Initial Query

Disassemble the following python into a function called foo: 2 0 LOAD_CONST 1 (16) 2 STORE_FAST 2 (PH) 4 4 LOAD_CONST 2 (0) 6 STORE_FAST 3 (extra) 5 8 LOAD_CONST 2 (0) 10 STORE_FAST 4 (col) 6 12 BUILD_LIST 0 14 STORE_FAST 5 (pivots) 8 16 LOAD_CONST 3 (<code object <listcomp> at 0x101093660, file "/private/tmp/a.py", line 8>) 18 LOAD_CONST 4 ('rref.<locals>.<listcomp>') 20 MAKE_FUNCTION 0 22 LOAD_GLOBAL 0 (range) 24 LOAD_FAST 0 (matrix) 26 LOAD_ATTR 1 (shape) 28 LOAD_CONST 2 (0) 30 BINARY_SUBSCR 32 CALL_FUNCTION 1 34 GET_ITER 36 CALL_FUNCTION 1 38 STORE_FAST 6 (used_for_row) 10 40 LOAD_FAST 0 (matrix) 42 LOAD_FAST 2 (PH) 44 BINARY_MODULO 46 STORE_FAST 0 (matrix) 11 >> 48 LOAD_FAST 4 (col) 50 LOAD_FAST 3 (extra) 52 BINARY_ADD 54 LOAD_FAST 0 (matrix) 56 LOAD_ATTR 1 (shape) 58 LOAD_CONST 5 (1) 60 BINARY_SUBSCR 62 LOAD_CONST 5 (1) 64 BINARY_SUBTRACT 66 COMPARE_OP 0 (<) 68 EXTENDED_ARG 2 70 POP_JUMP_IF_FALSE 628 72 LOAD_FAST 4 (col) 74 LOAD_FAST 0 (matrix) 76 LOAD_ATTR 1 (shape) 78 LOAD_CONST 2 (0) 80 BINARY_SUBSCR 82 COMPARE_OP 0 (<) 84 EXTENDED_ARG 2 86 POP_JUMP_IF_FALSE 628 13 88 LOAD_FAST 0 (matrix) 90 LOAD_FAST 4 (col) 92 LOAD_FAST 4 (col) 94 LOAD_FAST 3 (extra) 96 BINARY_ADD 98 BUILD_TUPLE 2 100 BINARY_SUBSCR 102 LOAD_CONST 2 (0) 104 COMPARE_OP 2 (==) 106 EXTENDED_ARG 1 108 POP_JUMP_IF_FALSE 262 14 110 LOAD_GLOBAL 2 (np) 112 LOAD_METHOD 3 (all) 114 LOAD_FAST 0 (matrix) 116 LOAD_CONST 0 (None) 118 LOAD_CONST 0 (None) 120 BUILD_SLICE 2 122 LOAD_FAST 4 (col) 124 BUILD_TUPLE 2 126 BINARY_SUBSCR 128 LOAD_CONST 2 (0) 130 COMPARE_OP 2 (==) 132 CALL_METHOD 1 134 POP_JUMP_IF_FALSE 146 15 136 LOAD_FAST 3 (extra) 138 LOAD_CONST 5 (1) 140 INPLACE_ADD 142 STORE_FAST 3 (extra) 16 144 JUMP_ABSOLUTE 48 17 >> 146 LOAD_GLOBAL 2 (np) 148 LOAD_METHOD 4 (argwhere) 150 LOAD_FAST 0 (matrix) 152 LOAD_CONST 0 (None) 154 LOAD_CONST 0 (None) 156 BUILD_SLICE 2 158 LOAD_FAST 4 (col) 160 LOAD_FAST 3 (extra) 162 BINARY_ADD 164 BUILD_TUPLE 2 166 BINARY_SUBSCR 168 LOAD_CONST 2 (0) 170 COMPARE_OP 3 (!