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)"