CODEWITHSUNDEEP
pythonsympy
Natan Bittencourt
Natan Bittencourt

Reputation: 57

How to define a relational condition between symbols in Sympy

I want to calculate the limit of the exp((a-b)*x) function to x tending to infinity, where symbols a and b were defined as real and positive:

a = Symbol('a', real=True, positive=True)
b = Symbol('b', real=True, positive=True)

However, the limit depends on the difference a-b. If a<b, the limit is zero. If a=b, the limit is 1. If a>b, the limit is infinity. How to set these conditions?

Upvotes: 4

Views: 328

Answers (1)

smichr
smichr

Reputation: 19029

Let d = a - b then define a Piecewise with the limits for different conditions:

>>> oolim = lambda A: limit(exp(A*x),x,oo)
>>> f = Piecewise((oolim(d), a>b), (oolim(0), Eq(a,b)), (oolim(-d),True)); f
Piecewise((oo, a > b), (1, Eq(a, b)), (0, True))

You could substitute a value for a and/or b into f and the expression will evaluate/update:

>>> f.subs({a:3, b:5})
0

Upvotes: 1

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