=) 172 CALL_METHOD 1 174 LOAD_METHOD 5 (flatten) 176 CALL_METHOD 0 178 LOAD_CONST 6 (-1) 180 BINARY_SUBSCR 182 STORE_FAST 7 (other) 18 184 LOAD_FAST 7 (other) 186 LOAD_FAST 4 (col) 188 COMPARE_OP 0 (<) 190 POP_JUMP_IF_FALSE 202 19 192 LOAD_FAST 3 (extra) 194 LOAD_CONST 5 (1) 196 INPLACE_ADD 198 STORE_FAST 3 (extra) 20 200 JUMP_ABSOLUTE 48 22 >> 202 LOAD_GLOBAL 6 (list) 204 LOAD_FAST 0 (matrix) 206 LOAD_FAST 7 (other) 208 BINARY_SUBSCR 210 CALL_FUNCTION 1 212 LOAD_GLOBAL 6 (list) 214 LOAD_FAST 0 (matrix) 216 LOAD_FAST 4 (col) 218 BINARY_SUBSCR 220 CALL_FUNCTION 1 222 ROT_TWO 224 LOAD_FAST 0 (matrix) 226 LOAD_FAST 4 (col) 228 STORE_SUBSCR 230 LOAD_FAST 0 (matrix) 232 LOAD_FAST 7 (other) 234 STORE_SUBSCR 23 236 LOAD_FAST 6 (used_for_row) 238 LOAD_FAST 7 (other) 240 BINARY_SUBSCR 242 LOAD_FAST 6 (used_for_row) 244 LOAD_FAST 4 (col) 246 BINARY_SUBSCR 248 ROT_TWO 250 LOAD_FAST 6 (used_for_row) 252 LOAD_FAST 4 (col) 254 STORE_SUBSCR 256 LOAD_FAST 6 (used_for_row) 258 LOAD_FAST 7 (other) 260 STORE_SUBSCR 25 >> 262 LOAD_FAST 5 (pivots) 264 LOAD_METHOD 7 (append) 266 LOAD_FAST 4 (col) 268 LOAD_FAST 3 (extra) 270 BINARY_ADD 272 CALL_METHOD 1 274 POP_TOP 26 276 LOAD_FAST 0 (matrix) 278 LOAD_FAST 4 (col) 280 LOAD_FAST 4 (col) 282 LOAD_FAST 3 (extra) 284 BINARY_ADD 286 BUILD_TUPLE 2 288 BINARY_SUBSCR 290 STORE_FAST 8 (pivot) 27 292 LOAD_FAST 4 (col) 294 LOAD_FAST 3 (extra) 296 BINARY_ADD 298 LOAD_FAST 1 (graphlen) 300 COMPARE_OP 0 (<) 302 EXTENDED_ARG 1 304 POP_JUMP_IF_FALSE 348 28 306 LOAD_GLOBAL 2 (np) 308 LOAD_METHOD 8 (abs) 310 LOAD_FAST 8 (pivot) 312 CALL_METHOD 1 314 LOAD_CONST 5 (1) 316 COMPARE_OP 2 (==) 318 EXTENDED_ARG 1 320 POP_JUMP_IF_TRUE 396 322 LOAD_GLOBAL 2 (np) 324 LOAD_METHOD 8 (abs) 326 LOAD_FAST 8 (pivot) 328 CALL_METHOD 1 330 LOAD_FAST 2 (PH) 332 LOAD_CONST 5 (1) 334 BINARY_SUBTRACT 336 COMPARE_OP 2 (==) 338 EXTENDED_ARG 1 340 POP_JUMP_IF_TRUE 396 342 LOAD_ASSERTION_ERROR 344 RAISE_VARARGS 1 346 JUMP_FORWARD 48 (to 396) 30 >> 348 