def test_vector_entries_hadamard():
# For a row or column, user might to use the other dimension
A = Matrix([[1, sin(2 / x), 3 * pi / x / 5]])
assert maple_code(A) == \
'Matrix([[1, sin(2/x), (3/5)*Pi/x]], storage = rectangular)'
assert maple_code(A.T) == \
'Matrix([[1], [sin(2/x)], [(3/5)*Pi/x]], storage = rectangular)'
def test_maple_piecewise_times_const():
pw = Piecewise((x, x < 1), (x**2, True))
assert maple_code(2 * pw) == "2*piecewise(x < 1, x, x^2)"
assert maple_code(pw / x) == "piecewise(x < 1, x, x^2)/x"
assert maple_code(pw / (x * y)) == "piecewise(x < 1, x, x^2)/(x*y)"
assert maple_code(pw / 3) == "(1/3)*piecewise(x < 1, x, x^2)"
def test_imag():
I = S('I')
assert maple_code(I) == "I"
assert maple_code(5 * I) == "5*I"
assert maple_code((S(3) / 2) * I) == "(3/2)*I"
assert maple_code(3 + 4 * I) == "3 + 4*I"
def test_maple_matrix_assign_to():
A = Matrix([[1, 2, 3]])
assert (maple_code(
A, assign_to="a") == "a := Matrix([[1, 2, 3]], storage = rectangular)")
A = Matrix([[1, 2], [3, 4]])
assert (maple_code(A, assign_to="A") ==
"A := Matrix([[1, 2], [3, 4]], storage = rectangular)")
def test_maple_matrix_assign_to_more():
# assigning to Symbol or MatrixSymbol requires lhs/rhs match
A = Matrix([[1, 2, 3]])
B = MatrixSymbol('B', 1, 3)
C = MatrixSymbol('C', 2, 3)
assert maple_code(
A, assign_to=B) == "B := Matrix([[1, 2, 3]], storage = rectangular)"
raises(ValueError, lambda: maple_code(A, assign_to=x))
raises(ValueError, lambda: maple_code(A, assign_to=C))
def test_maple_matrix_elements():
A = Matrix([[x, 2, x * y]])
assert maple_code(A[0, 0]**2 + A[0, 1] + A[0, 2]) == "x^2 + x*y + 2"
AA = MatrixSymbol('AA', 1, 3)
assert maple_code(AA) == "AA"
assert maple_code(AA[0, 0] ** 2 + sin(AA[0, 1]) + AA[0, 2]) == \
"sin(AA[1, 2]) + AA[1, 1]^2 + AA[1, 3]"
assert maple_code(sum(AA)) == "AA[1, 1] + AA[1, 2] + AA[1, 3]"
def test_MatrixElement_printing():
# test cases for issue #11821
A = MatrixSymbol("A", 1, 3)
B = MatrixSymbol("B", 1, 3)
assert (maple_code(A[0, 0]) == "A[1, 1]")
assert (maple_code(3 * A[0, 0]) == "3*A[1, 1]")
F = A - B
assert (maple_code(F[0, 0]) == "A[1, 1] - B[1, 1]")
def test_maple_piecewise():
expr = Piecewise((x, x < 1), (x**2, True))
assert maple_code(expr) == "piecewise(x < 1, x, x^2)"
assert maple_code(expr, assign_to="r") == ("r := piecewise(x < 1, x, x^2)")
expr = Piecewise((x**2, x < 1), (x**3, x < 2), (x**4, x < 3), (x**5, True))
expected = "piecewise(x < 1, x^2, x < 2, x^3, x < 3, x^4, x^5)"
assert maple_code(expr) == expected
assert maple_code(expr, assign_to="r") == "r := " + expected
# Check that Piecewise without a True (default) condition error
expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
raises(ValueError, lambda: maple_code(expr))
def test_hadamard():
A = MatrixSymbol('A', 3, 3)
B = MatrixSymbol('B', 3, 3)
v = MatrixSymbol('v', 3, 1)
h = MatrixSymbol('h', 1, 3)
C = HadamardProduct(A, B)
assert maple_code(C) == "A*B"
assert maple_code(C * v) == "(A*B).v"
