Sponsored links: Algebra eBooks
 

Related

tcontract

? tcontract;

Calculate

tcontract

? tcontract;

Calculate

tcontract

Run Example
(%i1)tcontract(a^2+b^2,[a,b]);
resolvante 
generale 
 
NOTE: To compile the system do 
load("sym/compile"); 
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
                                       2
(%o1)                                 a
(%i2) 
Run Example
v1:x1+2*x2+3*x3;
(%o1)                          3 x3 + 2 x2 + x1
(%i2) v2:x2+2*x3+3*x1;
(%o2)                          2 x3 + x2 + 3 x1
(%i3) v3:x3+2*x1+3*x2;
(%o3)                          x3 + 3 x2 + 2 x1
(%i4) v4:x1+2*x3+3*x2;
(%o4)                          2 x3 + 3 x2 + x1
(%i5) v5:x2+2*x1+3*x3;
(%o5)                          3 x3 + x2 + 2 x1
(%i6) v6:x3+2*x2+3*x1;
(%o6)                          x3 + 2 x2 + 3 x1
(%i7) g:(v-v1)*(v-v2)*(v-v3)*(v-v4)*(v-v5)*(v-v6);
(%o7) (- 3 x3 - 2 x2 - x1 + v) (- 3 x3 - x2 - 2 x1 + v)
 (- 2 x3 - 3 x2 - x1 + v) (- 2 x3 - x2 - 3 x1 + v) (- x3 - 3 x2 - 2 x1 + v)
 (- x3 - 2 x2 - 3 x1 + v)
(%i8) e:expand(g);
           6            5            5           5         2   4
(%o8) 36 x3  + 288 x2 x3  + 288 x1 x3  - 132 v x3  + 863 x2  x3
                4              4         2   4              4        2   4
 + 1802 x1 x2 x3  - 828 v x2 x3  + 863 x1  x3  - 828 v x1 x3  + 193 v  x3
          3   3             2   3            2   3          2      3
 + 1226 x2  x3  + 4030 x1 x2  x3  - 1860 v x2  x3  + 4030 x1  x2 x3
                  3        2      3          3   3            2   3
 - 3888 v x1 x2 x3  + 910 v  x2 x3  + 1226 x1  x3  - 1860 v x1  x3
        2      3        3   3         4   2             3   2            3   2
 + 910 v  x1 x3  - 144 v  x3  + 863 x2  x3  + 4030 x1 x2  x3  - 1860 v x2  x3
          2   2   2               2   2         2   2   2          3      2
 + 6378 x1  x2  x3  - 6156 v x1 x2  x3  + 1443 v  x2  x3  + 4030 x1  x2 x3
            2      2         2         2        3      2         4   2
 - 6156 v x1  x2 x3  + 3024 v  x1 x2 x3  - 480 v  x2 x3  + 863 x1  x3
            3   2         2   2   2        3      2       4   2         5
 - 1860 v x1  x3  + 1443 v  x1  x3  - 480 v  x1 x3  + 58 v  x3  + 288 x2  x3
             4              4             2   3                  3
 + 1802 x1 x2  x3 - 828 v x2  x3 + 4030 x1  x2  x3 - 3888 v x1 x2  x3
        2   3             3   2               2   2            2      2
 + 910 v  x2  x3 + 4030 x1  x2  x3 - 6156 v x1  x2  x3 + 3024 v  x1 x2  x3
        3   2             4                  3               2   2
 - 480 v  x2  x3 + 1802 x1  x2 x3 - 3888 v x1  x2 x3 + 3024 v  x1  x2 x3
         3                 4               5              4           2   3
 - 1008 v  x1 x2 x3 + 122 v  x2 x3 + 288 x1  x3 - 828 v x1  x3 + 910 v  x1  x3
        3   2           4             5           6            5           5
 - 480 v  x1  x3 + 122 v  x1 x3 - 12 v  x3 + 36 x2  + 288 x1 x2  - 132 v x2
         2   4              4        2   4          3   3            2   3
 + 863 x1  x2  - 828 v x1 x2  + 193 v  x2  + 1226 x1  x2  - 1860 v x1  x2
        2      3        3   3         4   2            3   2         2   2   2
 + 910 v  x1 x2  - 144 v  x2  + 863 x1  x2  - 1860 v x1  x2  + 1443 v  x1  x2
        3      2       4   2         5              4           2   3
 - 480 v  x1 x2  + 58 v  x2  + 288 x1  x2 - 828 v x1  x2 + 910 v  x1  x2
        3   2           4             5           6           5        2   4
 - 480 v  x1  x2 + 122 v  x1 x2 - 12 v  x2 + 36 x1  - 132 v x1  + 193 v  x1
        3   3       4   2       5       6
 - 144 v  x1  + 58 v  x1  - 12 v  x1 + v
(%i9) ee:elem([3],tcontract(e,[x1,x2,x3]),[x1,x2,x3]);
resolvante 
generale 
 
NOTE: To compile the system do 
load("sym/compile"); 
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
       6             5           4
(%o9) v  + e1 (- 12 v  + e1 (58 v  + e1
         3            2
 (- 144 v  + e1 (193 v  + e1 (36 e1 - 132 v) + 252 e2) + e2 (- 696 v - 36 e1)
                      2
 - 176 e3) + e2 (717 v  - e1 (36 e1 - 132 v) + 611 e2) + e3 (528 v + 36 e1))
              3            2
 + e2 (- 336 v  - e1 (193 v  + e1 (36 e1 - 132 v) + 252 e2) - 1860 e2 v
 - e2 (- 696 v - 36 e1) + 2117 e3) + e3
             2                    2
 (- 2 (1443 v  + 1226 e2) + 2307 v  + e1 (36 e1 - 132 v) - 611 e2))
                4              3            2
 + e2 (- 2 (58 v  + e1 (- 144 v  + e1 (193 v  + e1 (36 e1 - 132 v) + 252 e2)
                                             2
 + e2 (- 696 v - 36 e1) - 176 e3) + e2 (717 v  - e1 (36 e1 - 132 v) + 611 e2)
                              4             2
 + e3 (528 v + 36 e1)) + 122 v  + e2 (1443 v  + 1226 e2) - 2436 e3 v)
               3             3            2
 + e3 (- 1008 v  - 3 (- 336 v  - e1 (193 v  + e1 (36 e1 - 132 v) + 252 e2)
 - 1860 e2 v - e2 (- 696 v - 36 e1) + 2117 e3) + 6378 e3)
(%i10) ex:expand(ee);
        6          5         4        2  4             3         3  3
(%o10) v  - 12 e1 v  + 6 e2 v  + 58 e1  v  - 48 e1 e2 v  - 144 e1  v
       2  2         2     2         4  2           2           3
 + 9 e2  v  + 138 e1  e2 v  + 193 e1  v  - 36 e1 e2  v - 168 e1  e2 v
         5          2                     3          3        2   2        4
 - 132 e1  v + 27 e3  - 18 e1 e2 e3 + 4 e1  e3 + 4 e2  + 35 e1  e2  + 72 e1  e2
        6
 + 36 e1
(%i11) ex,e1=0,e2=1,e3=1;
                              6      4      2
(%o11)                       v  + 6 v  + 9 v  + 31
(%i12) 
Run Example
tcontract(a^24+b^24,[a,b]);
resolvante 
generale 
 
NOTE: To compile the system do 
load("sym/compile"); 
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
                                       24
(%o1)                                 a
(%i2) 

Related Help

Help for Tcontract