# how to reference "much greater than"

22 views

### Ben

Aug 15, 2020, 4:07:27 PM8/15/20
to sympy
Hello,

I'm attempting to translate Latex into SymPy and am seeking guidance on how to handle the notation of "much greater than."

For example, "a + b = c" is replaced by "a = c" under the condition "b << a". How would that be represented in Sympy?

I like the explanation of ">>" provided in this StackOverflow answer, so there is some deeper meaning to the notation. However, that doesn't indicate what the appropriate representation in SymPy would be.

For comparison with other Computer Algebra Systems, I'm not able to find the concept in Sage documentation. I did find this post on Mathematica.

### Aaron Meurer

Aug 18, 2020, 5:21:04 PM8/18/20
to sympy
If I understand the references correctly, you'd want to replace
instances of a and b in the expression with b/a, replace that with a
single variable like x, then do a series expansion and remove higher
order x terms. There isn't anything in SymPy that automates this in
one step but you can get a lot of it automatically with subs() and
series(). The hard part is that in some of the examples you may have
to perform this on subexpressions rather than the whole expression.

For example, one of the examples you linked to is 1/(b*(b + a)) =
1/(b*a) if a >> b.

>>> expr = 1/(b*(a + b))
>>> # Set x = b/a
>>> expr.subs(a, b/x).cancel()
x/(b**2*x + b**2)
>>> # Expand as a series up to O(x**2)
>>> expr.subs(a, b/x).cancel().series(x, n=2)
x/b**2 + O(x**2)
>>> # Remove the O() term and substitute back
>>> expr.subs(a, b/x).cancel().series(x, n=2).removeO().subs(x, b/a)
1/(a*b)

Aaron Meurer
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