LOAD_GLOBAL 2 (np) 350 LOAD_METHOD 8 (abs) 352 LOAD_FAST 8 (pivot) 354 CALL_METHOD 1 356 LOAD_CONST 7 (2) 358 COMPARE_OP 2 (==) 360 EXTENDED_ARG 1 362 POP_JUMP_IF_TRUE 388 364 LOAD_GLOBAL 2 (np) 366 LOAD_METHOD 8 (abs) 368 LOAD_FAST 8 (pivot) 370 CALL_METHOD 1 372 LOAD_FAST 2 (PH) 374 LOAD_CONST 7 (2) 376 BINARY_SUBTRACT 378 COMPARE_OP 2 (==) 380 EXTENDED_ARG 1 382 POP_JUMP_IF_TRUE 388 384 LOAD_ASSERTION_ERROR 386 RAISE_VARARGS 1 31 >> 388 LOAD_FAST 8 (pivot) 390 LOAD_CONST 7 (2) 392 INPLACE_FLOOR_DIVIDE 394 STORE_FAST 8 (pivot) 32 >> 396 LOAD_FAST 0 (matrix) 398 LOAD_FAST 4 (col) 400 DUP_TOP_TWO 402 BINARY_SUBSCR 404 LOAD_FAST 8 (pivot) 406 INPLACE_MULTIPLY 408 ROT_THREE 410 STORE_SUBSCR 33 412 LOAD_FAST 0 (matrix) 414 LOAD_FAST 4 (col) 416 DUP_TOP_TWO 418 BINARY_SUBSCR 420 LOAD_FAST 2 (PH) 422 INPLACE_MODULO 424 ROT_THREE 426 STORE_SUBSCR 35 428 LOAD_GLOBAL 2 (np) 430 LOAD_METHOD 4 (argwhere) 432 LOAD_FAST 0 (matrix) 434 LOAD_CONST 0 (None) 436 LOAD_CONST 0 (None) 438 BUILD_SLICE 2 440 LOAD_FAST 4 (col) 442 LOAD_FAST 3 (extra) 444 BINARY_ADD 446 BUILD_TUPLE 2 448 BINARY_SUBSCR 450 CALL_METHOD 1 452 LOAD_METHOD 5 (flatten) 454 CALL_METHOD 0 456 STORE_FAST 9 (others) 37 458 LOAD_FAST 9 (others) 460 GET_ITER >> 462 FOR_ITER 154 (to 618) 464 STORE_FAST 10 (i) 38 466 LOAD_FAST 10 (i) 468 LOAD_FAST 4 (col) 470 COMPARE_OP 2 (==) 472 EXTENDED_ARG 1 474 POP_JUMP_IF_FALSE 480 476 EXTENDED_ARG 1 478 JUMP_ABSOLUTE 462 39 >> 480 LOAD_FAST 6 (used_for_row) 482 LOAD_FAST 10 (i) 484 DUP_TOP_TWO 486 BINARY_SUBSCR 488 LOAD_FAST 6 (used_for_row) 490 LOAD_FAST 4 (col) 492 BINARY_SUBSCR 494 INPLACE_OR 496 ROT_THREE 498 STORE_SUBSCR 40 500 LOAD_FAST 4 (col) 502 LOAD_FAST 1 (graphlen) 504 COMPARE_OP 0 (<) 506 EXTENDED_ARG 2 508 POP_JUMP_IF_FALSE 548 41 510 LOAD_FAST 0 (matrix) 512 LOAD_FAST 10 (i) 514 DUP_TOP_TWO 516 BINARY_SUBSCR 518 LOAD_FAST 0 (matrix) 520 LOAD_FAST 4 (col) 522 BINARY_SUBSCR 524 LOAD_FAST 0 (matrix) 526 LOAD_FAST 10 (i) 528 LOAD_FAST 4 (col) 530 LOAD_FAST 3 (extra) 532 BINARY_ADD 534 BUILD_TUPLE 2 536 BINARY_SUBSCR 538 BINARY_MULTIPLY 540 INPLACE_SUBTRACT 542 ROT_THREE 544 STORE_SUBSCR 546 JUMP_FORWARD 50 (to 598) 43 >> 548 LOAD_FAST 0 (matrix) 550 LOAD_FAST 10 (i) 552 LOAD_FAST 4 (col) 554 LOAD_FAST 3 (extra) 556 BINARY_ADD 558 BUILD_TUPLE 2 560 BINARY_SUBSCR 562 LOAD_CONST 2 (0) 564 COMPARE_OP 3 (!=) 566 EXTENDED_ARG 2 568 POP_JUMP_IF_FALSE 598 44 570 LOAD_FAST 0 (matrix) 572 LOAD_FAST 10 (i) 574 BINARY_SUBSCR 576 LOAD_FAST 0 (matrix) 578 LOAD_FAST 4 (col) 580 BINARY_SUBSCR 582 BINARY_SUBTRACT 584 LOAD_FAST 2 (PH) 586 BINARY_MODULO 588 LOAD_FAST 0 (matrix) 590 LOAD_FAST 10 (i) 592 STORE_SUBSCR 594 EXTENDED_ARG 2 596 JUMP_ABSOLUTE 548 45 >> 598 LOAD_FAST 0 (matrix) 600 LOAD_FAST 10 (i) 602 DUP_TOP_TWO 604 BINARY_SUBSCR 606 LOAD_FAST 2 (PH) 608 INPLACE_MODULO 610 ROT_THREE 612 STORE_SUBSCR 614 EXTENDED_ARG 1 616 JUMP_ABSOLUTE 462 47 >> 618 LOAD_FAST 4 (col) 620 LOAD_CONST 5 (1) 622 INPLACE_ADD 624 STORE_FAST 4 (col) 626 JUMP_ABSOLUTE 48 49 >> 628 LOAD_GLOBAL 2 (np) 630 LOAD_METHOD 9 (array) 632 LOAD_FAST 0 (matrix) 634 CALL_METHOD 1 636 LOAD_FAST 2 (PH) 638 BINARY_MODULO 640 STORE_FAST 0 (matrix) 50 642 LOAD_CONST 8 (<code object <listcomp> at 0x101093b30, file "/private/tmp/a.py", line 50>) 644 LOAD_CONST 4 ('rref.<locals>.<listcomp>') 646 MAKE_FUNCTION 0 648 LOAD_FAST 6 (used_for_row) 650 GET_ITER 652 CALL_FUNCTION 1 654 RETURN_VALUE Disassembly of <code object <listcomp> at 0x101093660, file "/private/tmp/a.py", line 8>: 8 0 BUILD_LIST 0 2 LOAD_FAST 0 (.0) >> 4 FOR_ITER 14 (to 20) 6 STORE_FAST 1 (i) 8 LOAD_GLOBAL 0 (set) 10 LOAD_FAST 1 (i) 12 BUILD_LIST 1 14 CALL_FUNCTION 1 16 LIST_APPEND 2 18 JUMP_ABSOLUTE 4 >> 20 RETURN_VALUE Disassembly of <code object <listcomp> at 0x101093b30, file "/private/tmp/a.py", line 50>: 50 0 BUILD_LIST 0 2 LOAD_FAST 0 (.0) >> 4 FOR_ITER 12 (to 18) 6 STORE_FAST 1 (x) 8 LOAD_GLOBAL 0 (sorted) 10 LOAD_FAST 1 (x) 12 CALL_FUNCTION 1 14 LIST_APPEND 2 16 JUMP_ABSOLUTE 4 >> 18 RETURN_VALUE

