Shape constructors and scalars

• Vector (itemSchema itemCount -- vectorSchema): builds one vector schema as one unnamed fixed-size combined value.
• Matrix (itemSchema columnCount rowCount -- matrixSchema): builds one matrix schema as a fixed-size vector of fixed-size row vectors.
• vector?, matrix?, getColCount, and getRowCount: vector and matrix shape queries.
• E, E64, PI, and PI64: scalar constants.
• acos, asin, atan, atan2, exp, tan, and cosSin: scalar trigonometric and exponential helpers.

Shape compatibility

• Elementwise vector operations such as +, -, multiply, divide, and vector equality require vectors of the same size.
• dot requires two vectors of the same size.
• cross requires two 3-item vectors.
• * supports scalar-vector, vector-scalar, vector-matrix, and matrix-matrix multiplication.
• Vector-matrix multiplication requires the vector size to equal the matrix row count.
• Matrix-matrix multiplication requires the left matrix column count to equal the right matrix row count.
• The vector-vector overload of * is invalid. The corresponding operations are dot, cross, and multiply.
• trans converts one vector to a one-column matrix and swaps matrix rows and columns.
• | concatenates matrices vertically when their column counts match, and one overload appends a same-width vector as one additional row.
• & concatenates vectors directly or concatenates matrices row-wise when their row counts match.
• det, adj, and inv require square matrices. The module provides determinant and adjugate formulas for sizes 1 through 4.

Value operations

• =: compares equal-size vectors item by item. One additional overload compares one vector with one one-row matrix of equal width.
• lerp: linear interpolation between two same-shaped numeric values with one blend factor.
• + and -: elementwise vector addition and subtraction for equal-size vectors.
• *: scalar-vector multiplication, vector-scalar multiplication, vector-matrix multiplication, and matrix-matrix multiplication.
• /: divides every vector item by one scalar.
• multiply: Hadamard product of equal-size vectors.
• divide: elementwise division of equal-size vectors.
• neg: negates every vector item.
• cast: casts every vector item to the target vector item schema.
• |: concatenates matrices vertically or appends one vector as one additional row.
• &: concatenates vectors or concatenates matrix rows horizontally.
• trans: transposes a matrix or converts a vector to a one-column matrix.

Vector-only operations

• angle: polar angle of a 2-item vector.
• toColumn: converts one vector to a one-column matrix.
• dot: scalar dot product of equal-size vectors.
• cross: cross product of two 3-item vectors.
• squaredLength: squared Euclidean length.
• length: Euclidean length.
• unit: normalized vector.
• unitChecked: normalized vector with a short-length fallback to the first basis vector.

Matrix-only operations

• rotationMatrix: builds a 2×2 rotation matrix from one Real32 angle.
• det: determinant for square matrices of sizes 1, 2, 3, and 4.
• adj: adjugate for square matrices of sizes 1, 2, 3, and 4.
• inv: inverse of a square matrix through adj / det.

Examples

Vector addition and dot product

"algebra" use
"control" use

{} () {} [
  v: (1i32 2i32 3i32);
  w: (4i32 5i32 6i32);
  v w + printStack _:;
  v w dot printStack _:;
] "main" exportFunction

Expected Output During Compilation

(5 7 9)
32

Matrix determinant

"algebra" use
"control" use

{} () {} [
  m: ((1i32 2i32) (3i32 4i32));
  m det printStack _:;
] "main" exportFunction

Expected Output During Compilation

-2

Runtime vector check

"algebra" use
"String" use
"control" use

{} Int32 {} [
  v: (1i32 2i32 3i32);
  w: (4i32 5i32 6i32);
  sum: v w +;
  expected: (5i32 7i32 9i32);
  sum expected = print
  LF print
  v w dot 32 same print
  LF print
  0
] "main" exportFunction

Expected Output

TRUE
TRUE

See also

• Quaternion: Quaternion construction, normalization, interpolation, and matrix conversion.
• Pose: Rigid-transform helpers over position vectors and quaternions.