# Revision history [back]

Use substitute_expression as follows:

sage: t = var('t')
sage: psi = function('psi',t)
sage: a = 3 * diff(psi)^2 - 2 * diff(psi) + 1
sage: a
3*D(psi)(t)^2 - 2*D(psi)(t) + 1
sage: a.substitute_expression(diff(psi)==t)
3*t^2 - 2*t + 1


Use [Edited to answer your second question as well.]

To replace diff(psi) by say t, use substitute_expression as follows:

sage: t = var('t')
sage: psi = function('psi',t)
sage: a = 3 * diff(psi)^2 - 2 * diff(psi) + 1
sage: a
3*D(psi)(t)^2 - 2*D(psi)(t) + 1
sage: a.substitute_expression(diff(psi)==t)
3*t^2 - 2*t + 1


To use the result of solve to perform replacement, do as follows:

sage: var('V V_f chi l psi')
sage: eq0 = V == V_f * cos(chi)
sage: eq1 = l * psi == V_f * sin(chi)
sage: sol = solve(eq0, V_f)
sage: sol
[V_f == V/cos(chi)]
sage: eq0.subs_expr(sol)
V == V


(Note that sol is a list with one element, which is an equation, and we want to use that equation for the replacement).

[Edited to answer your second question as well.]

To replace diff(psi) by say t, use substitute_expression as follows:

sage: t = var('t')
sage: psi = function('psi',t)
sage: a = 3 * diff(psi)^2 - 2 * diff(psi) + 1
sage: a
3*D(psi)(t)^2 - 2*D(psi)(t) + 1
sage: a.substitute_expression(diff(psi)==t)
3*t^2 - 2*t + 1


To use the result of solve to perform replacement, do as follows:

sage: var('V V_f chi l psi')
sage: eq0 = V == V_f * cos(chi)
sage: eq1 = l * psi == V_f * sin(chi)
sage: sol = solve(eq0, V_f)
sage: sol
[V_f == V/cos(chi)]
sage: eq0.subs_expr(sol)
V == V
sage: eq1.subs_expr(sol)
l*psi == V*sin(chi)/cos(chi)


(Note Note that sol is a list with containing one element, which is an equation, and we want to equation. We use that equation (item 0 of the list) for the replacement).replacement.