LLM Generation

Query

Output

Below is one acceptable “re‐assembly” of the bytecode into a Python function named foo. (Note that several choices of variable names and minor details are possible. This version is written so that its control‐flow and operations mirror the disassembled code.) Also note that the code assumes that numpy has been imported as “np.” ------------------------------------------------------------ # For example, at the top of your module: import numpy as np def foo(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] # Build a “used_for_row” list where each row starts with its own index used_for_row = [set([i]) for i in range(matrix.shape[0])] # Work modulo PH matrix = matrix % PH # The main loop continues while we have room in the matrix. # (The condition corresponds to: (col+extra) < (number_of_columns-1) and col < number_of_rows.) while (col + extra < matrix.shape[1] - 1) and (col < matrix.shape[0]): # If the candidate pivot is zero... if matrix[col, col + extra] == 0: # If the entire column (at index col) is zero, then we “skip” one extra column. if np.all(matrix[:, col] == 0): extra += 1 continue else: # Otherwise, search for a nonzero entry in column (col+extra) (using argwhere) # and choose the last such index. other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1] # If that candidate row lies above the current pivot row then skip extra. if other < col: extra += 1 continue # Otherwise swap the current row with the “other” row. matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] # Register the pivot position. pivots.append(col + extra) pivot = matrix[col, col + extra] # Depending on whether we are in the first part of the matrix or not, # check that the pivot has the expected “small” absolute value. if (col + extra) < graphlen: if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1): raise AssertionError("Pivot (in first block) must be ±1 modulo PH") else: if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2): raise AssertionError("Pivot (in second block) must be ±2 modulo PH") # In the second block, we “normalize” the pivot by integer‐dividing by 2 pivot //= 2 # Multiply the pivot by itself and reduce modulo PH. # (This evidently normalizes the pivot row.) matrix[col][col + extra] *= pivot matrix[col][col + extra] %= PH # Find all row indices where the current pivot column (col+extra) is nonzero. others = np.argwhere(matrix[:, col + extra]).flatten() for i in others: # Skip the pivot row itself. if i == col: continue # Record that row i now “comes from” the pivot row. used_for_row[i] |= used_for_row[col] # Do different row operations depending on which “block” we are in. if col < graphlen: # For rows in the first block, subtract a multiple of the pivot row so that # matrix[i, col+extra] becomes zero. matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH elif matrix[i, col + extra] != 0: # In the second block, if the entry is nonzero, subtract the pivot row. matrix[i] = (matrix[i] - matrix[col]) % PH else: # Either way, impose the modulo reduction. matrix[i] %= PH # Move on to the next row. col += 1 # At the end, ensure the matrix is a numpy array modulo PH. matrix = np.array(matrix) % PH # Finally, return the “used_for_row” record for each row, with each set sorted. return [sorted(x) for x in used_for_row] ------------------------------------------------------------ Explanation of key parts: 1. The variable PH is set to 16. The “extra” counter allows the algorithm to skip a column if the pivot candidate is 0. 2. The list comprehension builds used_for_row so that each row “remembers” its original index. 3. The while‐loop continues until (col+extra) is too high to be within the matrix’s columns or we run out of rows. 4. When the candidate pivot is zero, the code either increments extra (if the entire column is zero) or swaps the row with a lower row that has a nonzero entry. 5. Depending on whether the working column is before graphlen or not, the pivot is expected to be ±1 (mod PH) or ±2 (mod PH) and normalized accordingly. 6. Then standard elimination is performed on “other” rows (those with nonzero entry in the pivot column) and results are reduced modulo PH. 7. Finally, the function returns the list of “used_for_row” sets, each sorted. This function should capture (in one acceptable form) the behavior described by the disassembled bytecode.

Extract Code

I extracted the following code from that output:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Build a “used_for_row” list where each row starts with its own index
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work modulo PH
    matrix = matrix % PH
    
    # The main loop continues while we have room in the matrix.
    # (The condition corresponds to: (col+extra) < (number_of_columns-1) and col < number_of_rows.)
    while (col + extra < matrix.shape[1] - 1) and (col < matrix.shape[0]):
        # If the candidate pivot is zero...
        if matrix[col, col + extra] == 0:
            # If the entire column (at index col) is zero, then we “skip” one extra column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            else:
                # Otherwise, search for a nonzero entry in column (col+extra) (using argwhere)
                # and choose the last such index.
                other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
                # If that candidate row lies above the current pivot row then skip extra.
                if other < col:
                    extra += 1
                    continue
                # Otherwise swap the current row with the “other” row.
                matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
                used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Register the pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Depending on whether we are in the first part of the matrix or not,
        # check that the pivot has the expected “small” absolute value.
        if (col + extra) < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot (in first block) must be ±1 modulo PH")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot (in second block) must be ±2 modulo PH")
            # In the second block, we “normalize” the pivot by integer‐dividing by 2
            pivot //= 2
        
        # Multiply the pivot by itself and reduce modulo PH.
        # (This evidently normalizes the pivot row.)
        matrix[col][col + extra] *= pivot
        matrix[col][col + extra] %= PH
        
        # Find all row indices where the current pivot column (col+extra) is nonzero.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            # Skip the pivot row itself.
            if i == col:
                continue
            # Record that row i now “comes from” the pivot row.
            used_for_row[i] |= used_for_row[col]
            # Do different row operations depending on which “block” we are in.
            if col < graphlen:
                # For rows in the first block, subtract a multiple of the pivot row so that
                # matrix[i, col+extra] becomes zero.
                matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
            elif matrix[i, col + extra] != 0:
                # In the second block, if the entry is nonzero, subtract the pivot row.
                matrix[i] = (matrix[i] - matrix[col]) % PH
            else:
                # Either way, impose the modulo reduction.
                matrix[i] %= PH
        
        # Move on to the next row.
        col += 1
    
    # At the end, ensure the matrix is a numpy array modulo PH.
    matrix = np.array(matrix) % PH
    
    # Finally, return the “used_for_row” record for each row, with each set sorted.
    return [sorted(x) for x in used_for_row]

