3, 2], [------, -]),
6     2                      6     2
cos(3)  1                    cos(4)  1
vector([3, 3], [------, -]), vector([3, 4], [------, -]),
6     2                      6     2
cos(4)  2                      cos(3)  2
vector([4, - 4], [------, -]), vector([4, - 3], [------, -]),
6     3                        6     3
cos(2)  2                      cos(1)  2
vector([4, - 2], [------, -]), vector([4, - 1], [------, -]),
6     3                        6     3
1  2                    cos(1)  2
vector([4, 0], [-, -]), vector([4, 1], [------, -]),
6  3                      6     3
cos(2)  2                    cos(3)  2
vector([4, 2], [------, -]), vector([4, 3], [------, -]),
6     3                      6     3
cos(4)  2
vector([4, 4], [------, -])]
6     3
(%i6) apply(draw2d , append ([ color=blue], vect2 ));
(%o6) [gr2d(vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector, vector, vector, vector, vector, vector, vector, vector, vector,
vector)]
(%i7) ```
Run Example
```coord: setify(makelist(k,k,-2,2));
(%o1)                         {- 2, - 1, 0, 1, 2}
(%i2) points3d: listify(cartesian_product(coord ,coord ,coord));
(%o2) [[- 2, - 2, - 2], [- 2, - 2, - 1], [- 2, - 2, 0], [- 2, - 2, 1],
[- 2, - 2, 2], [- 2, - 1, - 2], [- 2, - 1, - 1], [- 2, - 1, 0], [- 2, - 1, 1],
[- 2, - 1, 2], [- 2, 0, - 2], [- 2, 0, - 1], [- 2, 0, 0], [- 2, 0, 1],
[- 2, 0, 2], [- 2, 1, - 2], [- 2, 1, - 1], [- 2, 1, 0], [- 2, 1, 1],
[- 2, 1, 2], [- 2, 2, - 2], [- 2, 2, - 1], [- 2, 2, 0], [- 2, 2, 1],
[- 2, 2, 2], [- 1, - 2, - 2], [- 1, - 2, - 1], [- 1, - 2, 0], [- 1, - 2, 1],
[- 1, - 2, 2], [- 1, - 1, - 2], [- 1, - 1, - 1], [- 1, - 1, 0], [- 1, - 1, 1],
[- 1, - 1, 2], [- 1, 0, - 2], [- 1, 0, - 1], [- 1, 0, 0], [- 1, 0, 1],
[- 1, 0, 2], [- 1, 1, - 2], [- 1, 1, - 1], [- 1, 1, 0], [- 1, 1, 1],
[- 1, 1, 2], [- 1, 2, - 2], [- 1, 2, - 1], [- 1, 2, 0], [- 1, 2, 1],
[- 1, 2, 2], [0, - 2, - 2], [0, - 2, - 1], [0, - 2, 0], [0, - 2, 1],
[0, - 2, 2], [0, - 1, - 2], [0, - 1, - 1], [0, - 1, 0], [0, - 1, 1],
[0, - 1, 2], [0, 0, - 2], [0, 0, - 1], [0, 0, 0], [0, 0, 1], [0, 0, 2],
[0, 1, - 2], [0, 1, - 1], [0, 1, 0], [0, 1, 1], [0, 1, 2], [0, 2, - 2],
[0, 2, - 1], [0, 2, 0], [0, 2, 1], [0, 2, 2], [1, - 2, - 2], [1, - 2, - 1],
[1, - 2, 0], [1, - 2, 1], [1, - 2, 2], [1, - 1, - 2], [1, - 1, - 1],
[1, - 1, 0], [1, - 1, 1], [1, - 1, 2], [1, 0, - 2], [1, 0, - 1], [1, 0, 0],
[1, 0, 1], [1, 0, 2], [1, 1, - 2], [1, 1, - 1], [1, 1, 0], [1, 1, 1],
[1, 1, 2], [1, 2, - 2], [1, 2, - 1], [1, 2, 0], [1, 2, 1], [1, 2, 2],
[2, - 2, - 2], [2, - 2, - 1], [2, - 2, 0], [2, - 2, 1], [2, - 2, 2],
[2, - 1, - 2], [2, - 1, - 1], [2, - 1, 0], [2, - 1, 1], [2, - 1, 2],
[2, 0, - 2], [2, 0, - 1], [2, 0, 0], [2, 0, 1], [2, 0, 2], [2, 1, - 2],
[2, 1, - 1], [2, 1, 0], [2, 1, 1], [2, 1, 2], [2, 2, - 2], [2, 2, - 1],
[2, 2, 0], [2, 2, 1], [2, 2, 2]]
(%i3) vf3d(x,y,z):=  vector([x,y,z],[z,x,y]/8);
[z, x, y]
(%o3)            vf3d(x, y, z) := vector([x, y, z], ---------)
8
(%i4) vect3: makelist(vf3d(k[1],k[2],k[3]),k,points3d);
1    1    1
(%o4) [vector([- 2, - 2, - 2], [- -, - -, - -]),
4    4    4
1    1    1
vector([- 2, - 2, - 1], [- -, - -, - -]),
8    4    4
1    1                           1    1    1
vector([- 2, - 2, 0], [0, - -, - -]), vector([- 2, - 2, 1], [-, - -, - -]),
4    4                           8    4    4
1    1    1
vector([- 2, - 2, 2], [-, - -, - -]), vector([- 2, - 1, - 2],
4    4    4
1    1    1                               1    1    1
[- -, - -, - -]), vector([- 2, - 1, - 1], [- -, - -, - -]),
4    4    8                               8    4    8
