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InverseFunctions

Status: Experimental

present and registered, but lightly documented and not yet covered by dedicated tests.

Description

InverseFunctions is an option for Solve that enables the inverse-function specialist for elementary invertible heads (Log, Exp, Sin, Cos, Tan, ArcSin, ArcCos, Sinh, ..., and integer Power). Default: Automatic (enabled). Setting it to False disables the specialist; equations that can only be solved through inversion then return unevaluated.

Examples (3)

Every input below was run against the current Mathilda build and its output recorded.

Applications (3)

In[1]:= Solve[Sin[x] == 1/2, x]
Out[1]= {{x -> ConditionalExpression[2 C[1] Pi + 5/6 Pi, Element[C[1], Integers]]}, {x -> ConditionalExpression[2 C[1] Pi + 1/6 Pi, Element[C[1], Integers]]}}

In[2]:= Solve[Sin[x] == 1/2, x, InverseFunctions -> False]
Out[2]= Solve[Sin[x] == 1/2, x, InverseFunctions -> False]

In[3]:= Solve[Exp[x] == 5, x]
Out[3]= {{x -> ConditionalExpression[Log[5] + (2*I) C[1] Pi, Element[C[1], Integers]]}}

Implementation notes

InverseFunctions is an option symbol for Solve, not a callable function. It is interned in sym_names.c and documented in solve.c; it has no builtin handler. solve.c's option parser recognises InverseFunctions -> spec: the default Automatic (and any value other than False) leaves the enabled flag set in the solver state (solveinv.h), while InverseFunctions -> False disables it. When enabled, Solve is allowed to "peel" invertible heads (Exp, Log, trig, powers) off an equation by applying their inverse function ā€” the work is done by the inverse-function specialist registered as Solve`SolveInverseFunctions in solveinv.c. The symbol is consumed only as a configuration key.

Attributes: none registered.

References

Notes & additional examples

Notes

InverseFunctions is a Solve option (default Automatic, i.e. enabled) that controls the inverse-function specialist for invertible heads such as Sin, Log, Exp, and integer Power. With it on, Sin[x] == 1/2 is inverted to the full periodic solution set; setting InverseFunctions -> False disables the specialist, so the equation is returned unevaluated.