Ejemplo n.º 1
0
def test_deltaproduct_mul_add_x_kd_add_y_kd():
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 3)) == \
        KD(i, 1)*(KD(i, k) + x)*((KD(i, k) + x)*y)**2 + \
        KD(i, 2)*(KD(i, k) + x)*y*(KD(i, k) + x)**2*y + \
        KD(i, 3)*((KD(i, k) + x)*y)**2*(KD(i, k) + x) + \
        ((KD(i, k) + x)*y)**3
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 1)) == \
        (x + KD(i, k))*(y + KD(i, 1))
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 2, 2)) == \
        (x + KD(i, k))*(y + KD(i, 2))
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 3, 3)) == \
        (x + KD(i, k))*(y + KD(i, 3))
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, k)) == \
        ((x + KD(i, k))*y)**k + Piecewise(
            (((x + KD(i, k))*y)**(i - 1)*(x + KD(i, k))*
             ((x + KD(i, k))*y)**(-i + k), And(S(1) <= i, i <= k)),
            (0, True)
        )
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, 3)) == \
        ((x + KD(i, k))*y)**(4 - k) + Piecewise(
            (((x + KD(i, k))*y)**(i - k)*(x + KD(i, k))*
             ((x + KD(i, k))*y)**(-i + 3), And(k <= i, i <= 3)),
            (0, True)
        )
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, l)) == \
        ((x + KD(i, k))*y)**(-k + l + 1) + Piecewise(
            (((x + KD(i, k))*y)**(i - k)*(x + KD(i, k))*
             ((x + KD(i, k))*y)**(-i + l), And(k <= i, i <= l)),
            (0, True)
        )
Ejemplo n.º 2
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def test_deltaproduct_mul_add_x_kd_add_y_kd():
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 3)) == \
        KD(i, 1)*(KD(i, k) + x)*((KD(i, k) + x)*y)**2 + \
        KD(i, 2)*(KD(i, k) + x)*y*(KD(i, k) + x)**2*y + \
        KD(i, 3)*((KD(i, k) + x)*y)**2*(KD(i, k) + x) + \
        ((KD(i, k) + x)*y)**3
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, 1)) == \
        (x + KD(i, k))*(y + KD(i, 1))
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 2, 2)) == \
        (x + KD(i, k))*(y + KD(i, 2))
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 3, 3)) == \
        (x + KD(i, k))*(y + KD(i, 3))
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, 1, k)) == \
        ((x + KD(i, k))*y)**k + Piecewise(
            (((x + KD(i, k))*y)**(i - 1)*(x + KD(i, k))*
             ((x + KD(i, k))*y)**(-i + k), And(S(1) <= i, i <= k)),
            (0, True)
        )
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, 3)) == \
        ((x + KD(i, k))*y)**(4 - k) + Piecewise(
            (((x + KD(i, k))*y)**(i - k)*(x + KD(i, k))*
             ((x + KD(i, k))*y)**(-i + 3), And(k <= i, i <= 3)),
            (0, True)
        )
    assert dp((x + KD(i, k))*(y + KD(i, j)), (j, k, l)) == \
        ((x + KD(i, k))*y)**(-k + l + 1) + Piecewise(
            (((x + KD(i, k))*y)**(i - k)*(x + KD(i, k))*