1    1                           1    1    1
vector([- 2, - 1, 0], [0, - -, - -]), vector([- 2, - 1, 1], [-, - -, - -]),
4    8                           8    4    8
1    1    1                             1    1
vector([- 2, - 1, 2], [-, - -, - -]), vector([- 2, 0, - 2], [- -, - -, 0]),
4    4    8                             4    4
1    1                                 1
vector([- 2, 0, - 1], [- -, - -, 0]), vector([- 2, 0, 0], [0, - -, 0]),
8    4                                 4
1    1                            1    1
vector([- 2, 0, 1], [-, - -, 0]), vector([- 2, 0, 2], [-, - -, 0]),
8    4                            4    4
1    1  1                             1    1  1
vector([- 2, 1, - 2], [- -, - -, -]), vector([- 2, 1, - 1], [- -, - -, -]),
4    4  8                             8    4  8
1  1                         1    1  1
vector([- 2, 1, 0], [0, - -, -]), vector([- 2, 1, 1], [-, - -, -]),
4  8                         8    4  8
1    1  1                             1    1  1
vector([- 2, 1, 2], [-, - -, -]), vector([- 2, 2, - 2], [- -, - -, -]),
4    4  8                             4    4  4
1    1  1                              1  1
vector([- 2, 2, - 1], [- -, - -, -]), vector([- 2, 2, 0], [0, - -, -]),
8    4  4                              4  4
1    1  1                         1    1  1
vector([- 2, 2, 1], [-, - -, -]), vector([- 2, 2, 2], [-, - -, -]),
8    4  4                         4    4  4
1    1    1
vector([- 1, - 2, - 2], [- -, - -, - -]),
4    8    4
1    1    1
vector([- 1, - 2, - 1], [- -, - -, - -]),
8    8    4
1    1                           1    1    1
vector([- 1, - 2, 0], [0, - -, - -]), vector([- 1, - 2, 1], [-, - -, - -]),
8    4                           8    8    4
1    1    1
vector([- 1, - 2, 2], [-, - -, - -]), vector([- 1, - 1, - 2],
4    8    4
1    1    1                               1    1    1
[- -, - -, - -]), vector([- 1, - 1, - 1], [- -, - -, - -]),
4    8    8                               8    8    8
1    1                           1    1    1
vector([- 1, - 1, 0], [0, - -, - -]), vector([- 1, - 1, 1], [-, - -, - -]),
8    8                           8    8    8
1    1    1                             1    1
vector([- 1, - 1, 2], [-, - -, - -]), vector([- 1, 0, - 2], [- -, - -, 0]),
4    8    8                             4    8
1    1                                 1
vector([- 1, 0, - 1], [- -, - -, 0]), vector([- 1, 0, 0], [0, - -, 0]),
8    8                                 8
1    1                            1    1
vector([- 1, 0, 1], [-, - -, 0]), vector([- 1, 0, 2], [-, - -, 0]),
8    8                            4    8
1    1  1                             1    1  1
vector([- 1, 1, - 2], [- -, - -, -]), vector([- 1, 1, - 1], [- -, - -, -]),
4    8  8                             8    8  8
1  1                         1    1  1
vector([- 1, 1, 0], [0, - -, -]), vector([- 1, 1, 1], [-, - -, -]),
8  8                         8    8  8
1    1  1                             1    1  1
vector([- 1, 1, 2], [-, - -, -]), vector([- 1, 2, - 2], [- -, - -, -]),
4    8  8                             4    8  4
1    1  1                              1  1
vector([- 1, 2, - 1], [- -, - -, -]), vector([- 1, 2, 0], [0, - -, -]),
8    8  4                              8  4
1    1  1                         1    1  1
vector([- 1, 2, 1], [-, - -, -]), vector([- 1, 2, 2], [-, - -, -]),
8    8  4                         4    8  4
1       1                             1       1
vector([0, - 2, - 2], [- -, 0, - -]), vector([0, - 2, - 1], [- -, 0, - -]),
