def test_Mul():
A, B, C, D = symbols('A B C D', commutative=False)
assert mcode(x*y*z) == "x*y*z"
assert mcode(x*y*A) == "x*y*A"
assert mcode(x*y*A*B) == "x*y*A**B"
assert mcode(x*y*A*B*C) == "x*y*A**B**C"
assert mcode(x*A*B*(C + D)*A*y) == "x*y*A**B**(C + D)**A"
def test_Integral():
assert mcode(Integral(sin(sin(x)), x)) == "Hold[Integrate[Sin[Sin[x]], x]]"
assert mcode(Integral(exp(-x**2 - y**2),
(x, -oo, oo),
(y, -oo, oo))) == \
"Hold[Integrate[E^(-x^2 - y^2), {x, -Infinity, Infinity}, " \
"{y, -Infinity, Infinity}]]"
def test_Sum():
assert mcode(Sum(sin(x), (x, 0, 10))) == "Hold[Sum[Sin[x], {x, 0, 10}]]"
assert mcode(Sum(exp(-x**2 - y**2),
(x, -oo, oo),
(y, -oo, oo))) == \
"Hold[Sum[E^(-x^2 - y^2), {x, -Infinity, Infinity}, " \
"{y, -Infinity, Infinity}]]"
def test_Pow():
assert mcode(x**3) == "x^3"
assert mcode(x**(y**3)) == "x^(y^3)"
assert mcode(1/(f(x)*3.5)**(x - y**x)/(x**2 + y)) == \
"(3.5*f[x])^(-x + y^x)/(x^2 + y)"
assert mcode(x**-1.0) == 'x^(-1.0)'
assert mcode(x**Rational(2, 3)) == 'x^(2/3)'
def test_Limit():
e = Limit(sin(x)/x, x, 0)
assert mcode(e) == "Hold[Limit[Sin[x]/x, x -> 0, Direction -> -1]]"
e = Limit(sin(x)/x, x, 0, "-")
assert mcode(e) == "Hold[Limit[Sin[x]/x, x -> 0, Direction -> 1]]"
e = Limit(sin(x)/x, x, 0, "real")
assert mcode(e) == "Hold[Limit[Sin[x]/x, x -> 0, Direction -> Reals]]"
def test_Pow():
assert mcode(x**3) == "x.^3"
assert mcode(x**(y**3)) == "x.^(y.^3)"
assert mcode(x**Rational(2, 3)) == 'x.^(2/3)'
g = implemented_function('g', Lambda(x, 2*x))
assert mcode(1/(g(x)*3.5)**(x - y**x)/(x**2 + y)) == \
"(3.5*2*x).^(-x + y.^x)./(x.^2 + y)"
def test_containers():
assert mcode([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \
"{1, 2, 3, {4, 5, {6, 7}}, 8, {9, 10}, 11}"
assert mcode((1, 2, (3, 4))) == "{1, 2, {3, 4}}"
assert mcode([1]) == "{1}"
assert mcode((1,)) == "{1}"
assert mcode(Tuple(*[1, 2, 3])) == "{1, 2, 3}"
def test_Matrix():
assert mcode(Matrix()) == '{}'
m = Matrix([[1, 2], [3, 4444]])
assert mcode(m) == mcode(m.as_immutable()) == '{{1, 2}, {3, 4444}}'
m = SparseMatrix(m)
assert mcode(m) == mcode(m.as_immutable()) == '{{1, 2}, {3, 4444}}'
def test_octave_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 mcode(A, assign_to=B) == "B = [1 2 3];"
pytest.raises(ValueError, lambda: mcode(A, assign_to=x))
pytest.raises(ValueError, lambda: mcode(A, assign_to=C))
def test_octave_matrix_1x1():
A = Matrix([[3]])
B = MatrixSymbol('B', 1, 1)
C = MatrixSymbol('C', 1, 2)
assert mcode(A, assign_to=B) == "B = 3;"
