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euler

euler(21);

Calculate

euler

euler(12);

Calculate

euler

euler (50);

Calculate

euler

euler(12);

Calculate

euler

Run Example
(%i1)euler (50);
(%o1)      - 6053285248188621896314383785111649088103498225146815121
(%i2) 
Run Example
a:matrix([a,b],[c,d]);
                                   [ a  b ]
(%o1)                              [      ]
                                   [ c  d ]
(%i2) b:matrix([3,0],[0,8]);
                                   [ 3  0 ]
(%o2)                              [      ]
                                   [ 0  8 ]
(%i3) mod((a.b.a^(-1))^totient(7),7);
      [          8 b     6  6     6            6  8 b   3 a 6  6     6  6  ]
      [     mod((--- + 3)  c , 7 c )      mod(b  (--- + ---)  d , 7 b  d ) ]
      [           c                                d     b                 ]
      [     ------------------------      -------------------------------- ]
      [                 6                               6  6               ]
      [                c                               b  d                ]
(%o3) [                                                                    ]
      [      6  6  8 d   3 c 6     6  6            6  3 c     6     6      ]
      [ mod(a  c  (--- + ---) , 7 a  c )      mod(b  (--- + 8) , 7 b )     ]
      [             c     a                            b                   ]
      [ --------------------------------      ------------------------     ]
      [               6  6                                6                ]
      [              a  c                                b                 ]
(%i4) determinant(a);
(%o4)                              a d - b c
(%i5)  euler(7);
(%o5)                                  0
(%i6) 
Run Example
u:a*x^2+2*h*y+b*y^2;
                                 2              2
(%o1)                         b y  + 2 h y + a x
(%i2) ux:diff(u,x);
(%o2)                                2 a x
(%i3) uy:diff(u,y);
(%o3)                             2 b y + 2 h
(%i4) euler:x*ux+y*uy;
                                                  2
(%o4)                      y (2 b y + 2 h) + 2 a x
(%i5) eulersimply:ratsimp(euler);
                                 2                2
(%o5)                       2 b y  + 2 h y + 2 a x
(%i6) fact:factorial(eulersimply);
                                2                2
(%o6)                     (2 b y  + 2 h y + 2 a x )!
(%i7) is(equal(fact,2*u));
(%o7)                               unknown
(%i8) 

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