4       4                             8       4
1                         1       1
vector([0, - 2, 0], [0, 0, - -]), vector([0, - 2, 1], [-, 0, - -]),
4                         8       4
1       1                             1       1
vector([0, - 2, 2], [-, 0, - -]), vector([0, - 1, - 2], [- -, 0, - -]),
4       4                             4       8
1       1                                 1
vector([0, - 1, - 1], [- -, 0, - -]), vector([0, - 1, 0], [0, 0, - -]),
8       8                                 8
1       1                         1       1
vector([0, - 1, 1], [-, 0, - -]), vector([0, - 1, 2], [-, 0, - -]),
8       8                         4       8
1                                 1
vector([0, 0, - 2], [- -, 0, 0]), vector([0, 0, - 1], [- -, 0, 0]),
4                                 8
1
vector([0, 0, 0], [0, 0, 0]), vector([0, 0, 1], [-, 0, 0]),
8
1                                 1     1
vector([0, 0, 2], [-, 0, 0]), vector([0, 1, - 2], [- -, 0, -]),
4                                 4     8
1     1                             1
vector([0, 1, - 1], [- -, 0, -]), vector([0, 1, 0], [0, 0, -]),
8     8                             8
1     1                       1     1
vector([0, 1, 1], [-, 0, -]), vector([0, 1, 2], [-, 0, -]),
8     8                       4     8
1     1                           1     1
vector([0, 2, - 2], [- -, 0, -]), vector([0, 2, - 1], [- -, 0, -]),
4     4                           8     4
1                       1     1
vector([0, 2, 0], [0, 0, -]), vector([0, 2, 1], [-, 0, -]),
4                       8     4
1     1                             1  1    1
vector([0, 2, 2], [-, 0, -]), vector([1, - 2, - 2], [- -, -, - -]),
4     4                             4  8    4
1  1    1                            1    1
vector([1, - 2, - 1], [- -, -, - -]), vector([1, - 2, 0], [0, -, - -]),
8  8    4                            8    4
1  1    1                         1  1    1
vector([1, - 2, 1], [-, -, - -]), vector([1, - 2, 2], [-, -, - -]),
8  8    4                         4  8    4
1  1    1                             1  1    1
vector([1, - 1, - 2], [- -, -, - -]), vector([1, - 1, - 1], [- -, -, - -]),
4  8    8                             8  8    8
1    1                         1  1    1
vector([1, - 1, 0], [0, -, - -]), vector([1, - 1, 1], [-, -, - -]),
8    8                         8  8    8
1  1    1                           1  1
vector([1, - 1, 2], [-, -, - -]), vector([1, 0, - 2], [- -, -, 0]),
4  8    8                           4  8
1  1                             1
vector([1, 0, - 1], [- -, -, 0]), vector([1, 0, 0], [0, -, 0]),
8  8                             8
1  1                          1  1
vector([1, 0, 1], [-, -, 0]), vector([1, 0, 2], [-, -, 0]),
8  8                          4  8
1  1  1                           1  1  1
vector([1, 1, - 2], [- -, -, -]), vector([1, 1, - 1], [- -, -, -]),
4  8  8                           8  8  8
1  1                       1  1  1
vector([1, 1, 0], [0, -, -]), vector([1, 1, 1], [-, -, -]),
8  8                       8  8  8
1  1  1                           1  1  1
vector([1, 1, 2], [-, -, -]), vector([1, 2, - 2], [- -, -, -]),
4  8  8                           4  8  4
1  1  1                          1  1
vector([1, 2, - 1], [- -, -, -]), vector([1, 2, 0], [0, -, -]),
8  8  4                          8  4
1  1  1                       1  1  1
vector([1, 2, 1], [-, -, -]), vector([1, 2, 2], [-, -, -]),
8  8  4                       4  8  4