             ((x + KD(i, k))*y)**(-i + l), And(k <= i, i <= l)),
            (0, True)
        )
Ejemplo n.º 3
0
def test_deltaproduct_mul_add_x_y_add_y_kd():
    assert dp((x + y)*(y + KD(i, j)), (j, 1, 3)) == ((x + y)*y)**3 + \
        (x + y)*((x + y)*y)**2*KD(i, 1) + \
        (x + y)*y*(x + y)**2*y*KD(i, 2) + \
        ((x + y)*y)**2*(x + y)*KD(i, 3)
    assert dp((x + y)*(y + KD(i, j)), (j, 1, 1)) == (x + y)*(y + KD(i, 1))
    assert dp((x + y)*(y + KD(i, j)), (j, 2, 2)) == (x + y)*(y + KD(i, 2))
    assert dp((x + y)*(y + KD(i, j)), (j, 3, 3)) == (x + y)*(y + KD(i, 3))
    assert dp((x + y)*(y + KD(i, j)), (j, 1, k)) == \
        ((x + y)*y)**k + Piecewise(
            (((x + y)*y)**(i - 1)*(x + y)*((x + y)*y)**(k - i),
             And(S(1) <= i, i <= k)),
            (0, True)
        )
    assert dp((x + y)*(y + KD(i, j)), (j, k, 3)) == \
        ((x + y)*y)**(-k + 4) + Piecewise(
            (((x + y)*y)**(i - k)*(x + y)*((x + y)*y)**(3 - i),
             And(k <= i, i <= 3)),
            (0, True)
        )
    assert dp((x + y)*(y + KD(i, j)), (j, k, l)) == \
        ((x + y)*y)**(-k + l + 1) + Piecewise(
            (((x + y)*y)**(i - k)*(x + y)*((x + y)*y)**(l - i),
             And(k <= i, i <= l)),
            (0, True)
        )
Ejemplo n.º 4
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def test_deltaproduct_mul_add_x_y_add_y_kd():
    assert dp((x + y)*(y + KD(i, j)), (j, 1, 3)) == ((x + y)*y)**3 + \
        (x + y)*((x + y)*y)**2*KD(i, 1) + \
        (x + y)*y*(x + y)**2*y*KD(i, 2) + \
        ((x + y)*y)**2*(x + y)*KD(i, 3)
    assert dp((x + y) * (y + KD(i, j)), (j, 1, 1)) == (x + y) * (y + KD(i, 1))
    assert dp((x + y) * (y + KD(i, j)), (j, 2, 2)) == (x + y) * (y + KD(i, 2))
    assert dp((x + y) * (y + KD(i, j)), (j, 3, 3)) == (x + y) * (y + KD(i, 3))
    assert dp((x + y)*(y + KD(i, j)), (j, 1, k)) == \
        ((x + y)*y)**k + Piecewise(
            (((x + y)*y)**(i - 1)*(x + y)*((x + y)*y)**(k - i),
             And(S(1) <= i, i <= k)),
            (0, True)
        )
    assert dp((x + y)*(y + KD(i, j)), (j, k, 3)) == \
        ((x + y)*y)**(-k + 4) + Piecewise(
            (((x + y)*y)**(i - k)*(x + y)*((x + y)*y)**(3 - i),
             And(k <= i, i <= 3)),
            (0, True)
        )
    assert dp((x + y)*(y + KD(i, j)), (j, k, l)) == \
        ((x + y)*y)**(-k + l + 1) + Piecewise(
            (((x + y)*y)**(i - k)*(x + y)*((x + y)*y)**(l - i),
             And(k <= i, i <= l)),
            (0, True)
        )
Ejemplo n.º 5
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def test_deltaproduct_mul_x_kd():
    assert dp(x*KD(i, j), (j, 1, 3)) == 0
    assert dp(x*KD(i, j), (j, 1, 1)) == x*KD(i, 1)
    assert dp(x*KD(i, j), (j, 2, 2)) == x*KD(i, 2)
    assert dp(x*KD(i, j), (j, 3, 3)) == x*KD(i, 3)
    assert dp(x*KD(i, j), (j, 1, k)) == x*KD(i, 1)*KD(k, 1) + KD(k, 0)
