8.1.17 Eliminating one or more variables from a list of equations
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 cannot eliminate them.
Examples
Assuming the variables used haven’t been set to any values:
eliminate([x=v0*t,y=y0-g*t^2], t) |
eliminate([x+y+z+t-2,x*y*t=1,x^2+t^2=z^2],[x,z]) |
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| ⎡
⎣ | 2 t2 y2−4 t2 y+t y3−4 t y2+4 t y+2 t+2 y−4 | ⎤
⎦ |
| | | | | | | | | | |
|
If the variable(s) cannot be eliminated, then eliminate
returns [1] or [-1]. If eliminate returns
an empty list, that means the equations determine the values of the
variables to be eliminated.
x:=2;y:=-5
eliminate([x=2*t,y=1-10*t^2],t) |
since t cannot be eliminated from both equations.
x:=2;y:=-9
eliminate([x=2*t,y=1-10*t^2],t) |
since the first equation gives t=1, which satisfies the
second equation.
x:=2; y:=-9
eliminate([x=2*t,y=1-10*t^2,z=x+y-t],t) |
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.