1  1    1                             1  1    1
vector([2, - 2, - 2], [- -, -, - -]), vector([2, - 2, - 1], [- -, -, - -]),
4  4    4                             8  4    4
1    1                         1  1    1
vector([2, - 2, 0], [0, -, - -]), vector([2, - 2, 1], [-, -, - -]),
4    4                         8  4    4
1  1    1                             1  1    1
vector([2, - 2, 2], [-, -, - -]), vector([2, - 1, - 2], [- -, -, - -]),
4  4    4                             4  4    8
1  1    1                            1    1
vector([2, - 1, - 1], [- -, -, - -]), vector([2, - 1, 0], [0, -, - -]),
8  4    8                            4    8
1  1    1                         1  1    1
vector([2, - 1, 1], [-, -, - -]), vector([2, - 1, 2], [-, -, - -]),
8  4    8                         4  4    8
1  1                              1  1
vector([2, 0, - 2], [- -, -, 0]), vector([2, 0, - 1], [- -, -, 0]),
4  4                              8  4
1                          1  1
vector([2, 0, 0], [0, -, 0]), vector([2, 0, 1], [-, -, 0]),
4                          8  4
1  1                              1  1  1
vector([2, 0, 2], [-, -, 0]), vector([2, 1, - 2], [- -, -, -]),
4  4                              4  4  8
1  1  1                          1  1
vector([2, 1, - 1], [- -, -, -]), vector([2, 1, 0], [0, -, -]),
8  4  8                          4  8
1  1  1                       1  1  1
vector([2, 1, 1], [-, -, -]), vector([2, 1, 2], [-, -, -]),
8  4  8                       4  4  8
1  1  1                           1  1  1
vector([2, 2, - 2], [- -, -, -]), vector([2, 2, - 1], [- -, -, -]),
4  4  4                           8  4  4
1  1                       1  1  1
vector([2, 2, 0], [0, -, -]), vector([2, 2, 1], [-, -, -]),
4  4                       8  4  4
1  1  1
vector([2, 2, 2], [-, -, -])]
4  4  4
(%i5) apply(draw3d , append([color=blue], vect3));
1    1    1
(%o5) draw3d(color = blue, vector([- 2, - 2, - 2], [- -, - -, - -]),
4    4    4
1    1    1
vector([- 2, - 2, - 1], [- -, - -, - -]),
8    4    4
1    1                           1    1    1
vector([- 2, - 2, 0], [0, - -, - -]), vector([- 2, - 2, 1], [-, - -, - -]),
4    4                           8    4    4
1    1    1
vector([- 2, - 2, 2], [-, - -, - -]), vector([- 2, - 1, - 2],
4    4    4
1    1    1                               1    1    1
[- -, - -, - -]), vector([- 2, - 1, - 1], [- -, - -, - -]),
4    4    8                               8    4    8
1    1                           1    1    1
vector([- 2, - 1, 0], [0, - -, - -]), vector([- 2, - 1, 1], [-, - -, - -]),
4    8                           8    4    8
1    1    1                             1    1
vector([- 2, - 1, 2], [-, - -, - -]), vector([- 2, 0, - 2], [- -, - -, 0]),
4    4    8                             4    4
1    1                                 1
vector([- 2, 0, - 1], [- -, - -, 0]), vector([- 2, 0, 0], [0, - -, 0]),
8    4                                 4
1    1                            1    1
vector([- 2, 0, 1], [-, - -, 0]), vector([- 2, 0, 2], [-, - -, 0]),
8    4                            4    4
1    1  1                             1    1  1
vector([- 2, 1, - 2], [- -, - -, -]), vector([- 2, 1, - 1], [- -, - -, -]),
4    4  8                             8    4  8
1  1                         1    1  1
vector([- 2, 1, 0], [0, - -, -]), vector([- 2, 1, 1], [-, - -, -]),
4  8                         8    4  8
1    1  1                             1    1  1
vector([- 2, 1, 2], [-, - -, -]), vector([- 2, 2, - 2], [- -, - -, -]),
4    4  8                             4    4  4
