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numeric::indets

Search for indeterminates

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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.

See Also

MuPAD Functions

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