CODEWITHSUNDEEP
pythonsympy
bernd
bernd

Reputation: 121

Intelligent replacement using given terms in sympy

I'm using sympy to do symbolic calculations in Python3. My problem is to enforce a substitution of a known term a, defined as a product of x, y and z. See this minimal example:

import sympy as sp
from sympy.abc import a,x,y,z
expr=(x*y)/z**3 *(x**2*y**2-5*x*y*z+12*z**2)
print (expr) #as typed in line 3
print (expr.subs(x*y/z,a)) #only substitues the first factor to a**1/z**2
print (sp.simplify(expr)) #not any better

What I'd like to see is an expression of the form

a**3-5*a**2+12*a

with a=x*y/z Neither line 4 nor lines 5 or 6 do the trick. Can anyone help me? Thank you!

Upvotes: 2

Views: 254

Answers (2)

moorepants
moorepants

Reputation: 1869

Use expand first:

In [13]: expr.expand()
Out[13]: 
 3  3      2  2         
x ⋅y    5⋅x ⋅y    12⋅x⋅y
───── - ─────── + ──────
   3        2       z   
  z        z            

In [14]: expr.expand().subs({x * y / z: a})
Out[14]: 
 3      2       
a  - 5⋅a  + 12⋅a

Upvotes: 1

Berci
Berci

Reputation: 594

Well, for this particular example, the following idea leads to a solution, but in more generality, I don't know how to achieve the goal.

So, instead of substituting x*y/z as a, substitute equivalently x*y to a*z, and then simplify.

expr2 = expr.subs(x*y, a*z)
print(expr2)
print(sp.simplify(expr2))

Upvotes: 1

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