1    1  1                              1  1
vector([- 2, 2, - 1], [- -, - -, -]), vector([- 2, 2, 0], [0, - -, -]),
8    4  4                              4  4
1    1  1                         1    1  1
vector([- 2, 2, 1], [-, - -, -]), vector([- 2, 2, 2], [-, - -, -]),
8    4  4                         4    4  4
1    1    1
vector([- 1, - 2, - 2], [- -, - -, - -]),
4    8    4
1    1    1
vector([- 1, - 2, - 1], [- -, - -, - -]),
8    8    4
1    1                           1    1    1
vector([- 1, - 2, 0], [0, - -, - -]), vector([- 1, - 2, 1], [-, - -, - -]),
8    4                           8    8    4
1    1    1
vector([- 1, - 2, 2], [-, - -, - -]), vector([- 1, - 1, - 2],
4    8    4
1    1    1                               1    1    1
[- -, - -, - -]), vector([- 1, - 1, - 1], [- -, - -, - -]),
4    8    8                               8    8    8
1    1                           1    1    1
vector([- 1, - 1, 0], [0, - -, - -]), vector([- 1, - 1, 1], [-, - -, - -]),
8    8                           8    8    8
1    1    1                             1    1
vector([- 1, - 1, 2], [-, - -, - -]), vector([- 1, 0, - 2], [- -, - -, 0]),
4    8    8                             4    8
1    1                                 1
vector([- 1, 0, - 1], [- -, - -, 0]), vector([- 1, 0, 0], [0, - -, 0]),
8    8                                 8
1    1                            1    1
vector([- 1, 0, 1], [-, - -, 0]), vector([- 1, 0, 2], [-, - -, 0]),
8    8                            4    8
1    1  1                             1    1  1
vector([- 1, 1, - 2], [- -, - -, -]), vector([- 1, 1, - 1], [- -, - -, -]),
4    8  8                             8    8  8
1  1                         1    1  1
vector([- 1, 1, 0], [0, - -, -]), vector([- 1, 1, 1], [-, - -, -]),
8  8                         8    8  8
1    1  1                             1    1  1
vector([- 1, 1, 2], [-, - -, -]), vector([- 1, 2, - 2], [- -, - -, -]),
4    8  8                             4    8  4
1    1  1                              1  1
vector([- 1, 2, - 1], [- -, - -, -]), vector([- 1, 2, 0], [0, - -, -]),
8    8  4                              8  4
1    1  1                         1    1  1
vector([- 1, 2, 1], [-, - -, -]), vector([- 1, 2, 2], [-, - -, -]),
8    8  4                         4    8  4
1       1                             1       1
vector([0, - 2, - 2], [- -, 0, - -]), vector([0, - 2, - 1], [- -, 0, - -]),
4       4                             8       4
1                         1       1
vector([0, - 2, 0], [0, 0, - -]), vector([0, - 2, 1], [-, 0, - -]),
4                         8       4
1       1                             1       1
vector([0, - 2, 2], [-, 0, - -]), vector([0, - 1, - 2], [- -, 0, - -]),
4       4                             4       8
1       1                                 1
vector([0, - 1, - 1], [- -, 0, - -]), vector([0, - 1, 0], [0, 0, - -]),
8       8                                 8
1       1                         1       1
vector([0, - 1, 1], [-, 0, - -]), vector([0, - 1, 2], [-, 0, - -]),
8       8                         4       8
1                                 1
vector([0, 0, - 2], [- -, 0, 0]), vector([0, 0, - 1], [- -, 0, 0]),
4                                 8
1
vector([0, 0, 0], [0, 0, 0]), vector([0, 0, 1], [-, 0, 0]),
8
1                                 1     1
vector([0, 0, 2], [-, 0, 0]), vector([0, 1, - 2], [- -, 0, -]),
4                                 4     8
1     1                             1
vector([0, 1, - 1], [- -, 0, -]), vector([0, 1, 0], [0, 0, -]),
