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Note that, as with the ugly var, the function() function injects its returned value in the namespace, even if it is used during a .subs() call:

sage: function('aze')
aze
sage: aze
aze

Why don't you just define B, E and H directly as symbolic functions ?

sage: var('T_s')
T_s
sage: B = function('B')(T_s)
sage: E = function('E')(T_s)
sage: H = function('H')(T_s)
sage: eq_B_TS = B == H/E
sage: diff(eq_B_TS, T_s)
D[0](B)(T_s) == -H(T_s)*D[0](E)(T_s)/E(T_s)^2 + D[0](H)(T_s)/E(T_s)
sage: B*E
B(T_s)*E(T_s)

Note that, as with the ugly var, the function() function injects its returned value in the namespace, even if it is used during a .subs() call:

sage: function('aze')
aze
sage: aze
aze

sage: b = function('qsd')(x)
sage: b
qsd(x)
sage: qsd
qsd

Why don't you just define B, E and H directly as symbolic functions ?

sage: var('T_s')
T_s
sage: B = function('B')(T_s)
sage: E = function('E')(T_s)
sage: H = function('H')(T_s)
sage: eq_B_TS = B == H/E
sage: diff(eq_B_TS, T_s)
D[0](B)(T_s) == -H(T_s)*D[0](E)(T_s)/E(T_s)^2 + D[0](H)(T_s)/E(T_s)
sage: B*E
B(T_s)*E(T_s)