# FIXME?
# assert mcode(A, assign_to=x) == "x = 3;"
pytest.raises(ValueError, lambda: mcode(A, assign_to=C))
def test_octave_matrix_elements():
A = Matrix([[x, 2, x*y]])
assert mcode(A[0, 0]**2 + A[0, 1] + A[0, 2]) == "x.^2 + x.*y + 2"
A = MatrixSymbol('AA', 1, 3)
assert mcode(A) == "AA"
assert mcode(A[0, 0]**2 + sin(A[0, 1]) + A[0, 2]) == \
"sin(AA(1, 2)) + AA(1, 1).^2 + AA(1, 3)"
assert mcode(sum(A)) == "AA(1, 1) + AA(1, 2) + AA(1, 3)"
def test_octave_not_supported():
assert mcode(zoo) == (
"% Not supported in Octave:\n"
"% ComplexInfinity\n"
"zoo"
)
f = Function('f')
assert mcode(f(x).diff(x)) == (
"% Not supported in Octave:\n"
"% Derivative\n"
"Derivative(f(x), x)"
)
def test_haramard():
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 mcode(C) == "A.*B"
assert mcode(C*v) == "(A.*B)*v"
assert mcode(h*C*v) == "h*(A.*B)*v"
assert mcode(C*A) == "(A.*B)*A"
# mixing Hadamard and scalar strange b/c we vectorize scalars
assert mcode(C*x*y) == "(x.*y)*(A.*B)"
def test_boolean():
assert mcode(True) == "true"
assert mcode(False) == "false"
assert mcode(x & y) == "x & y"
assert mcode(x | y) == "x | y"
assert mcode(~x) == "~x"
assert mcode(x & y & z) == "x & y & z"
assert mcode(x | y | z) == "x | y | z"
assert mcode((x & y) | z) == "z | x & y"
assert mcode((x | y) & z) == "z & (x | y)"
def test_octave_noninline():
source = mcode((x+y)/Catalan, assign_to='me', inline=False)
expected = (
"Catalan = 0.915965594177219;\n"
"me = (x + y)/Catalan;"
)
assert source == expected
def test_constants():
assert mcode(pi) == "pi"
assert mcode(oo) == "inf"
assert mcode(-oo) == "-inf"
assert mcode(nan) == "NaN"
assert mcode(E) == "exp(1)"
assert mcode(exp(1)) == "exp(1)"
assert mcode(true) == "true"
assert mcode(false) == "false"
def test_octave_piecewise():
expr = Piecewise((x, x < 1), (x**2, True))
assert mcode(expr) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))"
assert mcode(expr, assign_to="r") == (
"r = ((x < 1).*(x) + (~(x < 1)).*(x.^2));")
assert mcode(expr, assign_to="r", inline=False) == (
"if (x < 1)\n"
" r = x;\n"
"else\n"
" r = x.^2;\n"
"end")
expr = Piecewise((x**2, x < 1), (x**3, x < 2), (x**4, x < 3), (x**5, True))
expected = ("((x < 1).*(x.^2) + (~(x < 1)).*( ...\n"
"(x < 2).*(x.^3) + (~(x < 2)).*( ...\n"
"(x < 3).*(x.^4) + (~(x < 3)).*(x.^5))))")
assert mcode(expr) == expected
assert mcode(expr, assign_to="r") == "r = " + expected + ";"
assert mcode(expr, assign_to="r", inline=False) == (
"if (x < 1)\n"
" r = x.^2;\n"
"elseif (x < 2)\n"
" r = x.^3;\n"
"elseif (x < 3)\n"
" r = x.^4;\n"
"else\n"
" r = x.^5;\n"
"end")
# Check that Piecewise without a True (default) condition error
expr = Piecewise((x, x < 1), (x**2, x > 1), (sin(x), x > 0))
pytest.raises(ValueError, lambda: mcode(expr))
def test_MatrixSymbol():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, n)
assert mcode(A*B) == "A*B"
assert mcode(B*A) == "B*A"
assert mcode(2*A*B) == "2*A*B"
assert mcode(B*2*A) == "2*B*A"
assert mcode(A*(B + 3*Identity(n))) == "A*(B + 3*eye(n))"
assert mcode(A**(x**2)) == "A^(x.^2)"
assert mcode(A**3) == "A^3"
assert mcode(A**Rational(1, 2)) == "A^(1/2)"
