eliminates variables between a set of simultaneous equations.
Details and Options
- Equations are given in the form lhs==rhs.
- Simultaneous equations can be combined either in a list or with &&.
- A single variable or a list of variables can be specified.
- Variables can be any expressions.
- Eliminate works primarily with linear and polynomial equations.
Examplesopen allclose all
Basic Examples (2)
By default, Eliminate uses inverse functions but prints warning messages:
By default, Eliminate computes with exact coefficients:
Properties & Relations (3)
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:
Possible Issues (1)
When the input contains only equations, Eliminate returns only equations:
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:
Wolfram Research (1988), Eliminate, Wolfram Language function, https://reference.wolfram.com/language/ref/Eliminate.html.
Wolfram Language. 1988. "Eliminate." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Eliminate.html.
Wolfram Language. (1988). Eliminate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Eliminate.html