### Related

array(T, 901);

array(N_c, 901);

array(N_v, 901);

Calculate

##### array

array (aa, 2, 3);

Calculate

##### array-block-float-listarray-plot2d-print-random

n : 1000;

array(Lx, flonum, n) ;

array(Ly, flonum, n) ;

Calculate

##### array-block-float-listarray-make_random_state-plot2d-print-set_random_state

s1: make_random_state...

set_random_state (s1) ;

n : 100;

Calculate

##### array-cos-float-round-sqrt

maxX:100;

maxY:100;

array(m1,flonum,maxX,...

Calculate

##### array-do-if-listarray-plot2d-sin

array([rs,rsy],float,5);

i:0;

n:100;

Calculate

##### array-expand-plot2d

p:[[4,3.5],[1.56,2.42...

n:6;

array (d, n, n);

Calculate

##### array-expand-plot2d

p:[[1.44,0.53],[1.52,...

n:6;

array (d, n, n);

Calculate

##### array-diff-kill-ratexpand-sum

kill(all);

array(c,11);

y:sum(c[n]*x^n,n,0,10);

Calculate

array(var,4);

var[0]:t;

var[1]:r;

Calculate

### array

Run Example
```(%i1)p:[[1.44,0.53],[1.52,2.21],[1,2],[2.15,1.8],[3,0.15],[4.5,2.25]];
(%o1) [[1.44, 0.53], [1.52, 2.21], [1, 2], [2.15, 1.8], [3, 0.15], [4.5, 2.25]]
(%i2) n:6;
(%o2)                                  6
(%i3) array (d, n, n);
(%o3)                                  d
(%i4) for j : 1 thru n do d[1, j] : p[j][2];
(%o4)                                done
(%i5) /* вычисление таблицы конечных разностей, верхнетреугольная часть таблицы */for i : 2 thru n do for j : 1 thru n+1-i do d[i, j] : (d[i-1,j+1]-d[i-1,j])/(p[j+i-1][1]-p[j][1]);
(%o5)                                done
(%i6) f(x):= d[1,1]+ d[2,1]*(x-p[1][1])+ d[3,1]*(x-p[1][1])*(x-p[2][1])+ d[4,1]*(x-p[1][1])*(x-p[2][1])*(x-p[3][1])+ d[5,1]*(x-p[1][1])*(x-p[2][1])*(x-p[3][1])*(x-p[4][1])+ d[6,1]*(x-p[1][1])*(x-p[2][1])*(x-p[3][1])*(x-p[4][1])*(x-p[5][1]);
(%o6) f(x) := d     + d     (x - (p ) ) + d     (x - (p ) ) (x - (p ) )
1, 1    2, 1        1       3, 1        1           2
1                   1           1
+ d     (x - (p ) ) (x - (p ) ) (x - (p ) )
4, 1        1           2           3
1           1           1
+ d     (x - (p ) ) (x - (p ) ) (x - (p ) ) (x - (p ) )
5, 1        1           2           3           4
1           1           1           1
+ d     (x - (p ) ) (x - (p ) ) (x - (p ) ) (x - (p ) ) (x - (p ) )
6, 1        1           2           3           4           5
1           1           1           1           1
(%i7) expand(f(x));
5                      4                     3
(%o7) - 14.01668789360094 x  + 170.7965444716648 x  - 779.022144765288 x
2
+ 1662.295773252168 x  - 1658.662754800805 x + 620.6092697358614
(%i8) plot2d([[discrete, p],f(x)], [x,0.7,3.2], [style, points, lines],  [color, red, blue], [point_type, asterisk],  [legend, "data", "approximation"], [xlabel, "x"], [ylabel, "y"]);
plotf(1.25);
(%o9)                         - 2.701440186481309
(%i10) ```
Run Example
```array(rs,1,5);
(%o1)                                 rs
(%i2) i:0;
(%o2)                                  0
(%i3) for x: 0 step 2*%pi/4 thru 2*%pi do (rs[0,i]:x, i:i+1);
(%o3)                                done
(%i4) array(arr,2,101);
(%o4)                                 arr
(%i5) i:0;
(%o5)                                  0
(%i6) for x: 0 step %pi/50 thru 2*%pi do (arr[0,i]:x, i:i+1);
(%o6)                                done
(%i7) for i:0 thru 100 do display(arr[0,i]);
arr     = 0
0, 0

