1> p =[3 -7 2 0 1 -1 1];


2> p(2)
ans = -7


3> p(3)
ans =  2


4> % per trovare il valore del polinomio p(x) per x = 2 si scrive polyval(p,2)


4> polyval(p,2)
ans =  3


5> p =[3 -7 2 0 -1 1];


6> polyval(p,2)
ans = -1


7> q=[3 -1 0 0 -1];


8> p/q
error: operator /: nonconformant arguments (op1 is 1x6, op2 is 1x5)


8> pd=[15 -28 6 0 -1];  % la derivata del polinomio p


9> polyval(pd,2)
ans =  39


10> polyval(q,2)
ans =  39


11> % p'(2) = q(2), dove p(x) = q(x)(x-2)+p(2), ne deriva: p'(2)=q'(2)(2-2) +q(2)


11> polyder(p)
ans =

   15  -28    6    0   -1



12> polyint(pd) % l'integrale di pd(x)
ans =

   3  -7   2   0  -1   0



13> % polyder(p) per calcolare la derivata di un polinomio, 
% polyint(p) per calcolare l'integrale di p


13> conv(p,q)
ans =

    9  -24   13   -2   -6   11   -3    0    1   -1



14> % per calcolare (x-1)^7 si possono scrivere i polinomi x-1 e moltiplicarli tra loro con il comando conv


14> p1 = [1 -1];


15> p2=conv(p1,p1)
p2 =
   1  -2   1



16> p3=conv(p2,p1)
p3 =

   1  -3   3  -1



17> % facendo un ciclo si calcola in maniera piu' veloce e comoda 


17> f=p1;


18> for k=1:6 f=conv(f,p1); end


19> f
f =

    1   -7   21  -35   35  -21    7   -1



20> quit

%%%%%%%%%%%%%%%%%%%%% pausa %%%%%%%%%%%%%%%%%%%%%


1> 0^0
ans =  1


2> % si costruisce il Triangolo di Tartaglia con Octave


2> f1=[1]
f1 =  1


3> f2=[1 1];


4> f=f1;


5> for k=1:7 f=conv(f,f2) end
f =

   1   1

f =

   1   2   1

f =

   1   3   3   1

f =

   1   4   6   4   1

f =

    1    5   10   10    5    1

f =

    1    6   15   20   15    6    1

f =

    1    7   21   35   35   21    7    1



6> f
f =

    1    7   21   35   35   21    7    1



7> for k=1:8 f=conv(f,f2); end


8> f
f =

 Columns 1 through 11:

      1     15    105    455   1365   3003   5005   6435   6435   5005   3003

 Columns 12 through 16:

   1365    455    105     15      1



9> for k=1:8 f=conv(f,f2) end
f =

 Columns 1 through 9:

       1      16     120     560    1820    4368    8008   11440   12870

 Columns 10 through 17:

   11440    8008    4368    1820     560     120      16       1

f =

 Columns 1 through 9:

       1      17     136     680    2380    6188   12376   19448   24310

 Columns 10 through 18:

   24310   19448   12376    6188    2380     680     136      17       1

f =

 Columns 1 through 9:

       1      18     153     816    3060    8568   18564   31824   43758

 Columns 10 through 18:

   48620   43758   31824   18564    8568    3060     816     153      18

 Column 19:

       1

f =

 Columns 1 through 9:

       1      19     171     969    3876   11628   27132   50388   75582

 Columns 10 through 18:

   92378   92378   75582   50388   27132   11628    3876     969     171

 Columns 19 and 20:

      19       1

f =

 Columns 1 through 8:

        1       20      190     1140     4845    15504    38760    77520

 Columns 9 through 16:

   125970   167960   184756   167960   125970    77520    38760    15504

 Columns 17 through 21:

     4845     1140      190       20        1

f =

 Columns 1 through 8:

        1       21      210     1330     5985    20349    54264   116280

 Columns 9 through 16:

   203490   293930   352716   352716   293930   203490   116280    54264

 Columns 17 through 22:

    20349     5985     1330      210       21        1

f =

 Columns 1 through 8:

        1       22      231     1540     7315    26334    74613   170544

 Columns 9 through 16:

   319770   497420   646646   705432   646646   497420   319770   170544

 Columns 17 through 23:

    74613    26334     7315     1540      231       22        1

f =

 Columns 1 through 7:

         1        23       253      1771      8855     33649    100947

 Columns 8 through 14:

    245157    490314    817190   1144066   1352078   1352078   1144066

 Columns 15 through 21:

    817190    490314    245157    100947     33649      8855      1771

 Columns 22 through 24:

       253        23         1



10> clear f


11> f1=[1]
f1 =  1


12> f2=[1 1];


13> f=f1;


14> for k=1:8 f=conv(f,f2); end


15> f
f =

    1    8   28   56   70   56   28    8    1



16> quit