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length -- the ``length'' of a MuPAD object (heuristic complexity)

Introduction

length(object) returns an integer indicating the complexity of the object.

Call(s)

length(object)

Parameters

object - an arbitrary MuPAD object

Returns

a nonnegative integer.

Related Functions

nops, op

Details

Example 1

Intuitively, the length measures the complexity of an object:

>> length(1 + x) < length(x^3 + exp(a - b)/ln(45 - t) - 1234*I)
                                  3 < 25

Example 2

We compute the lengths of some simple objects:

>> length(1.2), length(-1234.5), length(123456), length(-123456)
                                1, 1, 6, 6
>> length(17), length(123), length(17/123) 
                                  2, 3, 6
>> length(12), length(123), length(12 + 123*I) 
                                  2, 3, 6
>> length(x), length(x^2), length(x^12345)
                                  1, 3, 7
>> length("123"), length("")
                                   3, 0
>> length(x), length(a_long_name)
                                   1, 1

Example 3

The length of an array is the sum of the lengths of all its elements plus 1:

>> A := array(1..2, [x, y]): length(A) = length(x) + length(y) + 1
                                   3 = 3
>> A[1] := 12345: length(A) = length(12345) + length(y) + 1
                                   7 = 7
>> delete A:

Example 4

The operands of a table are the equations associating indices and entries. The length of each operand is the length of the index plus the length of the corresponding entry plus 1:

>> T[1] := 45: T
                                 table(
                                   1 = 45
                                 )
>> length(T) = length(1 = 45) + 1
                                   5 = 5
>> delete T:

Changes




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