Eliminate variables

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groebner::eliminate(sys, vars)


groebner::eliminate(sys, vars) returns a list of polynomial expressions obtained by eliminating the elements of vars from sys. In other words, the return value does not contain the variables in vars, every zero of the original system sys must be a zero of the return value, and every tuple of numbers that makes the return value zero can be extended to a solution of sys.


Example 1

Suppose that x2 + y = 0 and x + y = 0, what does this imply for y?

groebner::eliminate({x^2 +y, y+x}, {x})

We infer that for every pair (x, y) solving the system, y must satisfy y2 + y = 0, that is, y = 0 or y = - 1. Indeed:

solve({x^2 +y, y+x}, {x, y})



A set or list of polynomial expressions. The coefficients in these polynomial expressions can be arbitrary arithmetical expressions.


A set or list of identifiers

Return Values

List of polynomial expressions


groebner::eliminate proceeds by computing a lexical-order Gröbner basis. Hence the computation complexity grows fast when increasing the number of variables.

See Also

MuPAD Functions