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 mcode(M) == (
"sparse([4 2 3 1 2], [1 3 3 4 4], [x.*y 20 10 30 22], 5, 6)"
)
def test_containers():
assert mcode([1, 2, 3, [4, 5, [6, 7]], 8, [9, 10], 11]) == \
"{1, 2, 3, {4, 5, {6, 7}}, 8, {9, 10}, 11}"
assert mcode((1, 2, (3, 4))) == "{1, 2, {3, 4}}"
assert mcode([1]) == "{1}"
assert mcode((1,)) == "{1}"
assert mcode(Tuple(*[1, 2, 3])) == "{1, 2, 3}"
assert mcode((1, x*y, (3, x**2))) == "{1, x.*y, {3, x.^2}}"
# scalar, matrix, empty matrix and empty list
assert mcode((1, eye(3), Matrix(0, 0, []), [])) == "{1, [1 0 0;\n0 1 0;\n0 0 1], [], {}}"
def test_mix_number_pow_symbols():
assert mcode(pi**3) == 'pi^3'
assert mcode(x**2) == 'x.^2'
assert mcode(x**(pi**3)) == 'x.^(pi^3)'
assert mcode(x**y) == 'x.^y'
assert mcode(x**(y**z)) == 'x.^(y.^z)'
assert mcode((x**y)**z) == '(x.^y).^z'
def test_constants():
assert mcode(pi) == "Pi"
assert mcode(oo) == "Infinity"
assert mcode(-oo) == "-Infinity"
assert mcode(EulerGamma) == "EulerGamma"
assert mcode(Catalan) == "Catalan"
assert mcode(E) == "E"
def test_Rational():
assert mcode(Rational(3, 7)) == "3/7"
assert mcode(Rational(18, 9)) == "2"
assert mcode(Rational(3, -7)) == "-3/7"
assert mcode(Rational(-3, -7)) == "3/7"
assert mcode(x + Rational(3, 7)) == "x + 3/7"
assert mcode(Rational(3, 7)*x) == "3*x/7"
def test_trick_indent_with_end_else_words():
# words starting with "end" or "else" do not confuse the indenter
t1 = Symbol('endless')
t2 = Symbol('elsewhere')
pw = Piecewise((t1, x < 0), (t2, x <= 1), (1, True))
assert mcode(pw, inline=False) == (
"if (x < 0)\n"
" endless\n"
"elseif (x <= 1)\n"
" elsewhere\n"
"else\n"
" 1\n"
"end")
def test_Matrices():
assert mcode(Matrix(1, 1, [10])) == "10"
A = Matrix([[1, sin(x/2), abs(x)],
[0, 1, pi],
[0, exp(1), ceiling(x)]])
expected = ("[1 sin(x/2) abs(x);\n"
"0 1 pi;\n"
"0 exp(1) ceil(x)]")
assert mcode(A) == expected
# row and columns
assert mcode(A[:, 0]) == "[1; 0; 0]"
assert mcode(A[0, :]) == "[1 sin(x/2) abs(x)]"
# empty matrices
assert mcode(Matrix(0, 0, [])) == '[]'
assert mcode(Matrix(0, 3, [])) == 'zeros(0, 3)'
# annoying to read but correct
assert mcode(Matrix([[x, x - y, -y]])) == "[x x - y -y]"
def test_symbols():
assert mcode(x) == "x"
d = Dummy("d")
assert mcode(d) == "Subscript[d, %s]" % d.dummy_index
def test_basic_ops():
assert mcode(x * y) == "x.*y"
assert mcode(x + y) == "x + y"
assert mcode(x - y) == "x - y"
assert mcode(-x) == "-x"
def test_octave_boolean():
assert mcode(True) == "true"
assert mcode(S.true) == "true"
assert mcode(False) == "false"
assert mcode(S.false) == "false"
def test_octave_piecewise_times_const():
pw = Piecewise((x, x < 1), (x**2, True))
assert mcode(2 * pw) == "2*((x < 1).*(x) + (~(x < 1)).*(x.^2))"
assert mcode(pw / x) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))./x"
assert mcode(pw / (x * y)) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))./(x.*y)"
assert mcode(pw / 3) == "((x < 1).*(x) + (~(x < 1)).*(x.^2))/3"
def test_Integer():
assert mcode(Integer(67)) == "67"
assert mcode(Integer(-1)) == "-1"
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 mcode(A) == "[1 sin(2./x) 3*pi./(5*x)]"