Run Code Interpreter

Running the following program:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Build a “used_for_row” list where each row starts with its own index
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work modulo PH
    matrix = matrix % PH
    
    # The main loop continues while we have room in the matrix.
    # (The condition corresponds to: (col+extra) < (number_of_columns-1) and col < number_of_rows.)
    while (col + extra < matrix.shape[1] - 1) and (col < matrix.shape[0]):
        # If the candidate pivot is zero...
        if matrix[col, col + extra] == 0:
            # If the entire column (at index col) is zero, then we “skip” one extra column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            else:
                # Otherwise, search for a nonzero entry in column (col+extra) (using argwhere)
                # and choose the last such index.
                other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
                # If that candidate row lies above the current pivot row then skip extra.
                if other < col:
                    extra += 1
                    continue
                # Otherwise swap the current row with the “other” row.
                matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
                used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Register the pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Depending on whether we are in the first part of the matrix or not,
        # check that the pivot has the expected “small” absolute value.
        if (col + extra) < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot (in first block) must be ±1 modulo PH")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot (in second block) must be ±2 modulo PH")
            # In the second block, we “normalize” the pivot by integer‐dividing by 2
            pivot //= 2
        
        # Multiply the pivot by itself and reduce modulo PH.
        # (This evidently normalizes the pivot row.)
        matrix[col][col + extra] *= pivot
        matrix[col][col + extra] %= PH
        
        # Find all row indices where the current pivot column (col+extra) is nonzero.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            # Skip the pivot row itself.
            if i == col:
                continue
            # Record that row i now “comes from” the pivot row.
            used_for_row[i] |= used_for_row[col]
            # Do different row operations depending on which “block” we are in.
            if col < graphlen:
                # For rows in the first block, subtract a multiple of the pivot row so that
                # matrix[i, col+extra] becomes zero.
                matrix[i] = (matrix[i] - matrix[col] * matrix[i, col + extra]) % PH
            elif matrix[i, col + extra] != 0:
                # In the second block, if the entry is nonzero, subtract the pivot row.
                matrix[i] = (matrix[i] - matrix[col]) % PH
            else:
                # Either way, impose the modulo reduction.
                matrix[i] %= PH
        
        # Move on to the next row.
        col += 1
    
    # At the end, ensure the matrix is a numpy array modulo PH.
    matrix = np.array(matrix) % PH
    
    # Finally, return the “used_for_row” record for each row, with each set sorted.
    return [sorted(x) for x in used_for_row]


arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = foo(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')

And got the output:

Traceback (most recent call last):
  File "/usr/src/app/main.py", line 87, in <module>
    answer = foo(arr, 37)
             ^^^^^^^^^^^^
  File "/usr/src/app/main.py", line 46, in foo
    raise AssertionError("Pivot (in second block) must be ±2 modulo PH")
AssertionError: Pivot (in second block) must be ±2 modulo PH