    assert dp(x*KD(i, j), (j, k, 3)) == x*KD(i, 3)*KD(k, 3) + KD(k, 4)
    assert dp(x*KD(i, j), (j, k, l)) == x*KD(i, l)*KD(k, l) + KD(k, l + 1)
Ejemplo n.º 6
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def test_deltaproduct_basic():
    assert dp(KD(i, j), (j, 1, 3)) == 0
    assert dp(KD(i, j), (j, 1, 1)) == KD(i, 1)
    assert dp(KD(i, j), (j, 2, 2)) == KD(i, 2)
    assert dp(KD(i, j), (j, 3, 3)) == KD(i, 3)
    assert dp(KD(i, j), (j, 1, k)) == KD(i, 1)*KD(k, 1) + KD(k, 0)
    assert dp(KD(i, j), (j, k, 3)) == KD(i, 3)*KD(k, 3) + KD(k, 4)
    assert dp(KD(i, j), (j, k, l)) == KD(i, l)*KD(k, l) + KD(k, l + 1)
Ejemplo n.º 7
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def test_deltaproduct_trivial():
    assert dp(x, (j, 1, 0)) == 1
    assert dp(x, (j, 1, 3)) == x**3
    assert dp(x + y, (j, 1, 3)) == (x + y)**3
    assert dp(x*y, (j, 1, 3)) == (x*y)**3
    assert dp(KD(i, j), (k, 1, 3)) == KD(i, j)
    assert dp(x*KD(i, j), (k, 1, 3)) == x**3*KD(i, j)
    assert dp(x*y*KD(i, j), (k, 1, 3)) == (x*y)**3*KD(i, j)
Ejemplo n.º 8
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def test_deltaproduct_basic():
    assert dp(KD(i, j), (j, 1, 3)) == 0
    assert dp(KD(i, j), (j, 1, 1)) == KD(i, 1)
    assert dp(KD(i, j), (j, 2, 2)) == KD(i, 2)
    assert dp(KD(i, j), (j, 3, 3)) == KD(i, 3)
    assert dp(KD(i, j), (j, 1, k)) == KD(i, 1) * KD(k, 1) + KD(k, 0)
    assert dp(KD(i, j), (j, k, 3)) == KD(i, 3) * KD(k, 3) + KD(k, 4)
    assert dp(KD(i, j), (j, k, l)) == KD(i, l) * KD(k, l) + KD(k, l + 1)
Ejemplo n.º 9
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def test_deltaproduct_trivial():
    assert dp(x, (j, 1, 0)) == 1
    assert dp(x, (j, 1, 3)) == x**3
    assert dp(x + y, (j, 1, 3)) == (x + y)**3
    assert dp(x * y, (j, 1, 3)) == (x * y)**3
    assert dp(KD(i, j), (k, 1, 3)) == KD(i, j)
    assert dp(x * KD(i, j), (k, 1, 3)) == x**3 * KD(i, j)
    assert dp(x * y * KD(i, j), (k, 1, 3)) == (x * y)**3 * KD(i, j)
Ejemplo n.º 10
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def test_deltaproduct_mul_x_kd():
    assert dp(x*KD(i, j), (j, 1, 3)) == 0
    assert dp(x*KD(i, j), (j, 1, 1)) == x*KD(i, 1)
    assert dp(x*KD(i, j), (j, 2, 2)) == x*KD(i, 2)
    assert dp(x*KD(i, j), (j, 3, 3)) == x*KD(i, 3)
    assert dp(x*KD(i, j), (j, 1, k)) == x*KD(i, 1)*KD(k, 1) + KD(k, 0)
    assert dp(x*KD(i, j), (j, k, 3)) == x*KD(i, 3)*KD(k, 3) + KD(k, 4)
    assert dp(x*KD(i, j), (j, k, l)) == x*KD(i, l)*KD(k, l) + KD(k, l + 1)
Ejemplo n.º 11
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def test_deltaproduct_add_kd_kd():
    assert dp(KD(i, k) + KD(j, k), (k, 1, 3)) == 0
    assert dp(KD(i, k) + KD(j, k), (k, 1, 1)) == KD(i, 1) + KD(j, 1)
    assert dp(KD(i, k) + KD(j, k), (k, 2, 2)) == KD(i, 2) + KD(j, 2)
