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SolveAlways

SolveAlways
gives 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 :
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A univariate polynomial equation:
A multivariate polynomial equation:
A list of polynomial equations:
An equation involving radicals:
An inequation:
Boolean combinations of equations and inequations:
By default, SolveAlways finds exact solutions:
This computes the solutions using 20-digit numbers:
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:
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