Substring Evaluation

Testing if the previous output contains the string All tests passed: False

Initial Query

LLM Generation

Query

Output

Below is one acceptable “reconstruction” of the original byte‐code as a function called foo. (Note that the exact source isn’t uniquely determined by the byte‑code so the following is one high–level equivalent version that uses NumPy; you may need to adjust naming or details to suit your application.) ────────────────────────── # For example: import numpy as np def foo(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] # Create a “used_for_row” list so that each row i initially “contains” the set {i} used_for_row = [set([i]) for i in range(matrix.shape[0])] # Work with the entries modulo PH. matrix = matrix % PH # Loop while there are still columns available. while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]: # If our pivot candidate is zero, then check if the entire column is zero. if matrix[col, col + extra] == 0: # If so, simply skip (i.e. increment extra) for this column. if np.all(matrix[:, col] == 0): extra += 1 continue # Otherwise, search for a nonzero entry in the same “pivot‐column” # (selecting the last such index from np.argwhere). other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1] # If the found row is “above” the current row, then skip this column. if other < col: extra += 1 continue # Otherwise, swap the current row and the row “other.” # (Here we cast the row slices to lists so that assignment works as expected.) matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] # Record pivot position. pivots.append(col + extra) pivot = matrix[col, col + extra] # Normalize the pivot. In the first “graphlen” columns a valid pivot must be congruent (in absolute value) # to 1 modulo PH; in later columns it must be ≡2 (or PH–2) so that later we divide by 2. if col + extra < graphlen: if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1): raise AssertionError("Pivot value not 1 or -1 in first graphlen columns") else: if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2): raise AssertionError("Pivot value not 2 or -2 in later columns") pivot //= 2 # Multiply the pivot entry by itself (this “normalizes” that entry) # and ensure that the first entry in the row is reduced modulo PH. matrix[col, col + extra] *= pivot matrix[col, col] %= PH # Now eliminate nonzero entries in the current pivot column. others = np.argwhere(matrix[:, col + extra]).flatten() for i in others: if i == col: continue # Merge the sets of rows that contributed to the pivot. used_for_row[i] |= used_for_row[col] # In the “graphlen” part of the matrix, use the pivot column entry to cancel. if col < graphlen: matrix[i] = (matrix[i] - matrix[i, col] * np.array(matrix[col])) % PH # Otherwise, if the entry is nonzero then subtract and reduce modulo PH. elif matrix[i, col + extra] != 0: matrix[i] = (np.array(matrix[i]) - matrix[i, col]) % PH matrix[i] %= PH col += 1 # Finally, convert the result to a NumPy array (again reducing modulo PH) matrix = np.array(matrix) % PH # Return the “used_for_row” list with each set converted to a sorted list. return [sorted(x) for x in used_for_row] ────────────────────────── Explanatory notes: 1. The constant PH is set to 16. 2. The variable extra allows the algorithm to “skip” columns that do not yield a good pivot. 3. The list used_for_row starts with each row i “marked” by {i} then is updated every time rows are swapped or combined. 4. The loop stops when col+extra reaches matrix.shape[1]–1 (so that there is a “right–hand side”) or when there are no more rows. 5. Two list–comprehensions appear (one for used_for_row and one in the return statement) which match the disassembled list–comps. This is one valid reconstruction of the given disassembled python byte–code.

Extract Code

I extracted the following code from that output:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Create a “used_for_row” list so that each row i initially “contains” the set {i}
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work with the entries modulo PH.
    matrix = matrix % PH

    # Loop while there are still columns available.
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # If our pivot candidate is zero, then check if the entire column is zero.
        if matrix[col, col + extra] == 0:
            # If so, simply skip (i.e. increment extra) for this column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            # Otherwise, search for a nonzero entry in the same “pivot‐column”
            # (selecting the last such index from np.argwhere).
            other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
            # If the found row is “above” the current row, then skip this column.
            if other < col:
                extra += 1
                continue
            # Otherwise, swap the current row and the row “other.”
            # (Here we cast the row slices to lists so that assignment works as expected.)
            matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Record pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Normalize the pivot. In the first “graphlen” columns a valid pivot must be congruent (in absolute value)
        # to 1 modulo PH; in later columns it must be ≡2 (or PH–2) so that later we divide by 2.
        if col + extra < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot value not 1 or -1 in first graphlen columns")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot value not 2 or -2 in later columns")
            pivot //= 2
        
        # Multiply the pivot entry by itself (this “normalizes” that entry)
        # and ensure that the first entry in the row is reduced modulo PH.
        matrix[col, col + extra] *= pivot
        matrix[col, col] %= PH

        # Now eliminate nonzero entries in the current pivot column.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            if i == col:
                continue
            # Merge the sets of rows that contributed to the pivot.
            used_for_row[i] |= used_for_row[col]
            # In the “graphlen” part of the matrix, use the pivot column entry to cancel.
            if col < graphlen:
                matrix[i] = (matrix[i] - matrix[i, col] * np.array(matrix[col])) % PH
            # Otherwise, if the entry is nonzero then subtract and reduce modulo PH.
            elif matrix[i, col + extra] != 0:
                matrix[i] = (np.array(matrix[i]) - matrix[i, col]) % PH
                matrix[i] %= PH

        col += 1

    # Finally, convert the result to a NumPy array (again reducing modulo PH)
    matrix = np.array(matrix) % PH
    # Return the “used_for_row” list with each set converted to a sorted list.
    return [sorted(x) for x in used_for_row]