# HadamardProduct is higher than dot product.
assert maple_code(h * C * v) == "h.(A*B).v"
assert maple_code(C * A) == "(A*B).A"
# mixing Hadamard and scalar strange b/c we vectorize scalars
assert maple_code(C * x * y) == "x*y*(A*B)"
def test_Matrices():
assert maple_code(Matrix(1, 1, [10])) == \
'Matrix([[10]], storage = rectangular)'
A = Matrix([[1, sin(x / 2), abs(x)], [0, 1, pi], [0, exp(1), ceiling(x)]])
expected = \
'Matrix(' \
'[[1, sin((1/2)*x), abs(x)],' \
' [0, 1, Pi],' \
' [0, exp(1), ceil(x)]], ' \
'storage = rectangular)'
assert maple_code(A) == expected
# row and columns
assert maple_code(A[:, 0]) == \
'Matrix([[1], [0], [0]], storage = rectangular)'
assert maple_code(A[0, :]) == \
'Matrix([[1, sin((1/2)*x), abs(x)]], storage = rectangular)'
assert maple_code(Matrix([[x, x - y, -y]])) == \
'Matrix([[x, x - y, -y]], storage = rectangular)'
# empty matrices
assert maple_code(Matrix(0, 0, [])) == \
'Matrix([], storage = rectangular)'
assert maple_code(Matrix(0, 3, [])) == \
'Matrix([], storage = rectangular)'
def test_boolean():
assert maple_code(x & y) == "x && y"
assert maple_code(x | y) == "x || y"
assert maple_code(~x) == "!x"
assert maple_code(x & y & z) == "x && y && z"
assert maple_code(x | y | z) == "x || y || z"
assert maple_code((x & y) | z) == "z || x && y"
assert maple_code((x | y) & z) == "z && (x || y)"
def test_constants():
assert maple_code(pi) == "Pi"
assert maple_code(oo) == "infinity"
assert maple_code(-oo) == "-infinity"
assert maple_code(S.NegativeInfinity) == "-infinity"
assert maple_code(S.NaN) == "undefined"
assert maple_code(S.Exp1) == "exp(1)"
assert maple_code(exp(1)) == "exp(1)"
def test_Rational():
assert maple_code(Rational(3, 7)) == "3/7"
assert maple_code(Rational(18, 9)) == "2"
assert maple_code(Rational(3, -7)) == "-3/7"
assert maple_code(Rational(-3, -7)) == "3/7"
assert maple_code(x + Rational(3, 7)) == "x + 3/7"
assert maple_code(Rational(3, 7) * x) == '(3/7)*x'
def test_Relational():
assert maple_code(Eq(x, y)) == "x = y"
assert maple_code(Ne(x, y)) == "x <> y"
assert maple_code(Le(x, y)) == "x <= y"
assert maple_code(Lt(x, y)) == "x < y"
assert maple_code(Gt(x, y)) == "x > y"
assert maple_code(Ge(x, y)) == "x >= y"
def test_sparse():
M = SparseMatrix(5, 6, {})
M[2, 2] = 10
M[1, 2] = 20
M[1, 3] = 22
M[0, 3] = 30
M[3, 0] = x * y
assert (maple_code(M) == "Matrix([[0, 0, 0, 30, 0, 0],"
" [0, 0, 20, 22, 0, 0],"
" [0, 0, 10, 0, 0, 0],"
" [x*y, 0, 0, 0, 0, 0],"
" [0, 0, 0, 0, 0, 0]], "
"storage = sparse)")
def test_MatrixSymbol():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, n)
assert maple_code(A * B) == "A.B"
assert maple_code(B * A) == "B.A"
assert maple_code(2 * A * B) == "2*A.B"
assert maple_code(B * 2 * A) == "2*B.A"
assert maple_code(
A * (B + 3 * Identity(n))) == "A.(3*Matrix(n, shape = identity) + B)"
assert maple_code(A**(x**2)) == "MatrixPower(A, x^2)"
assert maple_code(A**3) == "MatrixPower(A, 3)"
assert maple_code(A**(S.Half)) == "MatrixPower(A, 1/2)"
def test_mix_number_pow_symbols():
assert maple_code(pi**3) == 'Pi^3'
assert maple_code(x**2) == 'x^2'
assert maple_code(x**(pi**3)) == 'x^(Pi^3)'
assert maple_code(x**y) == 'x^y'
assert maple_code(x**(y**z)) == 'x^(y^z)'
assert maple_code((x**y)**z) == '(x^y)^z'
def test_mix_number_pow_symbols():
assert maple_code(pi**3) == "Pi^3"
assert maple_code(x**2) == "x^2"
assert maple_code(x**(pi**3)) == "x^(Pi^3)"
assert maple_code(x**y) == "x^y"
assert maple_code(x**(y**z)) == "x^(y^z)"
assert maple_code((x**y)**z) == "(x^y)^z"
def test_containers():
assert maple_code([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \
"[1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]"
assert maple_code((1, 2, (3, 4))) == "[1, 2, [3, 4]]"