assert mcode(A.T) == "[1; sin(2./x); 3*pi./(5*x)]"
def test_imag():
assert mcode(I) == "1i"
assert mcode(5 * I) == "5i"
assert mcode((Rational(3, 2)) * I) == "3*1i/2"
assert mcode(3 + 4 * I) == "3 + 4i"
def test_AlgebraicElement():
r = RootOf(x**7 + 3 * x - 1, 3)
K = QQ.algebraic_field(r)
a = K([1, 2, 3, 0, 1])
assert mcode(a) == ('AlgebraicNumber[Root[#^7 + 3*# - 1 &, 4],'
' {1, 0, 3, 2, 1}]')
def test_Piecewise():
g = Piecewise((0, Or(x <= -1, x >= 1)), (1 - x, x > 0), (1 + x, True))
assert (mcode(g) == 'Piecewise[{{0, x >= 1 || x <= -1}, '
'{-x + 1, x > 0}, {x + 1, True}}]')
def test_Matrix():
assert mcode(Matrix()) == '{}'
assert mcode(Matrix([[1, 2], [3, 4444]])) == '{{1, 2}, {3, 4444}}'
def test_AlgebraicNumber():
r = RootOf(x**7 + 3 * x - 1, 3)
a = AlgebraicNumber(r, (1, 2, 3, 0, 1))
assert mcode(a) == ('AlgebraicNumber[Root[#^7 + 3*# - 1 &, 4],'
' {1, 0, 3, 2, 1}]')
def test_mix_number_mult_symbols():
assert mcode(3*x) == "3*x"
assert mcode(pi*x) == "pi*x"
assert mcode(3/x) == "3./x"
assert mcode(pi/x) == "pi./x"
assert mcode(x/3) == "x/3"
assert mcode(x/pi) == "x/pi"
assert mcode(x*y) == "x.*y"
assert mcode(x*y, order="none") == "x.*y"
assert mcode(3*x*y) == "3*x.*y"
assert mcode(3*pi*x*y) == "3*pi*x.*y"
assert mcode(x/y) == "x./y"
assert mcode(x*y**-2) == "x./y.^2"
assert mcode(3*x/y) == "3*x./y"
assert mcode(x*y/z) == "x.*y./z"
assert mcode(x/y*z) == "x.*z./y"
assert mcode(1/x/y) == "1./(x.*y)"
assert mcode(2*pi*x/y/z) == "2*pi*x./(y.*z)"
assert mcode(3*pi/x) == "3*pi./x"
assert mcode(Rational(3, 5)) == "3/5"
assert mcode(Rational(3, 5)*x) == "3*x/5"
assert mcode(x/y/z) == "x./(y.*z)"
assert mcode((x+y)/z) == "(x + y)./z"
assert mcode((x+y)/(z+x)) == "(x + y)./(x + z)"
assert mcode((x+y)/EulerGamma) == "(x + y)/0.5772156649015329"
assert mcode(x/3/pi) == "x/(3*pi)"
assert mcode(Rational(3, 5)*x*y/pi) == "3*x.*y/(5*pi)"
def test_specfun():
for f in [besselj, bessely, besseli, besselk]:
assert mcode(f(n, x)) == f.__name__ + '(n, x)'
assert mcode(hankel1(n, x)) == 'besselh(n, 1, x)'
assert mcode(hankel2(n, x)) == 'besselh(n, 2, x)'
assert mcode(airyai(x)) == 'airy(0, x)'
assert mcode(airyaiprime(x)) == 'airy(1, x)'
assert mcode(airybi(x)) == 'airy(2, x)'
assert mcode(airybiprime(x)) == 'airy(3, x)'
assert mcode(uppergamma(n, x)) == 'gammainc(x, n, \'upper\')'
assert mcode(lowergamma(n, x)) == 'gammainc(x, n, \'lower\')'
assert mcode(jn(n,
x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
assert mcode(yn(n,
x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
assert mcode(Chi(x)) == 'coshint(x)'
assert mcode(Ci(x)) == 'cosint(x)'
assert mcode(laguerre(n, x)) == 'laguerreL(n, x)'
assert mcode(li(x)) == 'logint(x)'
assert mcode(loggamma(x)) == 'gammaln(x)'
assert mcode(polygamma(n, x)) == 'psi(n, x)'
assert mcode(Shi(x)) == 'sinhint(x)'
assert mcode(Si(x)) == 'sinint(x)'
assert mcode(LambertW(x)) == 'lambertw(x)'
assert mcode(LambertW(x, n)) == 'lambertw(n, x)'
assert mcode(zeta(x)) == 'zeta(x)'
assert mcode(zeta(x,
y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
def test_Function():
assert mcode(f(x, y, z)) == "f[x, y, z]"
