def test01():
    __cdbkernel__=create_scope()
    rl:= \sin{A??}**2 + \cos{A??}**2 = 1;
    ex:= \sin{x}**2 + 3 + \cos{x}**2 + Q;
    substitute(ex, rl)
    tst:= 4 + Q - @(ex);
    assert(tst==0)
    print("Test 01 passed")

test01()

def test02():
    __cdbkernel__=create_scope()
    rl:= \sin{A??}**2 + \cos{A??}**2 = 1;
    ex:= \sin{A_{m} A^{m}}**2 + \cos{A_{n} A^{n}}**2;
    substitute(ex, rl)
    tst:= 1 - @(ex);
    assert(tst==0)
    print("Test 02 passed")

test02()

def test03():
    __cdbkernel__=create_scope()
    rl:= \sin{A??}**2 + \cos{A??}**2 = 1;
    ex:= \sin{A_{m} A^{m} B_{n} B^{n}}**2 + \cos{A_{m} A^{n} B_{n} B^{m}}**2;
    substitute(ex, rl)
    tst:= \sin{A_{m} A^{m} B_{n} B^{n}}**2 + \cos{A_{m} A^{n} B_{n} B^{m}}**2 - @(ex);
    assert(tst==0)
    print("Test 03 passed")

test03()