multiply numerator and denominator of rational expression

[Scott Calabrese Barton]

Hi, I wonder if there is an easy way to multiply the numerator and denominator of a rational expression by the same factor. I'd like to do this to group terms so that I can make a substitution.

I tried making a function to do this:

def tb(exp,factor):

    if exp.func==Mul and exp.args[-1].func==Pow \

        and exp.args[-1].args[-1]==-1:

        e=exp*factor

        denom=e.args[-1].args[0] * factor

        e.args[-1].args[0] = denom

        

    return e

Unfortunately it doesn't work because of immutable tuples.

[Aaron Meurer]

SymPy expressions are immutable. You have to create a new expression.
I would recommend something like

def mul_and_div_factor(expr, factor):
n, d = expr.as_numer_denom()
return (n*factor)/(d*factor)

Aaron Meurer

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[Scott Calabrese Barton]

Aaron, thanks, that's definitely the right idea, but doesn't work, probably because of simplification. Here's an example:

What I really want is a k3/k1 term in the denominator that can be substituted. Any way to achieve this?

[Scott Calabrese Barton]

Unfortunately that image will not render.  Here's a link to it:  https://goo.gl/J1wn0P

[Aaron Meurer]

Ah, I forgot that if factor is not a number, it won't distribute
automatically. You'll want to do something like

n, d = expr.as_numer_denom()
expand(n*factor)/expand(d*factor)

The way it is now, factor just immediately cancels.

And by the way, if your goal is to write a rational function in
reduced terms, you can use cancel() or factor() (the latter will also
factor the numerator and denominator).

Aaron Meurer

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[Scott Calabrese Barton]

Thanks, that worked perfectly. My final function is:

def ndf(expr, factor): 

    n, d = expr.as_numer_denom() 

    return expand(n*factor)/expand(d*factor)