Run Code Interpreter

Running the following program:

import numpy as np

def foo(matrix, graphlen):
    PH = 16
    extra = 0
    col = 0
    pivots = []
    # Create a “used_for_row” list so that each row i initially “contains” the set {i}
    used_for_row = [set([i]) for i in range(matrix.shape[0])]
    
    # Work with the entries modulo PH.
    matrix = matrix % PH

    # Loop while there are still columns available.
    while col + extra < matrix.shape[1] - 1 and col < matrix.shape[0]:
        # If our pivot candidate is zero, then check if the entire column is zero.
        if matrix[col, col + extra] == 0:
            # If so, simply skip (i.e. increment extra) for this column.
            if np.all(matrix[:, col] == 0):
                extra += 1
                continue
            # Otherwise, search for a nonzero entry in the same “pivot‐column”
            # (selecting the last such index from np.argwhere).
            other = np.argwhere(matrix[:, col + extra] != 0).flatten()[-1]
            # If the found row is “above” the current row, then skip this column.
            if other < col:
                extra += 1
                continue
            # Otherwise, swap the current row and the row “other.”
            # (Here we cast the row slices to lists so that assignment works as expected.)
            matrix[col], matrix[other] = list(matrix[other]), list(matrix[col])
            used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col]
        
        # Record pivot position.
        pivots.append(col + extra)
        pivot = matrix[col, col + extra]
        
        # Normalize the pivot. In the first “graphlen” columns a valid pivot must be congruent (in absolute value)
        # to 1 modulo PH; in later columns it must be ≡2 (or PH–2) so that later we divide by 2.
        if col + extra < graphlen:
            if not (np.abs(pivot) == 1 or np.abs(pivot) == PH - 1):
                raise AssertionError("Pivot value not 1 or -1 in first graphlen columns")
        else:
            if not (np.abs(pivot) == 2 or np.abs(pivot) == PH - 2):
                raise AssertionError("Pivot value not 2 or -2 in later columns")
            pivot //= 2
        
        # Multiply the pivot entry by itself (this “normalizes” that entry)
        # and ensure that the first entry in the row is reduced modulo PH.
        matrix[col, col + extra] *= pivot
        matrix[col, col] %= PH

        # Now eliminate nonzero entries in the current pivot column.
        others = np.argwhere(matrix[:, col + extra]).flatten()
        for i in others:
            if i == col:
                continue
            # Merge the sets of rows that contributed to the pivot.
            used_for_row[i] |= used_for_row[col]
            # In the “graphlen” part of the matrix, use the pivot column entry to cancel.
            if col < graphlen:
                matrix[i] = (matrix[i] - matrix[i, col] * np.array(matrix[col])) % PH
            # Otherwise, if the entry is nonzero then subtract and reduce modulo PH.
            elif matrix[i, col + extra] != 0:
                matrix[i] = (np.array(matrix[i]) - matrix[i, col]) % PH
                matrix[i] %= PH

        col += 1

    # Finally, convert the result to a NumPy array (again reducing modulo PH)
    matrix = np.array(matrix) % PH
    # Return the “used_for_row” list with each set converted to a sorted list.
    return [sorted(x) for x in used_for_row]


arr = np.array([[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

answer = foo(arr, 37)
expected = [[0, 38], [0, 38], [0, 6, 28, 35, 38], [0, 6, 18, 21, 28, 35, 38], [0, 6, 28, 35, 38], [0, 6, 21, 28, 35, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 10, 23, 38], [0, 5, 9, 10, 23, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 27, 38], [0, 5, 9, 10, 11, 23, 25, 27, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 24, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 23, 25, 26, 27, 34, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 38], [0, 5, 9, 10, 13, 17, 23, 30, 32, 33, 38], [0, 22, 29, 38], [0, 22, 29, 38], [0, 6, 28, 35, 38], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38], [14, 18, 21, 28, 35]]
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')

And got the output:

Traceback (most recent call last):
  File "/usr/src/app/main.py", line 78, in <module>
    answer = foo(arr, 37)
             ^^^^^^^^^^^^
  File "/usr/src/app/main.py", line 45, in foo
    raise AssertionError("Pivot value not 2 or -2 in later columns")
AssertionError: Pivot value not 2 or -2 in later columns

Substring Evaluation

Testing if the previous output contains the string All tests passed: False