assert mcode(sin(x)**cos(x)) == "Sin[x]^Cos[x]"
assert mcode(sign(x)) == "Sign[x]"
assert mcode(atanh(x), user_functions={"atanh": "ArcTanh"}) == "ArcTanh[x]"
assert (mcode(meijerg(((1, 1), (3, 4)), ((1, ), ()),
x)) == "MeijerG[{{1, 1}, {3, 4}}, {{1}, {}}, x]")
assert (mcode(hyper((1, 2, 3), (3, 4),
x)) == "HypergeometricPFQ[{1, 2, 3}, {3, 4}, x]")
assert mcode(Min(x, y)) == "Min[x, y]"
assert mcode(Max(x, y)) == "Max[x, y]"
assert mcode(binomial(x, y)) == "Binomial[x, y]"
assert mcode(log(x)) == "Log[x]"
assert mcode(tan(x)) == "Tan[x]"
assert mcode(cot(x)) == "Cot[x]"
assert mcode(asin(x)) == "ArcSin[x]"
assert mcode(acos(x)) == "ArcCos[x]"
assert mcode(atan(x)) == "ArcTan[x]"
assert mcode(sinh(x)) == "Sinh[x]"
assert mcode(cosh(x)) == "Cosh[x]"
assert mcode(tanh(x)) == "Tanh[x]"
assert mcode(coth(x)) == "Coth[x]"
assert mcode(sech(x)) == "Sech[x]"
assert mcode(csch(x)) == "Csch[x]"
class myfunc1(Function):
@classmethod
def eval(cls, x):
pass
class myfunc2(Function):
@classmethod
def eval(cls, x, y):
pass
pytest.raises(
ValueError,
lambda: mcode(myfunc1(x), user_functions={"myfunc1": ["Myfunc1"]}))
assert mcode(myfunc1(x), user_functions={"myfunc1":
"Myfunc1"}) == "Myfunc1[x]"
assert mcode(myfunc2(x, y),
user_functions={"myfunc2": [(lambda *x: False, "Myfunc2")]
}) == "myfunc2[x, y]"
def test_constants_other():
assert mcode(2 * GoldenRatio) == "2*(1+sqrt(5))/2"
assert mcode(2 * Catalan) == "2*0.915965594177219"
assert mcode(2 * EulerGamma) == "2*0.5772156649015329"
def test_mix_number_mult_symbols():
assert mcode(3 * x) == "3*x"
assert mcode(pi * x) == "pi*x"
assert mcode(3 / x) == "3./x"
assert mcode(pi / x) == "pi./x"
assert mcode(x / 3) == "x/3"
assert mcode(x / pi) == "x/pi"
assert mcode(x * y) == "x.*y"
assert mcode(3 * x * y) == "3*x.*y"
assert mcode(3 * pi * x * y) == "3*pi*x.*y"
assert mcode(x / y) == "x./y"
assert mcode(3 * x / y) == "3*x./y"
assert mcode(x * y / z) == "x.*y./z"
assert mcode(x / y * z) == "x.*z./y"
assert mcode(1 / x / y) == "1./(x.*y)"
assert mcode(2 * pi * x / y / z) == "2*pi*x./(y.*z)"
assert mcode(3 * pi / x) == "3*pi./x"
assert mcode(Rational(3, 5)) == "3/5"
assert mcode(Rational(3, 5) * x) == "3*x/5"
assert mcode(x / y / z) == "x./(y.*z)"
assert mcode((x + y) / z) == "(x + y)./z"
assert mcode((x + y) / (z + x)) == "(x + y)./(x + z)"
assert mcode((x + y) / EulerGamma) == "(x + y)/0.5772156649015329"
assert mcode(x / 3 / pi) == "x/(3*pi)"
assert mcode(Rational(3, 5) * x * y / pi) == "3*x.*y/(5*pi)"
def test_special_matrices():
assert mcode(6 * Identity(3)) == "6*eye(3)"
def test_Relational():
assert mcode(Eq(x, y)) == 'x == y'
assert mcode(Ne(x, y / (1 + y**2))) == 'x != y/(y^2 + 1)'
assert mcode(Le(0, x**2)) == '0 <= x^2'
assert mcode(Gt(pi, 3, evaluate=False)) == 'Pi > 3'
def test_octave_noninline():
source = mcode((x + y) / Catalan, assign_to='me', inline=False)
expected = ("Catalan = 0.915965594177219;\n" "me = (x + y)/Catalan;")
assert source == expected
def test_Derivative():
assert mcode(Derivative(f(x), x, x)) == 'D[f[x], x, x]'
def test_octave_matrix_assign_to():
A = Matrix([[1, 2, 3]])
assert mcode(A, assign_to='a') == "a = [1 2 3];"
