83 lines
3.3 KiB
Python
83 lines
3.3 KiB
Python
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from sympy.core.function import (Derivative, Function)
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from sympy.core.numbers import (I, pi)
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from sympy.core.symbol import (Symbol, symbols)
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.trigonometric import (atan2, cos, sin)
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from sympy.simplify.simplify import simplify
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from sympy.abc import epsilon, mu
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from sympy.functions.elementary.exponential import exp
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from sympy.physics.units import speed_of_light, m, s
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from sympy.physics.optics import TWave
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from sympy.testing.pytest import raises
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c = speed_of_light.convert_to(m/s)
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def test_twave():
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A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
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n = Symbol('n') # Refractive index
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t = Symbol('t') # Time
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x = Symbol('x') # Spatial variable
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E = Function('E')
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w1 = TWave(A1, f, phi1)
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w2 = TWave(A2, f, phi2)
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assert w1.amplitude == A1
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assert w1.frequency == f
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assert w1.phase == phi1
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assert w1.wavelength == c/(f*n)
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assert w1.time_period == 1/f
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assert w1.angular_velocity == 2*pi*f
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assert w1.wavenumber == 2*pi*f*n/c
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assert w1.speed == c/n
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w3 = w1 + w2
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assert w3.amplitude == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2)
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assert w3.frequency == f
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assert w3.phase == atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2))
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assert w3.wavelength == c/(f*n)
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assert w3.time_period == 1/f
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assert w3.angular_velocity == 2*pi*f
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assert w3.wavenumber == 2*pi*f*n/c
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assert w3.speed == c/n
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assert simplify(w3.rewrite(sin) - w2.rewrite(sin) - w1.rewrite(sin)) == 0
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assert w3.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x)
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assert w3.rewrite(cos) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
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+ A2**2)*cos(pi*f*n*x*s/(149896229*m) - 2*pi*f*t + atan2(A1*sin(phi1)
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+ A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)))
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assert w3.rewrite(exp) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
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+ A2**2)*exp(I*(-2*pi*f*t + atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1)
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+ A2*cos(phi2)) + pi*s*f*n*x/(149896229*m)))
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w4 = TWave(A1, None, 0, 1/f)
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assert w4.frequency == f
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w5 = w1 - w2
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assert w5.amplitude == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2) + A2**2)
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assert w5.frequency == f
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assert w5.phase == atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1) - A2*cos(phi2))
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assert w5.wavelength == c/(f*n)
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assert w5.time_period == 1/f
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assert w5.angular_velocity == 2*pi*f
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assert w5.wavenumber == 2*pi*f*n/c
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assert w5.speed == c/n
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assert simplify(w5.rewrite(sin) - w1.rewrite(sin) + w2.rewrite(sin)) == 0
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assert w5.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x)
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assert w5.rewrite(cos) == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2)
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+ A2**2)*cos(-2*pi*f*t + atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1)
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- A2*cos(phi2)) + pi*s*f*n*x/(149896229*m))
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assert w5.rewrite(exp) == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2)
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+ A2**2)*exp(I*(-2*pi*f*t + atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1)
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- A2*cos(phi2)) + pi*s*f*n*x/(149896229*m)))
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w6 = 2*w1
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assert w6.amplitude == 2*A1
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assert w6.frequency == f
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assert w6.phase == phi1
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w7 = -w6
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assert w7.amplitude == -2*A1
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assert w7.frequency == f
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assert w7.phase == phi1
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raises(ValueError, lambda:TWave(A1))
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raises(ValueError, lambda:TWave(A1, f, phi1, t))
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