1201.sagews

#Triangle case

s0, s1, sm, d0, d1, a0, a1, t0, t1, d, t = var('s0, s1, sm, d0, d1, a0, a1, t0, t1, d, t')
eq1 = sm == s0 + a0*t0
eq2 = s1 == sm + a1*t1
eq3 = d0 == s0*t0 + (0.5)*a0*t0^2
eq4 = d1 == sm*t1 + (0.5)*a1*t1^2
eq5 = d == d0 + d1
eq6 = t == t0 + t1
solve([eq1,eq2,eq3, eq4, eq5, eq6], sm, t0, t1, d0, d1, t)

[[d0 == -1/2*(2*a1*d + s0^2 - s1^2)/(a0 - a1), d1 == 1/2*(2*a0*d + s0^2 - s1^2)/(a0 - a1), sm == -sqrt(-2*a0*a1*d/(a0 - a1) + a0*s1^2/(a0 - a1) - a1*s0^2/(a0 - a1)), t == (sqrt(-a0 + a1)*a0*s1 - sqrt(-a0 + a1)*a1*s0 + (a0 - a1)*sqrt(2*a0*a1*d - a0*s1^2 + a1*s0^2))/(sqrt(-a0 + a1)*a0*a1), t0 == -((a0 - a1)*s0 - sqrt(-a0 + a1)*sqrt(2*a0*a1*d - a0*s1^2 + a1*s0^2))/(a0^2 - a0*a1), t1 == (sqrt(-a0 + a1)*s1 + sqrt(2*a0*a1*d - a0*s1^2 + a1*s0^2))/(sqrt(-a0 + a1)*a1)], [d0 == -1/2*(2*a1*d + s0^2 - s1^2)/(a0 - a1), d1 == 1/2*(2*a0*d + s0^2 - s1^2)/(a0 - a1), sm == sqrt(-2*a0*a1*d/(a0 - a1) + a0*s1^2/(a0 - a1) - a1*s0^2/(a0 - a1)), t == (sqrt(-a0 + a1)*a0*s1 - sqrt(-a0 + a1)*a1*s0 - (a0 - a1)*sqrt(2*a0*a1*d - a0*s1^2 + a1*s0^2))/(sqrt(-a0 + a1)*a0*a1), t0 == -((a0 - a1)*s0 + sqrt(-a0 + a1)*sqrt(2*a0*a1*d - a0*s1^2 + a1*s0^2))/(a0^2 - a0*a1), t1 == (sqrt(-a0 + a1)*s1 - sqrt(2*a0*a1*d - a0*s1^2 + a1*s0^2))/(sqrt(-a0 + a1)*a1)]]

#Weak case
s0, a, d, t = var('s0, a, d, t')
eq1 = d == s0*t + (1/2)*a*t^2
solve( [eq1], t )

[t == -(s0 + sqrt(2*a*d + s0^2))/a, t == -(s0 - sqrt(2*a*d + s0^2))/a]

from sage.symbolic.expression import Expression
help( Expression.solve )

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