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# brackets [,;]

Concatenation. Recipients of an assignment. Results of a function

### Syntax

Mh = [m11 m12 m13.. m1N] or [m11, m12, m13,.., m1N] Mv = [m11 ; m21 ; m31..; mN1] M = [m11, m12,...; m21, m22,...;...] [r1, r2,...] = func(...) [r1, r2,.., rN] = (e1, e2, .., eN) [r1, r2,.., rk] = (e1, e2, .., ek,.., eN) [r1, r2,.., rN] = mylist(:) [r1, r2,.., rN] = S.field([i1 i2.. iN])

### Arguments

- m11, m12,...
Set of objects to be concatenated (and merged: the former individual containers are removed). The following subsets of types of objects can be mixed in-between, but are mutually exclusive:

- Matrices of booleans, reals, complex numbers,
polynomials, rationals: The data type of the
concatenated result is set by the rules defined below
(see the
*type conversions*rules). - Matrices of encoded integers of any
inttype.
Encoded integers of different inttypes can't be concatenated together.
- Arrays of structures with same fields. Fields may be in different orders from an array to other ones.
- Typed lists of type syslin.

- Matrices of booleans, reals, complex numbers,
polynomials, rationals: The data type of the
concatenated result is set by the rules defined below
(see the
- M, Mh, Mv
Matrices with the type of all

`m##`

(if they all have the same data type)- e1, e2,..
Input objects (literals like

`-1.23`

or`"abcd"`

, variables, or expressions like`a+%pi`

, etc).- mylist
a simple list

- S.field
Array of Structures with a field named

`field`

.- i1, i2,..
Indices of components selected from

`S`

.- r1, r2,...
Output variables

### Description

- [] on right-hand side: concatenators
[..] bundle their contents of simple and compatible types into a homogeneous vector, matrix or hypermatrix.

An horizontal or a vertical concatenation is a binary iterated operator. It is performed step-by-step from left-to-right, and from top-to-bottom. Thus,`[1 3 5 7]`

is performed as`[[[1 3] 5] 7]`

.Inside brackets,

- spaces (blanks or tabs) or commas are
used as columns separators.
Using commas instead of spaces is safer. For instance,
`[2 1 +%i]`

means`[2, 1, %i]`

, while`[2 1 + %i]`

means`[2, 1+%i]`

- semi-colons or carriage-return are used
as rows separators. Multiple rows do not need
the continuation dots
`..`

##### Types conversions

In some limits, brackets may be applied on a set of data having different but compatible types. In this case, some data are converted into the dominating type available in the set. The main conversion rules are the following:

- boolean < decimal number < complex
- decimal number < polynomial < rational
booleans and polynomials are not compatible.
`[%t 2. %z]`

is accepted:`[%t 2.]`

is first converted into`[1. 2.]`

, and then`[[1. 2.] %z]`

is accepted.`[%z %t 2.]`

is rejected and yields an error. Indeed,`[%z %t]`

can't be converted first.

- The result becomes complex-encoded as soon as
a complex-encoded component -- value, polynomial,
or rational -- is met in the list
(even with a null imaginary part)
Similarly, the result becomes sparse-encoded as soon as a sparse-encoded component is met and processed.

- It is possible to concatenate polynomials or/and
rationals having different variable names. Then,
the first polynomial or rational met in the list
sets the variable name to the concatenation result:
`[%z, 1+%s, 1-%i*%s] // => [z, 1+z, 1-iz]`

. - Any encoded integer can be concatenated
only with integers of the same inttype.
Thus, the expressions
`[%t int8(2)]`

,`[int8(2) uint8(7)]`

,`[int8(2) int16(7)]`

,`[int8(2) 1.]`

will all yield an error. - Text components can be concatenated
(in the set meaning, with brackets) only with other
text components or with the empty matrix.
`[]`

.

##### Overloading

- [,]: horizontal concatenation:
This operator is binary and automatically
iterated from left to right. Its overloading
code is
`"c"`

. - [;]: vertical concatenation:
This operator is binary and automatically
iterated from top to bottom. Its overloading
code is
`"f"`

.

