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GeneratedParameters

Status: Experimental

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

Description

GeneratedParameters is an option for Solve specifying the
    head used for fresh integer-parameter symbols introduced by
    the inverse-function specialist.  Default: C, giving
    C[1], C[2], ...  Only the bare-symbol form is honoured;
    the Function form is reserved.

Examples

No verified examples yet for this function.

Implementation notes

GeneratedParameters is an option symbol for Solve, not a callable function. It is interned in sym_names.c and given a docstring in solve.c; it has no builtin handler. solve.c's option parser recognises GeneratedParameters -> head and stores the (interned) head string in the solver state's param_head field (declared in solveinv.h, default "C"). When Solve returns a parameterised family (e.g. integer-multiple solutions of a trig equation), the inverse-function specialist (solveinv.c) emits the free parameters as head[k] — so GeneratedParameters -> C produces C[1], C[2], … This is purely a configuration key consulted during solving.

Attributes: none registered.

Implementation status

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

References

Notes & additional examples

Worked examples

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

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

In[1]:= Solve[Sin[x] == 0, x, GeneratedParameters -> n]
Out[1]= {{x -> ConditionalExpression[Pi + 2 Pi n[1], Element[n[1], Integers]]}, {x -> ConditionalExpression[2 Pi n[1], Element[n[1], Integers]]}}

Notes

GeneratedParameters is a Solve option that names the head used for the fresh integer-parameter symbols the inverse-function solver introduces for equations with infinitely many solutions. The default C produces C[1], C[2], ...; here GeneratedParameters -> K switches them to K[1]. The same indexed parameter labels every branch of a periodic solution set: Solve[Sin[x] == 0, x, GeneratedParameters -> n] returns the two families 2 Pi n[1] and Pi + 2 Pi n[1], each carrying its own Element[n[1], Integers] constraint.