8     8                             8
1     1                       1     1
vector([0, 1, 1], [-, 0, -]), vector([0, 1, 2], [-, 0, -]),
8     8                       4     8
1     1                           1     1
vector([0, 2, - 2], [- -, 0, -]), vector([0, 2, - 1], [- -, 0, -]),
4     4                           8     4
1                       1     1
vector([0, 2, 0], [0, 0, -]), vector([0, 2, 1], [-, 0, -]),
4                       8     4
1     1                             1  1    1
vector([0, 2, 2], [-, 0, -]), vector([1, - 2, - 2], [- -, -, - -]),
4     4                             4  8    4
1  1    1                            1    1
vector([1, - 2, - 1], [- -, -, - -]), vector([1, - 2, 0], [0, -, - -]),
8  8    4                            8    4
1  1    1                         1  1    1
vector([1, - 2, 1], [-, -, - -]), vector([1, - 2, 2], [-, -, - -]),
8  8    4                         4  8    4
1  1    1                             1  1    1
vector([1, - 1, - 2], [- -, -, - -]), vector([1, - 1, - 1], [- -, -, - -]),
4  8    8                             8  8    8
1    1                         1  1    1
vector([1, - 1, 0], [0, -, - -]), vector([1, - 1, 1], [-, -, - -]),
8    8                         8  8    8
1  1    1                           1  1
vector([1, - 1, 2], [-, -, - -]), vector([1, 0, - 2], [- -, -, 0]),
4  8    8                           4  8
1  1                             1
vector([1, 0, - 1], [- -, -, 0]), vector([1, 0, 0], [0, -, 0]),
8  8                             8
1  1                          1  1
vector([1, 0, 1], [-, -, 0]), vector([1, 0, 2], [-, -, 0]),
8  8                          4  8
1  1  1                           1  1  1
vector([1, 1, - 2], [- -, -, -]), vector([1, 1, - 1], [- -, -, -]),
4  8  8                           8  8  8
1  1                       1  1  1
vector([1, 1, 0], [0, -, -]), vector([1, 1, 1], [-, -, -]),
8  8                       8  8  8
1  1  1                           1  1  1
vector([1, 1, 2], [-, -, -]), vector([1, 2, - 2], [- -, -, -]),
4  8  8                           4  8  4
1  1  1                          1  1
vector([1, 2, - 1], [- -, -, -]), vector([1, 2, 0], [0, -, -]),
8  8  4                          8  4
1  1  1                       1  1  1
vector([1, 2, 1], [-, -, -]), vector([1, 2, 2], [-, -, -]),
8  8  4                       4  8  4
1  1    1                             1  1    1
vector([2, - 2, - 2], [- -, -, - -]), vector([2, - 2, - 1], [- -, -, - -]),
4  4    4                             8  4    4
1    1                         1  1    1
vector([2, - 2, 0], [0, -, - -]), vector([2, - 2, 1], [-, -, - -]),
4    4                         8  4    4
1  1    1                             1  1    1
vector([2, - 2, 2], [-, -, - -]), vector([2, - 1, - 2], [- -, -, - -]),
4  4    4                             4  4    8
1  1    1                            1    1
vector([2, - 1, - 1], [- -, -, - -]), vector([2, - 1, 0], [0, -, - -]),
8  4    8                            4    8
1  1    1                         1  1    1
vector([2, - 1, 1], [-, -, - -]), vector([2, - 1, 2], [-, -, - -]),
8  4    8                         4  4    8
1  1                              1  1
vector([2, 0, - 2], [- -, -, 0]), vector([2, 0, - 1], [- -, -, 0]),
4  4                              8  4
1                          1  1
vector([2, 0, 0], [0, -, 0]), vector([2, 0, 1], [-, -, 0]),
4                          8  4
1  1                              1  1  1
