This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SolveAlways

 SolveAlwaysgives the values of parameters that make the equations eqns valid for all values of the variables vars.
• Equations are given in the form .
• Simultaneous equations can be combined either in a list or with .
• A single variable or a list of variables can be specified.
• SolveAlways works primarily with linear and polynomial equations.
• SolveAlways produces relations between parameters that appear in eqns, but are not in the list of variables vars.
Find a condition for the equation to hold for any value of :
Find a condition for the equation to hold for any value of :
 Out[1]=
 Scope   (6)
A univariate polynomial equation:
A multivariate polynomial equation:
A list of polynomial equations:
An inequation:
Boolean combinations of equations and inequations:
 Options   (1)
By default, SolveAlways finds exact solutions:
This computes the solutions using 20-digit numbers:
 Applications   (2)
Find a condition for a cubic polynomial to have a triple root:
This solves the same problem using Reduce:
The same problem can also be solved using Subresultants and Solve:
Solve for undetermined coefficients in the series expansion:
Numeric solutions make the equations identically true:
An equivalent formulation using Solve and Eliminate:
An equivalent formulation using Solve and Resolve:
This solves the same problem using Reduce:
SolveAlways gives generic solutions:
The equations may not be identically true when parameters satisfy additional equations:
This finds conditions on parameters for which the solutions are not correct:
New in 1