A = Matrix([[1, 2], [3, 4]])
assert mcode(A, assign_to='A') == "A = [1 2;\n3 4];"
def test_symbols():
assert mcode(x) == "x"
d = Dummy("d")
assert mcode(d) == "d%s" % d.dummy_index
def test_Function():
assert mcode(sin(x)**cos(x)) == "sin(x).^cos(x)"
assert mcode(abs(x)) == "abs(x)"
assert mcode(ceiling(x)) == "ceil(x)"
def test_basic_ops():
assert mcode(x*y) == "x.*y"
assert mcode(x + y) == "x + y"
assert mcode(x - y) == "x - y"
assert mcode(-x) == "-x"
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 mcode(1 / x) == '1./x'
assert mcode(x**-1) == mcode(x**-1.0) == '1./x'
assert mcode(1 / sqrt(x)) == '1./sqrt(x)'
assert mcode(x**-S.Half) == mcode(x**-0.5) == '1./sqrt(x)'
assert mcode(sqrt(x)) == 'sqrt(x)'
assert mcode(x**S.Half) == mcode(x**0.5) == 'sqrt(x)'
assert mcode(1 / pi) == '1/pi'
assert mcode(pi**-1) == mcode(pi**-1.0) == '1/pi'
assert mcode(pi**-0.5) == '1/sqrt(pi)'
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 mcode(1/x) == '1./x'
assert mcode(x**-1) == mcode(x**-1.0) == '1./x'
assert mcode(1/sqrt(x)) == '1./sqrt(x)'
assert mcode(x**Rational(-1, 2)) == mcode(x**-0.5) == '1./sqrt(x)'
assert mcode(sqrt(x)) == mcode(x**0.5) == 'sqrt(x)'
assert mcode(1/pi) == '1/pi'
assert mcode(pi**-1) == mcode(pi**-1.0) == '1/pi'
assert mcode(pi**-0.5) == '1/sqrt(pi)'
def test_Lambda():
f1 = Lambda(x, x**2)
assert mcode(f1) == "Function[{x}, x^2]"
f2 = Lambda((x, y), x + 2 * y)
assert mcode(f2) == "Function[{x, y}, x + 2*y]"
def test_specfun():
for f in [besselj, bessely, besseli, besselk]:
assert mcode(f(n, x)) == f.__name__ + '(n, x)'
assert mcode(hankel1(n, x)) == 'besselh(n, 1, x)'
assert mcode(hankel2(n, x)) == 'besselh(n, 2, x)'
assert mcode(airyai(x)) == 'airy(0, x)'
assert mcode(airyaiprime(x)) == 'airy(1, x)'
assert mcode(airybi(x)) == 'airy(2, x)'
assert mcode(airybiprime(x)) == 'airy(3, x)'
assert mcode(uppergamma(n, x)) == 'gammainc(x, n, \'upper\')'
assert mcode(lowergamma(n, x)) == 'gammainc(x, n, \'lower\')'
assert mcode(jn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
assert mcode(yn(n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
assert mcode(Chi(x)) == 'coshint(x)'
assert mcode(Ci(x)) == 'cosint(x)'
assert mcode(laguerre(n, x)) == 'laguerreL(n, x)'
assert mcode(li(x)) == 'logint(x)'
assert mcode(loggamma(x)) == 'gammaln(x)'
assert mcode(polygamma(n, x)) == 'psi(n, x)'
assert mcode(Shi(x)) == 'sinhint(x)'
assert mcode(Si(x)) == 'sinint(x)'
assert mcode(LambertW(x)) == 'lambertw(x)'
assert mcode(LambertW(x, n)) == 'lambertw(n, x)'
assert mcode(zeta(x)) == 'zeta(x)'
assert mcode(zeta(x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
def test_Booleans():
assert mcode(true) == "True"
assert mcode(false) == "False"
def test_Function():
assert mcode(sin(x) ** cos(x)) == "sin(x).^cos(x)"
assert mcode(abs(x)) == "abs(x)"
assert mcode(ceiling(x)) == "ceil(x)"
def test_RootOf():
p = Poly(x**3 + y * x + 1, x)
assert mcode(RootOf(p, 0)) == 'Root[#^3 + #*y + 1 &, 1]'
def test_RootSum():
r = RootSum(x**3 + x + 3, Lambda(y, log(y * z)))
assert mcode(r) == ("RootSum[Function[{x}, x^3 + x + 3], "
"Function[{y}, Log[y*z]]]")
