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import sympy as sp
# See: http://docs.sympy.org/latest/tutorial/printing.html
sp.init_printing()
Make one symbol:
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x = sp.symbols("x")
Make several symbols at once:
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x, y, z = sp.symbols("x y z")
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x = sp.symbols("x")
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expr = sp.cos(x) + 1
expr.subs(x, 0)
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x = sp.symbols("x")
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sp.simplify((x**3 + x**2 - x - 1)/(x**2 + 2*x + 1))
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sp.simplify(sp.exp(sp.I * sp.pi) + sp.exp(sp.I * sp.pi))
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x = sp.symbols("x")
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sp.factor(x**3 - x**2 + x - 1)
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x = sp.symbols("x")
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sp.expand((x - 1)*(x**2 + 1))
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x = sp.symbols("x")
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eq = sp.Eq(x**2, 1)
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sp.solveset(eq, x)
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x, y, z = sp.symbols("x y z")
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sp.Derivative(sp.cos(x), x)
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diff = sp.Derivative(sp.cos(x), x)
diff
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diff.doit()
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sp.diff(sp.cos(x), x)
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expr = sp.exp(x*y*z)
diff = sp.Derivative(expr, x, y, y, z, z, z, z)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(sp.cos(x), x)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(3*sp.cos(x)**2, x)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(sp.exp(x**2), x)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(x**4, x, 2)
sp.Eq(diff, diff.doit())
or
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diff = sp.Derivative(x**4, x, x)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(x**4, x, 3)
sp.Eq(diff, diff.doit())
or
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diff = sp.Derivative(x**4, x, x, x)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(sp.exp(x*y), x, y)
sp.Eq(diff, diff.doit())
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diff = sp.Derivative(sp.exp(x*y*z), x, y, y, z, z, z, z)
sp.Eq(diff, diff.doit())
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x, y, z = sp.symbols("x y z")
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sp.Integral(sp.cos(x), x)
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integ = sp.Integral(sp.cos(x), x)
integ
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integ.doit()
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sp.integrate(sp.cos(x), x)
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integ = sp.Integral(sp.cos(x), x)
sp.Eq(integ, integ.doit())
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integ = sp.Integral(sp.cos(x), x)
sp.Eq(integ, integ.doit())
sp.oo means infinity.
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integ = sp.Integral(sp.cos(x), (x, -sp.oo, sp.oo))
sp.Eq(integ, integ.doit())
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integ = sp.Integral(sp.cos(x), (x, -sp.pi, sp.pi))
sp.Eq(integ, integ.doit())
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integ = sp.Integral(sp.exp(-x), (x, 0, sp.oo))
sp.Eq(integ, integ.doit())
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integ = sp.Integral(sp.cos(x), (x, -sp.oo, sp.oo), (x, -sp.oo, sp.oo))
sp.Eq(integ, integ.doit())
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integ = sp.Integral(sp.cos(x**2 + y**2), (x, -sp.oo, sp.oo), (y, -sp.oo, sp.oo))
sp.Eq(integ, integ.doit())