6.12.22 Eliminating one or more variables from a list of equations: eliminate
The eliminate command eliminates variables from a list of
equations.
-
eliminate takes two arguments:
-
eqns, a list of equations.
- vars, the variable or list of variables to eliminate.
The equations can be given as expressions, in which case they will be
assumed to be 0.
- eliminate(eqns,vars)
returns the equations with the variables vars eliminated or
an indication that Xcas can’t eliminate them.
Examples.
Assuming the variables used haven’t been set to any values:
-
Input:
eliminate([x = v0*t, y = y0-g*t^2], t)
Output:
- Input:
eliminate([x+y+z+t-2,x*y*t=1,x^2+t^2=z^2],[x,z])
Output:
| ⎡
⎣ | 2 t2 y2−4 t2 y+t y3−4 t y2+4 t y+2 t+2 y−4 | ⎤
⎦ |
If the variable(s) can’t be eliminated, then eliminate
returns [1] or [-1]. If eliminate returns
[], that means the equations determine the values of the
variables to be eliminated.
Examples.
-
Input:
x:=2;y:=-5 |
eliminate([x=2*t,y=1-10*t^2],t)
|
Output:
since t cannot be eliminated from both equations.
- Input:
x:=2;y:=-9 |
eliminate([x=2*t,y=1-10*t^2],t)
|
Output:
since the first equation gives t=1, which satisfies the
second equation.
- Input:
x:= 2; y:= -9 |
eliminate([x = 2*t, y = 1-10*t^2, z = x + y - t], t)
|
Output:
since the first equation gives t=1, which satisfies the
second equation, and so that leaves z = 2 - 9 - 1 = -8, or
z + 8 = 0.