Maple cheat sheet

• To substitute a function in an "output with unknowns functions"

allvalues(pdsolve(4*H(u, u1)*(diff(H(u, u1), u1))+4*(diff(H(u, u1), u))*u1-u1)); simplify(allvalues(eval(%, _F1 = ((x)->x) ) ) )

another example

Sol := pdsolve(LieDerivative(L2, F(x, u[], u[1], u[1, 1]))); 
inv11 := eval(rhs(Sol), _F1 = ((x, y)-> x))

• To extract components of vector fields, metrics, tensors, 1-forms

DGinfo(G, "CoefficientSet")

• To simplify with external assumptions

simplify(a*y+x, {-a*y+x = 0})

• Extract coefficients of a polynomial

coeffs(4*x*y^5+x^2+x*y+y, [x, y], 't')

in $t$ the terms are saved

• Generate the basis of 2-forms

base2formas := GenerateForms([baseformas], [2])

• To see the frames currently defined

DGinfo("FrameNames")

• To avoid, if possible, the RootOf:

allvalues()