- spaces (blanks or tabs) or commas are
used as columns separators.
- [] on left-hand side of a
`"="`

assignment In this case, brackets are no longer concatenators. They are used as left and right delimiters of a series of variables used as recipients.

- Recipients must be variables. Litteral expressions are not accepted.
- Variables shall be separated with comas.
- In a distributive assignment, there must
be at most as many LHS recipients
as output sources, not more. If there are less
recipients on the left than sources on the right,
non-collected data sources are ignored. Examples :
`[a,b]=(%pi,"Hi", %z)`

is OK, but`%z`

is ignored.`[a,b,c]=(%pi,"Hi")`

yields an error because`c`

expects some foods.

- The same variable may be used several times
in the list. Then, multiple assignments are done from
*right to left (!)*and overwrite the previous ones. Example :`[a,b,a] = (%pi, %z, "Allo")`

is equivalent to`a = %pi, b = %z`

.

### Examples

// Horizontal concatenations a = [ %pi 4 -1 ] b1 = grand(3,4,"uin",0,10) b2 = grand(3,2,"uin",0,10) b = [b1 b2] // they must have the same number of rows // Vertical concatenations a = [-2 ; 10 ; 7] b1 = grand(2,4,"uin",0,10) b2 = grand(3,4,"uin",0,10) b = [b1 ; b2] // they must have the same number of columns // Mixed horizontal and vertical concatenations a = [ 3 7 ; 6, 5 ] b = [ 1:3 ; 7:3:13] c = [ a b ; a b] d = [ 3 5 1 4 ] e = [ d d d d d d ] // Concatenation of various types of data: ['this is' ; 'a column' ; 'of texts'] s = poly(0,'s');[1/s,2/s] [tf2ss(1/s),tf2ss(2/s)] [%t %f %f %T %F] // Heterogeneous concatenations with automatical types conversions [%T %pi %f 2] [%pi, 2+%i, %F] v = [%pi+0*%i, %F, %z, (1-%z)^2 ]; typeof(v), isreal(v) v = [10 1/%z], typeof(v) // Incompatible heterogeneous concatenations => ERRORS [%F %z] [%F int8(5)] [int8(%pi) uint8(%e)] [int8(%pi) int16(%e)]

**Distributive assignments:**

// Output from a function. Most often, output results are serially optional: M = rand(3,3); [u, s] = schur(M) // we expect and use both results u and s u = schur(M) // we expect and store only the first result u // Direct RHS list [a, b, c] = (%pi, %t, "test") [a, b] = (%e, %f, "Hello") [a, b, a] = (%pi, %t, "test"); // Explicit RHS list L = list(%z, %i, %t, %pi, "Text"); [a, b, c] = L(:) // RHS structure s(2,3).r = %pi; s(2,1).r = %i; s(2,2) = %e; s(2,:).r s.r([2 4 6]) [a, b, c] = s.r([2 4 6]) // Forbidden / Rejected LHS expressions (=> error) [m, n, m+n] = myfun(a,b) // Symbolic expressions like "m+n" are forbidden [p, 4.5, q] = myfun(a,b) // Literal LHS values or expressions like "4.5" are forbidden [r, s+3 ] = myfun(a,b) // Expressions mixing literals and symbols like "s+3" can't be LHS recipients

--> [a, b, c] = (%pi, %t, "test") c = test b = T a = 3.1415927 --> [a, b] = (%e, %f, "Hello") b = F a = 2.7182818 --> [a, b, a] = (%pi, %t, "test"); a a = 3.1415927

### See also

- empty — ([]) empty matrix
- parentheses — ( ) left and right parenthesis
- lstcat — list concatenation
- comma — (,) comma; instruction, argument separator
- semicolon — (;) ending expression and row separator
- overloading — display, functions and operators overloading capabilities

### History

Version | Description |

6.0 | Brackets `[..]` and braces
`{..}` are no longer equivalent |

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