%pi
arr     = ---
0, 1   50

%pi
arr     = ---
0, 2   25

3 %pi
arr     = -----
0, 3    50

2 %pi
arr     = -----
0, 4    25

%pi
arr     = ---
0, 5   10

3 %pi
arr     = -----
0, 6    25

7 %pi
arr     = -----
0, 7    50

4 %pi
arr     = -----
0, 8    25

9 %pi
arr     = -----
0, 9    50

%pi
arr      = ---
0, 10    5

11 %pi
arr      = ------
0, 11     50

6 %pi
arr      = -----
0, 12    25

13 %pi
arr      = ------
0, 13     50

7 %pi
arr      = -----
0, 14    25

3 %pi
arr      = -----
0, 15    10

8 %pi
arr      = -----
0, 16    25

17 %pi
arr      = ------
0, 17     50

9 %pi
arr      = -----
0, 18    25

19 %pi
arr      = ------
0, 19     50

2 %pi
arr      = -----
0, 20     5

21 %pi
arr      = ------
0, 21     50

11 %pi
arr      = ------
0, 22     25

23 %pi
arr      = ------
0, 23     50

12 %pi
arr      = ------
0, 24     25

%pi
arr      = ---
0, 25    2

13 %pi
arr      = ------
0, 26     25

27 %pi
arr      = ------
0, 27     50

14 %pi
arr      = ------
0, 28     25

29 %pi
arr      = ------
0, 29     50

3 %pi
arr      = -----
0, 30     5

31 %pi
arr      = ------
0, 31     50

16 %pi
arr      = ------
0, 32     25

33 %pi
arr      = ------
0, 33     50

17 %pi
arr      = ------
0, 34     25

7 %pi
arr      = -----
0, 35    10

18 %pi
arr      = ------
0, 36     25

37 %pi
arr      = ------
0, 37     50

19 %pi
arr      = ------
0, 38     25

39 %pi
arr      = ------
0, 39     50

4 %pi
arr      = -----
0, 40     5

41 %pi
arr      = ------
0, 41     50

21 %pi
arr      = ------
0, 42     25

43 %pi
arr      = ------
0, 43     50

22 %pi
arr      = ------
0, 44     25

9 %pi
arr      = -----
0, 45    10

23 %pi
arr      = ------
0, 46     25

47 %pi
arr      = ------
0, 47     50

24 %pi
arr      = ------
0, 48     25

49 %pi
arr      = ------
0, 49     50

arr      = %pi
0, 50

51 %pi
arr      = ------
0, 51     50

26 %pi
arr      = ------
0, 52     25

53 %pi
arr      = ------
0, 53     50

27 %pi
arr      = ------
0, 54     25

11 %pi
arr      = ------
0, 55     10

28 %pi
arr      = ------
0, 56     25

57 %pi
arr      = ------
0, 57     50

29 %pi
arr      = ------
0, 58     25

59 %pi
arr      = ------
0, 59     50

6 %pi
arr      = -----
0, 60     5

61 %pi
arr      = ------
0, 61     50

31 %pi
arr      = ------
0, 62     25

63 %pi
arr      = ------
0, 63     50

32 %pi
arr      = ------
0, 64     25

13 %pi
arr      = ------
0, 65     10

33 %pi
arr      = ------
0, 66     25

67 %pi
arr      = ------
0, 67     50

34 %pi
arr      = ------
0, 68     25

69 %pi
arr      = ------
0, 69     50

7 %pi
arr      = -----
0, 70     5

71 %pi
arr      = ------
0, 71     50

36 %pi
arr      = ------
0, 72     25

73 %pi
arr      = ------
0, 73     50

37 %pi
arr      = ------
0, 74     25

3 %pi
arr      = -----
0, 75     2

38 %pi
arr      = ------
0, 76     25

77 %pi
arr      = ------
0, 77     50

39 %pi
arr      = ------
0, 78     25

79 %pi
arr      = ------
0, 79     50

8 %pi
arr      = -----
0, 80     5

81 %pi
arr      = ------
0, 81     50

41 %pi
arr      = ------
0, 82     25

83 %pi
arr      = ------
0, 83     50

42 %pi
arr      = ------
0, 84     25

17 %pi
arr      = ------
0, 85     10

43 %pi
arr      = ------
0, 86     25

87 %pi
arr      = ------
0, 87     50

44 %pi
arr      = ------
