numeric::indets

Search for indeterminates

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

```numeric::indets(`object`)
```

Description

`numeric::indets(object)` returns a set of the indeterminates contained in the `object`.

This is an auxiliary routine used by `numeric::polyroots`, `numeric::quadrature`, `numeric::realroots`, `numeric::solve` etc. to find indeterminates.

It recursively searches the operands of `object` for indeterminates. In particular, the search is applied to the elements of lists, sets, arrays, tables, etc.

Following objects are regarded as indeterminates: identifiers, indexed identifiers and the indeterminates of `DOM_POLY` objects. Also coefficients of such polynomials are searched for indeterminates.

The following objects are not regarded as indeterminates: the numerical constants PI, EULER, and CATALAN (cf. `Type::ConstantIdents`) and zero operands of expressions and subexpressions (i.e., the function names in unevaluated function calls such as `f(2)`, `sin(PI/13)` etc.). Also integration variables in unevaluated calls of `int`, `numeric::int` and `numeric::quadrature` and summation indices in unevaluated calls of `sum` and `numeric::sum` are not considered.

Examples

Example 1

Identifiers and indexed identifiers are regarded as indeterminates:

```numeric::indets([{a + b*PI}, sin(c + sqrt(2) + EULER), table(1 = d - cos(e), 2 = f + 0.1*I), array(1..2, [g, h]), F(i[2], i[2]), D([1], G)(j[1]), k[3 + L[4]]])```

Both indeterminates as well as symbolic coefficients are considered in polynomials of domain type `DOM_POLY`:

`numeric::indets(poly(a[1]*x^2 + a[2]*x +a, [x, y]))`

Example 2

The zero operands of unevaluated function calls such as `f(…)` or `sin(…)` are not regarded as indeterminates:

`numeric::indets(f(a + sin(b) + PI + EULER))`

Integration variables and summation indices are not regarded as indeterminates:

```numeric::indets({int(f(x), x = a..b), sum(f(i), i = c..infinity)})```

Parameters

 `object` An arbitrary MuPAD® object

Return Values

Set of indeterminates is returned, if the argument is an object of some basic data type of the kernel. The empty set is returned, if the object is from some library domain.