assert maple_code([1]) == "[1]"
assert maple_code((1, )) == "[1]"
assert maple_code(Tuple(*[1, 2, 3])) == "[1, 2, 3]"
assert maple_code((1, x * y, (3, x**2))) == "[1, x*y, [3, x^2]]"
# scalar, matrix, empty matrix and empty list
assert maple_code((1, eye(3), Matrix(0, 0, []), [])) == \
"[1, Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]], storage = rectangular), Matrix([], storage = rectangular), []]"
def test_Pow():
assert maple_code(x**3) == "x^3"
assert maple_code(x**(y**3)) == "x^(y^3)"
assert maple_code((x**3)**y) == "(x^3)^y"
assert maple_code(x**Rational(2, 3)) == 'x^(2/3)'
g = implemented_function('g', Lambda(x, 2 * x))
assert maple_code(1 / (g(x) * 3.5) ** (x - y ** x) / (x ** 2 + y)) == \
"(3.5*2*x)^(-x + y^x)/(x^2 + y)"
# For issue 14160
assert maple_code(
Mul(-2,
x,
Pow(Mul(y, y, evaluate=False), -1, evaluate=False),
evaluate=False)) == '-2*x/(y*y)'
def test_basic_ops():
assert maple_code(x * y) == "x*y"
assert maple_code(x + y) == "x + y"
assert maple_code(x - y) == "x - y"
assert maple_code(-x) == "-x"
def test_Function():
assert maple_code(sin(x)**cos(x)) == "sin(x)^cos(x)"
assert maple_code(abs(x)) == "abs(x)"
assert maple_code(ceiling(x)) == "ceil(x)"
def test_specfun():
assert maple_code('asin(x)') == 'arcsin(x)'
assert maple_code(besseli(x, y)) == 'BesselI(x, y)'
def test_maple_derivatives():
f = Function('f')
assert maple_code(f(x).diff(x)) == 'diff(f(x), x)'
assert maple_code(f(x).diff(x, 2)) == 'diff(f(x), x$2)'
def test_maple_noninline():
source = maple_code((x + y) / Catalan, assign_to='me', inline=False)
expected = "me := (x + y)/Catalan"
assert source == expected
def test_1_over_x_and_sqrt():
# 1.0 and 0.5 would do something different in regular StrPrinter,
# but these are exact in IEEE floating point so no different here.
assert maple_code(1 / x) == '1/x'
assert maple_code(x**-1) == maple_code(x**-1.0) == '1/x'
assert maple_code(1 / sqrt(x)) == '1/sqrt(x)'
assert maple_code(x**-S.Half) == maple_code(x**-0.5) == '1/sqrt(x)'
assert maple_code(sqrt(x)) == 'sqrt(x)'
assert maple_code(x**S.Half) == maple_code(x**0.5) == 'sqrt(x)'
assert maple_code(1 / pi) == '1/Pi'
assert maple_code(pi**-1) == maple_code(pi**-1.0) == '1/Pi'
assert maple_code(pi**-0.5) == '1/sqrt(Pi)'
def test_maple_boolean():
assert maple_code(True) == "true"
assert maple_code(S.true) == "true"
assert maple_code(False) == "false"
assert maple_code(S.false) == "false"
def test_maple_not_supported():
assert maple_code(S.ComplexInfinity) == ("# Not supported in maple:\n"
"# ComplexInfinity\n"
"zoo") # PROBLEM
def test_mix_number_mult_symbols():
assert maple_code(3 * x) == "3*x"
assert maple_code(pi * x) == "Pi*x"
assert maple_code(3 / x) == "3/x"
assert maple_code(pi / x) == "Pi/x"
assert maple_code(x / 3) == '(1/3)*x'
assert maple_code(x / pi) == "x/Pi"
assert maple_code(x * y) == "x*y"
assert maple_code(3 * x * y) == "3*x*y"
assert maple_code(3 * pi * x * y) == "3*Pi*x*y"
assert maple_code(x / y) == "x/y"
assert maple_code(3 * x / y) == "3*x/y"
assert maple_code(x * y / z) == "x*y/z"
assert maple_code(x / y * z) == "x*z/y"
assert maple_code(1 / x / y) == "1/(x*y)"
assert maple_code(2 * pi * x / y / z) == "2*Pi*x/(y*z)"
assert maple_code(3 * pi / x) == "3*Pi/x"
assert maple_code(S(3) / 5) == "3/5"
assert maple_code(S(3) / 5 * x) == '(3/5)*x'
assert maple_code(x / y / z) == "x/(y*z)"
assert maple_code((x + y) / z) == "(x + y)/z"
assert maple_code((x + y) / (z + x)) == "(x + y)/(x + z)"
assert maple_code((x + y) / EulerGamma) == '(x + y)/gamma'
assert maple_code(x / 3 / pi) == '(1/3)*x/Pi'
assert maple_code(S(3) / 5 * x * y / pi) == '(3/5)*x*y/Pi'
def test_maple_matrix_1x1():
A = Matrix([[3]])
assert maple_code(
A, assign_to='B') == "B := Matrix([[3]], storage = rectangular)"
