Eliminate

A system of linear equations:

A system of polynomial equations:

Eliminate two variables:

A system of equations involving radicals:

A system of transcendental equations:

A system of modular equations:

By default, Eliminate uses inverse functions but prints warning messages:

With InverseFunctions->True, Eliminate does not print inverse function messages:

With InverseFunctions->False, Eliminate does not use inverse functions:

Eliminating variables from algebraic equations does not require using inverse functions:

Find a modulus for which a system of equations has a solution and eliminate a variable:

By default, Eliminate computes with exact coefficients:

This performs the elimination using 20-digit approximate number coefficients:

Rewrite in terms of and :

Find a condition for two polynomials to have a common root:

This solves the same problem using Resolve:

The condition is equivalent to Resultant of the polynomials being zero:

Equations returned by Eliminate do not contain the elimination variables:

Equations returned by Eliminate are implied by the input equations:

Use Resolve to check this property:

Use Resolve to eliminate an existential quantifier:

Eliminate gives the same set of equations, but does not give inequations:

Eliminate a variable using GroebnerBasis:

Eliminate a variable from a pair of polynomials using Resultant:

Use Reduce to eliminate an existential quantifier and solve the resulting system:

When the input contains only equations, Eliminate returns only equations:

The zero set of the result is the Zariski closure of the projection of the zero set of eqns:

Use Resolve to get a result with zero set equal to the projection of the zero set of eqns:

When the input contains inequations, Eliminate returns equations and inequations:

The zero set of the result is equal to the projection of the zero set of eqin: