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jacobian

f(x,y):=x^3-2*y^3+3*x^2;

jac:jacobian([f(x,y)]...

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jacobian

J:jacobian ([-y, x, -...

A:J.[z, w, -x, -y];

K:jacobian ([z, w, -x...

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jacobian-sqrt

A=jacobian ([-(l1+l2+...

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jacobian

jacobian([5*x1-5*y,1*...

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jacobian

f(x,y) := [x^2+y^2-1,...

j(x,y) := jacobian(f(...

j(x,y);

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jacobian-solve

solve([a1*x+b1*y=s1, ...

jacobian([x*(1+a1*x^2...

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jacobian

f(x,y,z,w) := [y/x/(x...

jacobian (f(x,y,z,w),...

jacobian (f(x,y,z,w),...

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jacobian

jacobian ([ASIN(SIN(l...

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jacobian-sin

jacobian ([x*x*y, 5*x...

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jacobian

jacobian ([x + t*v], ...

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jacobian

Run Example
(%i1)jacobian([x*(1+a*(x*x+y*y) + b*(x*x+y*y)^2 + c*(x*x+y*y)^4 + d*(x*x+y*y)^6),y*(1+a*(x*x+y*y) + b*(x*x+y*y)^2 + c*(x*x+y*y)^4 + d*(x*x+y*y)^6) ],[x,y]);
                  2    2 6               2    2 5           2    2 3
(%o1) matrix([d (y  + x )  + x (12 d x (y  + x )  + 8 c x (y  + x )
           2    2                 2    2 4       2    2 2       2    2
 + 4 b x (y  + x ) + 2 a x) + c (y  + x )  + b (y  + x )  + a (y  + x ) + 1, 
            2    2 5           2    2 3           2    2
x (12 d y (y  + x )  + 8 c y (y  + x )  + 4 b y (y  + x ) + 2 a y)], 
             2    2 5           2    2 3           2    2
[y (12 d x (y  + x )  + 8 c x (y  + x )  + 4 b x (y  + x ) + 2 a x), 
    2    2 6               2    2 5           2    2 3           2    2
d (y  + x )  + y (12 d y (y  + x )  + 8 c y (y  + x )  + 4 b y (y  + x )
                2    2 4       2    2 2       2    2
 + 2 a y) + c (y  + x )  + b (y  + x )  + a (y  + x ) + 1])
(%i2) 
Run Example
f(x,y)=x-5*y;
(%o1)                          f(x, y) = x - 5 y
(%i2) g(x,y)=1*x-10*y;
(%o2)                         g(x, y) = x - 10 y
(%i3) a=jacobian([-5*x1^2+14*x1*x2+3*x1*x3-14*x2^2-25*x2*x3+5*x2*x4-30*x3^2+40*x3*x4-55*x4^2,4*x1*x2+3*x1*x3+x2^2,-4320*x1^4+22870*x1^3*x2-1190*x1^3*x3+12505*x1^3*x4-55135*x1^2*x2^2-51622*x1^2*x2*x3-14433*x1^2*x2*x4-83488*x1^2*x3^2+116232*x1^2*x3*x4-64404*x1^2*x4^2+66945*x1*x2^3+161185*x1*x2^2*x3-51296*x1*x2^2*x4+290771*x1*x2*x3^2-427012*x1*x2*x3*x4+169055*x1*x2*x4^2+79312*x1*x3^3-163575*x1*x3^2*x4+35815*x1*x3*x4^2-32875*x1*x4^3-34680*x2^4-146618*x2^3*x3+62329*x2^3*x4-335882*x2^2*x3^2+386700*x2^2*x3*x4-170625*x2^2*x4^2-277030*x2*x3^3+404945*x2*x3^2*x4-487365*x2*x3*x4^2+259760*x2*x4^3-125370*x3^4+325485*x3^3*x4-975395*x3^2*x4^2+1231350*x3*x4^3-727200*x4^4],[x1,x2,x3,x4]);
(%o3) a = matrix([3 x3 + 14 x2 - 10 x1, 5 x4 - 25 x3 - 28 x2 + 14 x1, 
40 x4 - 60 x3 - 25 x2 + 3 x1, - 110 x4 + 40 x3 + 5 x2], 
                                                3              2
[3 x3 + 4 x2, 2 x2 + 4 x1, 3 x1, 0], [- 32875 x4  + 35815 x3 x4
               2               2            2
 + 169055 x2 x4  - 128808 x1 x4  - 163575 x3  x4 - 427012 x2 x3 x4
                             2                               2              3
 + 232464 x1 x3 x4 - 51296 x2  x4 - 28866 x1 x2 x4 + 37515 x1  x4 + 79312 x3
               2               2            2
 + 290771 x2 x3  - 166976 x1 x3  + 161185 x2  x3 - 103244 x1 x2 x3
          2              3               2           2              3
 - 3570 x1  x3 + 66945 x2  - 110270 x1 x2  + 68610 x1  x2 - 17280 x1 , 
         3               2               2               2            2
259760 x4  - 487365 x3 x4  - 341250 x2 x4  + 169055 x1 x4  + 404945 x3  x4
                                                2
 + 773400 x2 x3 x4 - 427012 x1 x3 x4 + 186987 x2  x4 - 102592 x1 x2 x4
           2               3               2               2            2
 - 14433 x1  x4 - 277030 x3  - 671764 x2 x3  + 290771 x1 x3  - 439854 x2  x3
                             2               3               2            2
 + 322370 x1 x2 x3 - 51622 x1  x3 - 138720 x2  + 200835 x1 x2  - 110270 x1  x2
           3            3                2               2              2
 + 22870 x1 , 1231350 x4  - 1950790 x3 x4  - 487365 x2 x4  + 35815 x1 x4
            2                                                   2
 + 976455 x3  x4 + 809890 x2 x3 x4 - 327150 x1 x3 x4 + 386700 x2  x4
                              2               3               2               2
 - 427012 x1 x2 x4 + 116232 x1  x4 - 501480 x3  - 831090 x2 x3  + 237936 x1 x3
            2                                 2               3               2
 - 671764 x2  x3 + 581542 x1 x2 x3 - 166976 x1  x3 - 146618 x2  + 161185 x1 x2
           2             3              3                2               2
 - 51622 x1  x2 - 1190 x1 , - 2908800 x4  + 3694050 x3 x4  + 779280 x2 x4
              2             2
 - 98625 x1 x4  - 1950790 x3  x4 - 974730 x2 x3 x4 + 71630 x1 x3 x4
            2                                 2               3               2
 - 341250 x2  x4 + 338110 x1 x2 x4 - 128808 x1  x4 + 325485 x3  + 404945 x2 x3
               2            2                                 2              3
 - 163575 x1 x3  + 386700 x2  x3 - 427012 x1 x2 x3 + 116232 x1  x3 + 62329 x2
              2           2              3
 - 51296 x1 x2  - 14433 x1  x2 + 12505 x1 ])
(%i4) determinant(a);
(%o4)                           determinant(a)
(%i5) 
Run Example
jacobian ([x^2+y-4-z^2, x*y^2+sin(z), e^z+z-3*y], [x, y, z]);
                         [ 2 x    1        - 2 z     ]
                         [                           ]
                         [  2                        ]
(%o1)                    [ y    2 x y     cos(z)     ]
                         [                           ]
                         [              z            ]
                         [  0    - 3   e  log(e) + 1 ]
(%i2) 

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