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23 lines
1.2 KiB
Python
23 lines
1.2 KiB
Python
import sympy as sp
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a, b = (0, 1)
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x, y = sp.symbols("x, y") # Create sympy symbols
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f = x**2 + 3 * x - 2 # Create your function
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# In the below, for 1D differentiation, we can omit the symbol and just use sp.diff(f)
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df = sp.diff(f, x) # Add more arguments for derivatives in other variables
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F = sp.integrate(f, x) # Integrates the function analytically in x
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F = sp.integrate(f, (x, a, b)) # Indefinite integral in x in interval [a, b]
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lambda_f = sp.lambdify(x, F) # Creates a lambda function of F in variable x
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lambda_f = sp.lambdify([x, y], F) # Creates a lambda function of F in variables x and y
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roots = sp.roots(f) # Computes the roots of function f analytically
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sp.hermite_poly(5) # Creates hermite poly of degree 5
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sp.chebyshevt_poly(5) # Creates chebychev T (first kind) poly of degree 5
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sp.chebyshevu_poly(5) # Creates chebychev U (second kind) poly of degree 5
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system = [f + y, x**3 + 2 * y, 3 * y - 2 * x] # A system of equations
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sp.solve(system) # Solves a system of equations algebraically
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sp.nsolve(
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system, [x, y], (0, 1)
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) # Input the system, the variables to solve in and interval
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# To print nicely rendered math expressions, you can use
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sp.init_printing()
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