I have the following expression:
O = symbols('O', linear=True)
mu = symbols('mu')
zeta = symbols('zeta')
f = IndexedBase('f')
first_cc = Eq(f[0,0,1] - zeta*f[0,0,0], 0)
expression = -O*mu*zeta*f[0, 0, 0] + O*mu *f[0, 0, 1]
If equation first_cc is used, the expression should evaluate to 0. However, if I am doing this
pprint(expression.subs(first_cc.lhs, first_cc.rhs))
Nothing happens, I think because the equation is not explicitly written in terms of f[0,0,1] - zeta*f[0,0,0]`. In this specific case I can get around this by first simplifying:
pprint(simplify(expression).subs(first_cc.lhs, first_cc.rhs))
which gives 0 as expected. The problem is, that simplify doesnt always write expression in terms of first_cc.lhs, so this doest work for more complicated expression. How can I force sympy to use the information from first_cc?
The issue of trying to replace a sum with a symbol (or in your case, use a relationship in an expression) is an often asked question. Unless the sum appears exactly as given in subs -- not with a constant multiplying each term -- the substitution will fail. Solving for one of the symbols in the sum other than the one you want to have in the final expression is the usual solution, e.g.
>>> from sympy.abc import x,y,z
>>> rep= solve(Eq(x + z, y),exclude=[y],dict=True)[0]
>>> (2*x + 2*z).subs(rep)
2*y
In your case,
O = symbols('O', linear=True)
mu = symbols('mu')
zeta = symbols('zeta')
f = IndexedBase('f')
first_cc = Eq(f[0,0,1] - zeta*f[0,0,0], 0)
expression = -O*mu*zeta*f[0, 0, 0] + O*mu *f[0, 0, 1]
>>> expression.subs(solve(first_cc,dict=True)[0])
0
In this case there is no further (or preliminary) simplification that is necessary. I wouldn't be suprised if, for some case, an expand would be necessary to bring about the simplification to 0.