[NumCS] Add more sympy tricks

semester3/numcs/parts/06_python/03_sympy-ex.py

@@ -13,3 +13,5 @@ roots = sp.roots(f)  # Computes the roots of function f analytically
 sp.hermite_poly(5)  # Creates hermite poly of degree 5
 sp.chebyshevt_poly(5)  # Creates chebychev T (first kind) poly of degree 5
 sp.chebyshevu_poly(5)  # Creates chebychev U (second kind) poly of degree 5
+# To print nicely rendered math expressions, you can use
+sp.init_printing()

semester3/numcs/parts/06_python/03_sympy-hessian.py

@@ -0,0 +1,14 @@
+import sympy as sp
+
+sym = sp.symbols("x, y")
+x, y = sym
+f = x**2 + y**2
+
+# Compute gradient and hessian
+grad = [sp.diff(f, k) for k in sym]
+hess = [[sp.diff(f, k).diff(j) for j in sym] for k in sym]
+
+# Compute jacobian of vector function
+x_m = sp.MatrixSymbol('x', 2, 1)
+two_d_func = sp.Matrix([[x_m[0]**2], [x_m[1]**2]])
+jacobi = two_d_func.jacobian(x_m)

semester3/numcs/parts/06_python/03_sympy.tex

@@ -4,3 +4,6 @@ Sympy can be used to do symbolic operations, i.e. similar to what we would do in
 
 You usually want to follow something like the below code:
 \inputcode{python}{parts/06_python/03_sympy-ex.py}
+
+It is also possible to compute the hessian and gradient using sympy (or also the jacobian):
+\inputcode{python}{parts/06_python/03_sympy-hessian.py}