def test_erf2(): assert erf2(0, 0) == S.Zero assert erf2(x, x) == S.Zero assert erf2(nan, 0) == nan assert erf2(-oo, y) == erf(y) + 1 assert erf2(oo, y) == erf(y) - 1 assert erf2(x, oo) == 1 - erf(x) assert erf2(x, -oo) == -1 - erf(x) assert erf2(x, erf2inv(x, y)) == y assert erf2(-x, -y) == -erf2(x, y) assert erf2(-x, y) == erf(y) + erf(x) assert erf2(x, -y) == -erf(y) - erf(x) assert erf2(x, y).rewrite( 'fresnels') == erf(y).rewrite(fresnels) - erf(x).rewrite(fresnels) assert erf2(x, y).rewrite( 'fresnelc') == erf(y).rewrite(fresnelc) - erf(x).rewrite(fresnelc) assert erf2( x, y).rewrite('hyper') == erf(y).rewrite(hyper) - erf(x).rewrite(hyper) assert erf2(x, y).rewrite( 'meijerg') == erf(y).rewrite(meijerg) - erf(x).rewrite(meijerg) assert erf2( x, y).rewrite('uppergamma' ) == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma) assert erf2( x, y).rewrite('expint') == erf(y).rewrite(expint) - erf(x).rewrite(expint) assert erf2(I, 0).is_real is False assert erf2(0, 0).is_real is True assert expand_func(erf(x) + erf2(x, y)) == erf(y) assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y)) assert erf2(x, y).rewrite('erf') == erf(y) - erf(x) assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y) assert erf2(x, y).rewrite('erfi') == I * (erfi(I * x) - erfi(I * y)) assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1) assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2) assert erf2(x, y).diff(x) == -2 * exp(-x**2) / sqrt(pi) assert erf2(x, y).diff(y) == 2 * exp(-y**2) / sqrt(pi) raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3)) assert erf2(x, y).is_extended_real is None xr, yr = symbols('xr yr', extended_real=True) assert erf2(xr, yr).is_extended_real is True
def test_erf2(): assert erf2(0, 0) == S.Zero assert erf2(x, x) == S.Zero assert erf2(nan, 0) == nan assert erf2(-oo, y) == erf(y) + 1 assert erf2( oo, y) == erf(y) - 1 assert erf2( x, oo) == 1 - erf(x) assert erf2( x,-oo) == -1 - erf(x) assert erf2(x, erf2inv(x, y)) == y assert erf2(-x, -y) == -erf2(x,y) assert erf2(-x, y) == erf(y) + erf(x) assert erf2( x, -y) == -erf(y) - erf(x) assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels) assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc) assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper) assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg) assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma) assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint) assert erf2(I, 0).is_real is False assert erf2(0, 0).is_real is True assert expand_func(erf(x) + erf2(x, y)) == erf(y) assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y)) assert erf2(x, y).rewrite('erf') == erf(y) - erf(x) assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y) assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y)) raises(ArgumentIndexError, lambda: erfi(x).fdiff(3))
def test_erf2(): assert erf2(0, 0) is S.Zero assert erf2(x, x) is S.Zero assert erf2(nan, 0) is nan assert erf2(-oo, y) == erf(y) + 1 assert erf2(oo, y) == erf(y) - 1 assert erf2(x, oo) == 1 - erf(x) assert erf2(x, -oo) == -1 - erf(x) assert erf2(x, erf2inv(x, y)) == y assert erf2(-x, -y) == -erf2(x, y) assert erf2(-x, y) == erf(y) + erf(x) assert erf2(x, -y) == -erf(y) - erf(x) assert erf2(x, y).rewrite( "fresnels") == erf(y).rewrite(fresnels) - erf(x).rewrite(fresnels) assert erf2(x, y).rewrite( "fresnelc") == erf(y).rewrite(fresnelc) - erf(x).rewrite(fresnelc) assert erf2( x, y).rewrite("hyper") == erf(y).rewrite(hyper) - erf(x).rewrite(hyper) assert erf2(x, y).rewrite( "meijerg") == erf(y).rewrite(meijerg) - erf(x).rewrite(meijerg) assert erf2( x, y).rewrite("uppergamma" ) == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma) assert erf2( x, y).rewrite("expint") == erf(y).rewrite(expint) - erf(x).rewrite(expint) assert erf2(I, 0).is_real is False assert erf2(0, 0).is_real is True assert expand_func(erf(x) + erf2(x, y)) == erf(y) assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y)) assert erf2(x, y).rewrite("erf") == erf(y) - erf(x) assert erf2(x, y).rewrite("erfc") == erfc(x) - erfc(y) assert erf2(x, y).rewrite("erfi") == I * (erfi(I * x) - erfi(I * y)) assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1) assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2) assert erf2(x, y).diff(x) == -2 * exp(-(x**2)) / sqrt(pi) assert erf2(x, y).diff(y) == 2 * exp(-(y**2)) / sqrt(pi) raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3)) assert erf2(x, y).is_extended_real is None xr, yr = symbols("xr yr", extended_real=True) assert erf2(xr, yr).is_extended_real is True