DL2.sage

def generator():
    t = var("t")
    s = var("s")
    d = dirac_delta
    u = unit_step
    k = choice([-1,1])*randrange(2,5)
    m = choice([-1,1])*randrange(2,4)
    n = choice([-1,1])*randrange(2,5)
    q = choice([-1,1])*randrange(2,5)
    p = randrange(2,5)
    a = randrange(1,5)
    b = randrange(2,5)
    c = randrange(2,5)
    use_u = choice([True,False])
    use_sin = choice([True,False])
    pretransform = k+m*t^p
    if use_u:
        pretransform += n*u(t-a)
    else:
        pretransform += n*d(t-a)
    if use_sin:
        pretransform += q*sin(b*t)
    else:
        pretransform += q*cos(b*t)
    transform = k/s+m*factorial(p)/s^(p+1)
    if use_u:
        transform += n*e^(-a*s)/s
    else:
        transform += n*e^(-a*s)
    if use_sin:
        transform += q*b/(s^2+b^2)
    else:
        transform += q*s/(s^2+b^2)
    e_pretransform = b*e^(c*t)
    e_transform = b/(s-c)

    return {
        "pretransform": pretransform,
        "transform": transform,
        "e_pretransform": e_pretransform,
        "e_transform": e_transform,
    }