    assert dp(KD(i, k) + KD(j, k), (k, 3, 3)) == KD(i, 3) + KD(j, 3)
    assert dp(KD(i, k) + KD(j, k), (k, 1, l)) == KD(l, 0) + \
        KD(i, 1)*KD(l, 1) + KD(j, 1)*KD(l, 1) + \
        KD(i, 1)*KD(j, 2)*KD(l, 2) + KD(j, 1)*KD(i, 2)*KD(l, 2)
    assert dp(KD(i, k) + KD(j, k), (k, l, 3)) == KD(l, 4) + \
        KD(i, 3)*KD(l, 3) + KD(j, 3)*KD(l, 3) + \
        KD(i, 2)*KD(j, 3)*KD(l, 2) + KD(i, 3)*KD(j, 2)*KD(l, 2)
    assert dp(KD(i, k) + KD(j, k), (k, l, m)) == KD(l, m + 1) + \
        KD(i, m)*KD(l, m) + KD(j, m)*KD(l, m) + \
        KD(i, m)*KD(j, m - 1)*KD(l, m - 1) + KD(i, m - 1)*KD(j, m)*KD(l, m - 1)
Ejemplo n.º 12
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def test_deltaproduct_add_kd_kd():
    assert dp(KD(i, k) + KD(j, k), (k, 1, 3)) == 0
    assert dp(KD(i, k) + KD(j, k), (k, 1, 1)) == KD(i, 1) + KD(j, 1)
    assert dp(KD(i, k) + KD(j, k), (k, 2, 2)) == KD(i, 2) + KD(j, 2)
    assert dp(KD(i, k) + KD(j, k), (k, 3, 3)) == KD(i, 3) + KD(j, 3)
    assert dp(KD(i, k) + KD(j, k), (k, 1, l)) == KD(l, 0) + \
        KD(i, 1)*KD(l, 1) + KD(j, 1)*KD(l, 1) + \
        KD(i, 1)*KD(j, 2)*KD(l, 2) + KD(j, 1)*KD(i, 2)*KD(l, 2)
    assert dp(KD(i, k) + KD(j, k), (k, l, 3)) == KD(l, 4) + \
        KD(i, 3)*KD(l, 3) + KD(j, 3)*KD(l, 3) + \
        KD(i, 2)*KD(j, 3)*KD(l, 2) + KD(i, 3)*KD(j, 2)*KD(l, 2)
    assert dp(KD(i, k) + KD(j, k), (k, l, m)) == KD(l, m + 1) + \
        KD(i, m)*KD(l, m) + KD(j, m)*KD(l, m) + \
        KD(i, m)*KD(j, m - 1)*KD(l, m - 1) + KD(i, m - 1)*KD(j, m)*KD(l, m - 1)
Ejemplo n.º 13
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def test_deltaproduct_mul_x_add_kd_kd():
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 3)) == 0
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 1)) == x*(KD(i, 1) + KD(j, 1))
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 2, 2)) == x*(KD(i, 2) + KD(j, 2))
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 3, 3)) == x*(KD(i, 3) + KD(j, 3))
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, l)) == KD(l, 0) + \
        x*KD(i, 1)*KD(l, 1) + x*KD(j, 1)*KD(l, 1) + \
        x**2*KD(i, 1)*KD(j, 2)*KD(l, 2) + x**2*KD(j, 1)*KD(i, 2)*KD(l, 2)
    assert dp(x*(KD(i, k) + KD(j, k)), (k, l, 3)) == KD(l, 4) + \
        x*KD(i, 3)*KD(l, 3) + x*KD(j, 3)*KD(l, 3) + \
        x**2*KD(i, 2)*KD(j, 3)*KD(l, 2) + x**2*KD(i, 3)*KD(j, 2)*KD(l, 2)
    assert dp(x*(KD(i, k) + KD(j, k)), (k, l, m)) == KD(l, m + 1) + \
        x*KD(i, m)*KD(l, m) + x*KD(j, m)*KD(l, m) + \
        x**2*KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + \
        x**2*KD(i, m)*KD(j, m - 1)*KD(l, m - 1)
Ejemplo n.º 14
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def test_deltaproduct_mul_x_add_kd_kd():
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 3)) == 0
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, 1)) == x*(KD(i, 1) + KD(j, 1))
