# Example 090 — Matrix multiplication `matrix_multiplication.eml` multiplies a 2x3 matrix by a 3x2 matrix, producing the 2x2 product `[[58, 64], [139, 154]]`. ## EML ```eml # Self-authored for the EML case corpus (no external origin). Multiplies # two matrices by hand with the standard triple-nested loop over # lists-of-lists — no numpy, no ``/`^T` matrix overlays (which transpile # to numpy calls the browser interpreter defers on). Pairs with # examples/matrix-transpose-manual/ as the corpus's second hand-rolled # 2D-array case, and is the first to chain two subscripts (`a[i][k]`). def multiply(a, b): len(a) => rows_a len(b) => rows_b len(b[0]) => cols_b result^+[] 0 => i while i < rows_a: row^+[] 0 => j while j < cols_b: 0 => total 0 => k while k < rows_b: total + a[i][k] * b[k][j] => total k + 1 => k row + [total] => row j + 1 => j result + [row] => result i + 1 => i return result matrix_a^+[[1, 2, 3], [4, 5, 6]] matrix_b^+[[7, 8], [9, 10], [11, 12]] multiply(matrix_a, matrix_b) => product "A (2x3): " + str(matrix_a) => msg1 msg1^0 "B (3x2): " + str(matrix_b) => msg2 msg2^0 "A x B (2x2): " + str(product) => msg3 msg3^0 ``` ## Python (deterministic transpilation) ```python def multiply(a, b): rows_a = len(a) rows_b = len(b) cols_b = len(b[0]) result = [] i = 0 while i < rows_a: row = [] j = 0 while j < cols_b: total = 0 k = 0 while k < rows_b: total = total + a[i][k] * b[k][j] k = k + 1 row = row + [total] j = j + 1 result = result + [row] i = i + 1 return result matrix_a = [[1, 2, 3], [4, 5, 6]] matrix_b = [[7, 8], [9, 10], [11, 12]] product = multiply(matrix_a, matrix_b) msg1 = "A (2x3): " + str(matrix_a) print(msg1) msg2 = "B (3x2): " + str(matrix_b) print(msg2) msg3 = "A x B (2x2): " + str(product) print(msg3) ``` ## stdout (executed) ```text A (2x3): [[1, 2, 3], [4, 5, 6]] B (3x2): [[7, 8], [9, 10], [11, 12]] A x B (2x2): [[58, 64], [139, 154]] ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:def · eml:assign · eml:call · eml:return · eml:output · eml:run:done