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Options

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Options[f] gives the list of default option rules for the symbol f.

Options[expr] gives the options explicitly set in an expression such as a graphics object. Options[obj, name] gives the setting for the named option; Options[obj, {names}] gives a list of settings. Assign to Options[f] to redefine all default options at once.

Examples (3)

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

Basic examples (3)

In[1]:= Options[LinearSolve]
Out[1]= {Method -> Automatic, Modulus -> 0, ZeroTest -> Automatic}

In[2]:= Options[f] = {a -> 1, b -> 2}; f[OptionsPattern[]] := {OptionValue[a], OptionValue[b]} {f[], f[a -> 17], f[b -> 18], f[a -> 17, b -> 18]}

In[3]:= SetOptions[f, c -> 3] SetOptions::optnf: c is not a known option for f. AppendTo[Options[f], c -> 3]
Out[3]= Optional[{SetOptions::optnf (a -> 1), SetOptions::optnf (b -> 2), SetOptions::optnf (c -> 3)}, a c Dot[f, {a -> 1, b -> 2, c -> 3}] for is known not option]

Algorithm

options_builtin.c — Options, SetOptions, OptionValue and the registry of default option settings for option-accepting builtins.

Mathilda stores a symbol's default options as a List[Rule[name, val], ...] on SymbolDef.default_options (the DefaultValues-equivalent), reached through symtab_set_options / symtab_get_options. This file implements:

  Options[...]      query a symbol's defaults or an expression's explicit
                    options, optionally selected by name.
  SetOptions[...]   redefine individual default options of a symbol.
  OptionValue[...]  resolve a single option value from explicit options plus
                    defaults; the bare/2-arg forms are resolved inside a rule
                    by optionvalue_inject_context (see apply_down_values).
  options_register_defaults  the comprehensive table wired from core_init.

Memory: every result is freshly built. Sub-expressions taken from res or from the stored options are duplicated with expr_copy (a refcount bump), so nothing aliased is mutated in place and the evaluator remains free to release

`res` after a builtin returns.

Implementation notes

  • Options, SetOptions, and OptionValue all have attribute {Protected}.
  • Default options survive Clear[f] (only rules are cleared) and are removed with the symbol by Remove[f].
  • The registered defaults mirror the options each builtin's evaluator actually honors, with the value it falls back to when the option is absent. The sweep covers, among others: Integrate (Method), Limit (Direction, Assumptions), Series/PowerExpand (Assumptions), D/Dt (NonConstants), Sum/Product (Method), Simplify/FullSimplify (Assumptions, ComplexityFunction, TransformationFunctions), GroebnerBasis (MonomialOrder -> Lexicographic, CoefficientDomain -> Rationals, Method, Sort, Modulus), Factor/Together/Cancel/Apart and the Polynomial* family (Extension, Modulus), IrreduciblePolynomialQ /SquareFreeQ (GaussianIntegers, ...), the eigen/linear-algebra heads (Eigenvalues/Eigenvectors → Cubics, Quartics; LinearSolve, LeastSquares, NullSpace, MatrixRank, PseudoInverse, SingularValueDecomposition), PrimeQ/CoprimeQ/FactorInteger (GaussianIntegers), the Random* heads (WorkingPrecision), the numerical calculus/root-finding heads (NIntegrate, NSum, NProduct, NLimit, ND, NSeries, NResidue, FindRoot, FindMinimum, FindMaximum, NRoots, NSolve, Solve, Fit), Plot, and the structural family that reads Heads (Cases/Count/DeleteCases/MemberQ/Map/Apply/MapAll/Level /Depth/LeafCount default Heads -> False; Position/FreeQ default Heads -> True).

Attributes: Protected.

References

See also: SetOptions, OptionValue, Set, Hold, Integrate, Limit, Series, PowerExpand