0, 88     25

89 %pi
arr      = ------
0, 89     50

9 %pi
arr      = -----
0, 90     5

91 %pi
arr      = ------
0, 91     50

46 %pi
arr      = ------
0, 92     25

93 %pi
arr      = ------
0, 93     50

47 %pi
arr      = ------
0, 94     25

19 %pi
arr      = ------
0, 95     10

48 %pi
arr      = ------
0, 96     25

97 %pi
arr      = ------
0, 97     50

49 %pi
arr      = ------
0, 98     25

99 %pi
arr      = ------
0, 99     50

arr       = 2 %pi
0, 100

(%o7)                                done
(%i8) ```
Run Example
```kill(all);
(%o0)                                done
(%i1) array(c,11);
(%o1)                                  c
(%i2) y:sum(c[n]*x^n,n,0,10);
10       9       8       7       6       5       4       3       2
(%o2) c   x   + c  x  + c  x  + c  x  + c  x  + c  x  + c  x  + c  x  + c  x
10        9       8       7       6       5       4       3       2
+ c  x + c
1      0
(%i3) deq:(x^2-4)*diff(y,x,2)+3*x*diff(y,x,1)+y=0;
10                9         8         7         6         5
(%o3) c   x   + 3 x (10 c   x  + 9 c  x  + 8 c  x  + 7 c  x  + 6 c  x
10                10         9         8         7         6
4         3         2                      9
+ 5 c  x  + 4 c  x  + 3 c  x  + 2 c  x + c ) + c  x
5         4         3         2      1     9
2               8          7          6          5          4          3
+ (x  - 4) (90 c   x  + 72 c  x  + 56 c  x  + 42 c  x  + 30 c  x  + 20 c  x
10          9          8          7          6          5
2                        8       7       6       5       4       3
+ 12 c  x  + 6 c  x + 2 c ) + c  x  + c  x  + c  x  + c  x  + c  x  + c  x
4         3        2     8       7       6       5       4       3
2
+ c  x  + c  x + c  = 0
2       1      0
(%i4) ratexpand(deq);
10           9            8          8           7          7
(%o4) 121 c   x   + 100 c  x  - 360 c   x  + 81 c  x  - 288 c  x  + 64 c  x
10            9           10          8           9          7
6          6           5          5           4          4
- 224 c  x  + 49 c  x  - 168 c  x  + 36 c  x  - 120 c  x  + 25 c  x
8          6           7          5           6          4
3          3          2         2
- 80 c  x  + 16 c  x  - 48 c  x  + 9 c  x  - 24 c  x + 4 c  x - 8 c  + c  = 0
5          3          4         2          3        1        2    0
(%i5) eqn2:solve(%,x);
(%o5)                                 []
(%i6) eq1:-8*c[2]+c[0]=0;
(%o6)                            c  - 8 c  = 0
0      2
(%i7)  eq2:4*c[1]-24*c[3]=0;
(%o7)                          4 c  - 24 c  = 0
1       3
(%i8) eq3:9*c[2]-48*c[4]=0;
(%o8)                          9 c  - 48 c  = 0
2       4
(%i9) eq4:16*c[3]-80*c[5]=0;
(%o9)                          16 c  - 80 c  = 0
3       5
(%i10) eq5:25*c[4]-120*c[6]=0;
(%o10)                        25 c  - 120 c  = 0
4        6
(%i11) eq6:36*c[5]-168*c[7]=0;
(%o11)                        36 c  - 168 c  = 0
5        7
(%i12) eq7:49*c[6]-224*c[8]=0;
(%o12)                        49 c  - 224 c  = 0
6        8
(%i13) eq8:64*c[7]-288*c[9]=0;
(%o13)                        64 c  - 288 c  = 0
7        9
(%i14) eq9:81*c[8]-360*c[10]=0;
(%o14)                        81 c  - 360 c   = 0
8        10
(%i15) ```

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