math/add

Element-wise addition

Usage

Y:=math/add(X1, X2)

Performs element-wise addition of two numeric inputs. X1 and X2 may be scalars, vectors, or matrices. When one input is a scalar and the other is an array, the scalar is added to every element of the array (scalar broadcasting). When adding a vector to a matrix, the vector may be broadcast across rows or columns as described in Details.

Input

Argument	Kind	Description
`X1`	`int`, `uint`, `float`, `rational`, `complex`, `[T]`, `[[T]]`	First addend. Supports element-wise addition for scalars, vectors, and matrices.
`X2`	`int`, `uint`, `float`, `rational`, `complex`, `[T]`, `[[T]]`	Second addend. Must be shape-compatible with `X1` under the broadcasting rules.

Supported scalar types (matched and mixed where defined): i8, i16, i32, i64, i128, u8, u16, u32, u64, u128, f32, f64, rational (R64), and complex (C64).

Output

Argument	Kind	Description
`Y`	matches input	Element-wise sum of `X1` and `X2`. The shape of `Y` follows broadcasting.

Examples

Add two scalars

y:=math/add(2, 5)

Add two vectors (same length)

x1:=[

1

2

3

]x2:=[

4

5

6

]

Add two matrices (same shape)

a:=[

1 3

2 4

]b:=[

5 7

6 8

]

Add a scalar to a matrix (scalar broadcasting)

a:=[

1 3

2 4

]

Add a column vector to a matrix (broadcast by columns)

v:=[

10

20

]--

length 2 column vector

m:=[

1 3

2 4

]--

2x2

Add a row vector to a matrix (broadcast by rows)

r:=[

100

200

]--

row vector of length 2

m:=[

1 3

2 4

]--

2x2

Mixed types (float + int)

y:=math/add(2.5, 2)--

4.5

Complex addition

y:=math/add(1+2i, 3+-4i)--

(4 - 2i)

Details

Element-wise semantics. Addition is applied per element. Shapes must either match exactly or be compatible via broadcasting.

Broadcasting rules. The function supports these efficient broadcast cases:

Scalar + Array: The scalar is added to every element of the array.
Matrix + Column Vector (or Vector + Matrix): A length-m column vector can be added to an m×n matrix by adding the vector to each column of the matrix.
Matrix + Row Vector (or Row Vector + Matrix): A length-n row vector can be added to an m×n matrix by adding the vector to each row of the matrix.

Commutative & associative. math/add is commutative (X1 + X2 = X2 + X1) and associative where types and shapes allow.

Type support. Implementations exist for signed/unsigned integers, floating-point, rationals, and complex numbers. When types differ, standard numeric promotions apply where defined by the runtime; otherwise a type error is raised.

Errors.

Shape mismatch that cannot be resolved by broadcasting.
Unsupported type combination.