vector([2, 0, 2], [-, -, 0]), vector([2, 1, - 2], [- -, -, -]),
4  4                              4  4  8
1  1  1                          1  1
vector([2, 1, - 1], [- -, -, -]), vector([2, 1, 0], [0, -, -]),
8  4  8                          4  8
1  1  1                       1  1  1
vector([2, 1, 1], [-, -, -]), vector([2, 1, 2], [-, -, -]),
8  4  8                       4  4  8
1  1  1                           1  1  1
vector([2, 2, - 2], [- -, -, -]), vector([2, 2, - 1], [- -, -, -]),
4  4  4                           8  4  4
1  1                       1  1  1
vector([2, 2, 0], [0, -, -]), vector([2, 2, 1], [-, -, -]),
4  4                       8  4  4
1  1  1
vector([2, 2, 2], [-, -, -]))
4  4  4
(%i6) ```
Run Example
```load ("scifac") ;
(%o1)      /usr/share/maxima/5.21.1/share/simplification/scifac.lisp
(%o2) /usr/share/maxima/5.21.1/share/contrib/integration/abs_integrate.mac
(%o3)         /usr/share/maxima/5.21.1/share/calculus/fourie.mac
(%i4) nc_factor(e):= block([opsubst: true],  subst(lambda([[L]], apply(nc_factor_aux, L)), "+", e));
(%o4) nc_factor(e) := block([opsubst : true],
subst(lambda([[L]], apply(nc_factor_aux, L)), "+", e))
(%i5) dotassoc  : false;
(%o5)                                false
(%i6) dotdistrib: false;
(%o6)                                false
(%i7) dot2tic_tac(e):= block([inflag: true],  if safe_op(e)#"." then error("op(e) shoule be '.'"),  if length(e)#2 then error("the number of arguments should be 2"),  funmake('tic, [first(e)])*funmake('tac, [second(e)]));
(%o7) dot2tic_tac(e) := block([inflag : true],
if safe_op(e) # "." then error("op(e) shoule be '.'"),
if length(e) # 2 then error("the number of arguments should be 2"),
funmake('tic, [first(e)]) funmake('tac, [second(e)]))
(%i8) tic_tacify(e):= block([op: safe_op(e), inflag: true, seen_dot: false, prederror: true],  if op="." then dot2tic_tac(e)  else if op="*" then map(lambda([el],      if not seen_dot and op="." then (seen_dot: true, dot2tic_tac(el)) else el), e)  else e);
(%o8) tic_tacify(e) := block([op : safe_op(e), inflag : true,
seen_dot : false, prederror : true], if op = "." then dot2tic_tac(e)
else (if op = "*" then map(lambda([el],
if (not seen_dot) and (op = ".") then (seen_dot : true, dot2tic_tac(el))
else el), e) else e))
(%i9) ntic_or_ntac(e):= is(not funp('tic, e) or not funp('tac, e));
(%o9)  ntic_or_ntac(e) := is((not funp('tic, e)) or (not funp('tac, e)))
(%i10) de_tic_tacify_aux(e):= block([fst: 1, scn: 1, rst: 1, inflag: true, prederror: true],  for el in e do (if funp('tic, el) then fst: remfun('tic, el)    else if funp('tac, el) then scn: remfun('tac, el)    else rst: rst*el),  rst*(fst . scn));
(%o10) de_tic_tacify_aux(e) := block([fst : 1, scn : 1, rst : 1,
inflag : true, prederror : true], for el in e do if funp('tic, el)
then fst : remfun('tic, el) else (if funp('tac, el)
then scn : remfun('tac, el) else rst : rst el), rst (fst . scn))
(%i11) de_tic_tacify(e):= block([inflag: true, prederror: true, op: safe_op(e)],  if op="*" and every(ntic_or_ntac, args(e)) then de_tic_tacify_aux(e)  else if op#false then map('de_tic_tacify, e)  else e);
(%o11) de_tic_tacify(e) := block([inflag : true, prederror : true,
op : safe_op(e)], if (op = "*") and every(ntic_or_ntac, args(e))
then de_tic_tacify_aux(e) else (if op # false then map('de_tic_tacify, e)
else e))
(%i12) nc_factor_aux([L]):= block([M, op],  M: map('tic_tacify, L),  M: factorsum(factor(apply("+", M))),  de_tic_tacify(M));
(%o12) nc_factor_aux([L]) := block([M, op], M : map('tic_tacify, L),
M : factorsum(factor(apply("+", M))), de_tic_tacify(M))