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 2, 2)) == x*(KD(i, 2) + KD(j, 2))
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 3, 3)) == x*(KD(i, 3) + KD(j, 3))
    assert dp(x*(KD(i, k) + KD(j, k)), (k, 1, l)) == KD(l, 0) + \
        x*KD(i, 1)*KD(l, 1) + x*KD(j, 1)*KD(l, 1) + \
        x**2*KD(i, 1)*KD(j, 2)*KD(l, 2) + x**2*KD(j, 1)*KD(i, 2)*KD(l, 2)
    assert dp(x*(KD(i, k) + KD(j, k)), (k, l, 3)) == KD(l, 4) + \
        x*KD(i, 3)*KD(l, 3) + x*KD(j, 3)*KD(l, 3) + \
        x**2*KD(i, 2)*KD(j, 3)*KD(l, 2) + x**2*KD(i, 3)*KD(j, 2)*KD(l, 2)
    assert dp(x*(KD(i, k) + KD(j, k)), (k, l, m)) == KD(l, m + 1) + \
        x*KD(i, m)*KD(l, m) + x*KD(j, m)*KD(l, m) + \
        x**2*KD(i, m - 1)*KD(j, m)*KD(l, m - 1) + \
        x**2*KD(i, m)*KD(j, m - 1)*KD(l, m - 1)
Ejemplo n.º 15
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def test_deltaproduct_mul_x_add_y_kd():
    assert dp(x * (y + KD(i, j)),
              (j, 1, 3)) == (x * y)**3 + x * (x * y)**2 * KD(i, 1) + (
                  x * y) * x * (x * y) * KD(i, 2) + (x * y)**2 * x * KD(i, 3)
    assert dp(x * (y + KD(i, j)), (j, 1, 1)) == x * (y + KD(i, 1))
    assert dp(x * (y + KD(i, j)), (j, 2, 2)) == x * (y + KD(i, 2))
    assert dp(x * (y + KD(i, j)), (j, 3, 3)) == x * (y + KD(i, 3))
    assert dp(x * (y + KD(i, j)), (j, 1, k)) == (x * y)**k + Piecewise(
        ((x * y)**(i - 1) * x * (x * y)**(k - i), And(1 <= i, i <= k)),
        (0, True))
    assert dp(x * (y + KD(i, j)), (j, k, 3)) == (x * y)**(-k + 4) + Piecewise(
        ((x * y)**(i - k) * x * (x * y)**(3 - i), And(k <= i, i <= 3)),
        (0, True))
    assert dp(x * (y + KD(i, j)),
              (j, k, l)) == (x * y)**(-k + l + 1) + Piecewise(
                  ((x * y)**(i - k) * x *
                   (x * y)**(l - i), And(k <= i, i <= l)), (0, True))
Ejemplo n.º 16
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def test_deltaproduct_mul_x_add_y_twokd():
    assert dp(x*(y + 2*KD(i, j)), (j, 1, 3)) == (x*y)**3 + \
        2*x*(x*y)**2*KD(i, 1) + 2*x*y*x*x*y*KD(i, 2) + 2*(x*y)**2*x*KD(i, 3)
    assert dp(x*(y + 2*KD(i, j)), (j, 1, 1)) == x*(y + 2*KD(i, 1))
    assert dp(x*(y + 2*KD(i, j)), (j, 2, 2)) == x*(y + 2*KD(i, 2))
    assert dp(x*(y + 2*KD(i, j)), (j, 3, 3)) == x*(y + 2*KD(i, 3))
    assert dp(x*(y + 2*KD(i, j)), (j, 1, k)) == \
        (x*y)**k + Piecewise(
            (2*(x*y)**(i - 1)*x*(x*y)**(k - i), And(S(1) <= i, i <= k)),
            (0, True)
        )
    assert dp(x*(y + 2*KD(i, j)), (j, k, 3)) == \
        (x*y)**(-k + 4) + Piecewise(
            (2*(x*y)**(i - k)*x*(x*y)**(3 - i), And(k <= i, i <= 3)),
            (0, True)
        )
    assert dp(x*(y + 2*KD(i, j)), (j, k, l)) == \
        (x*y)**(-k + l + 1) + Piecewise(
            (2*(x*y)**(i - k)*x*(x*y)**(l - i), And(k <= i, i <= l)),
            (0, True)
        )