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 Documentation / Mathematica / Built-in Functions / Algebraic Computation / Equation Solving  /
SolveAlways

  • SolveAlways[ eqns , vars ] gives the values of parameters that make the equations eqns valid for all values of the variables vars.
  • 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.
  • Example: SolveAlways[a x + b == 0, x].
  • 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.
  • SolveAlways[ eqns , vars ] is equivalent to Solve[!Eliminate[! eqns , vars ]].
  • See the Mathematica book: Section 3.4.10.
  • See also: Eliminate, Solve, Reduce, PolynomialReduce.

    Further Examples

    Here is a simple example.

    In[1]:=

    Out[1]=

    This fails because it involves transcendentals.

    In[2]:=

    SolveAlways::ifun: Inverse functions are being used by SolveAlways, so some solutions may not be found.

    Out[2]=

    This is how to make it work.

    In[3]:=

    Out[3]=

    We check the result.

    In[4]:=

    Out[4]=

    In[5]:=