M2.sage

load("__common__.sage")

def generator():

    
    #Choose omitted op
    omitted_op = choice([0,1,2])
    if omitted_op==0: #Omit diagonal
        rows=sample([0,1,2,3],3)
        mat1 = identity_matrix(4).with_swapped_rows(rows[0],rows[1])
        row_op1 = rowOp("permutation",rows[0]+1, rows[1]+1)
        
        scale = randrange(2,6)*choice([-1,1])
        mat2 = identity_matrix(4).with_added_multiple_of_row(rows[1],rows[2],scale)
        row_op2 = rowOp("elementary",rows[1]+1,rows[2]+1,scale)

    if omitted_op==1: #Omit permutation
        rows=sample([0,1,2,3],2)
        scale = randrange(2,6)*choice([-1,1])
        mat1 = identity_matrix(4).with_rescaled_row(rows[0],scale)
        row_op1 = rowOp("diagonal",rows[0]+1,rows[0]+1,scale)
        
        scale = randrange(2,6)*choice([-1,1])
        mat2 = identity_matrix(4).with_added_multiple_of_row(rows[0],rows[1],scale)
        row_op2 = rowOp("elementary",rows[0]+1,rows[1]+1,scale)
        
    if omitted_op==2: #Omit elementary
        rows=sample([0,1,2,3],2)
        scale = randrange(2,6)*choice([-1,1])
        mat1 = identity_matrix(4).with_rescaled_row(rows[0],scale)
        row_op1 = rowOp("diagonal",rows[0]+1,rows[0]+1,scale)
        
        mat2 = identity_matrix(4).with_swapped_rows(rows[0],rows[1])
        row_op2 = rowOp("permutation",rows[0]+1, rows[1]+1)
            
    #Swap presentation order half the time
    if choice([True,False]):
        row_op1,row_op2 = row_op2,row_op1
        mat1,mat2 = mat2,mat1


    name1, name2 = sample(["B","C","M","N","P","Q"],2)

    #randomly swap order of ops
    swapped = choice([True,False])


    return {
      "row_op1": row_op1,
      "row_op2": row_op2,
      "mat1": mat1,
      "mat2": mat2,
      "name1": name1,
      "name2": name2,
      "swapped": swapped
    }