Mathematical substitution in SymPy

[Adrián Ashley]

Hello,

How can I substitute/replace something mathematically from an expression:

For example:

>>> exp(5*x).xreplace({exp(x): sin(x)})
>>> exp(5*x)   # I would expect sin(x)**5 here

In better way to do the above thing?

Thanks,

Best,

--

Adrian

[Sartaj Singh]

Try this,

>>> exp(5*x).xreplace({exp(5*x): sin(5*x)})

sin(5*x)

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Regards

Sartaj Singh

Mathematics and Computing,

Indian Institute of Technology,

Varanasi - 221 005 INDIA

E-mail: singhs...@gmail.com, sartaj.si...@itbhu.ac.in

[Adrián Ashley]

Hi Sartaj,

I think you didn't understood my point. I am looking for mathematical substitution, not exact

substitution.

exp(5*x).xreplace({exp(5*x): sin(5*x)}) is just a mere example of usage of xreplace. I am not

looking for exact replacement. the exponent can be anything

For example:

>>> sin(exp(x)).some_replace_func({exp: x})

>>> sin(x)

>>> exp(5*x).some_replace_func({exp(x): sin(x)})
>>> exp(5*x)

Thanks,

Best,

Adrian

[Adrián Ashley]

Correction previous example:

In [9]: sin(exp(a*x)).some_replace_func({exp(x): x})

Out[9]: sin(x**a)

[Gaurav Dhingra]

Do you want something like replacing some function f1 (say `exponential function` you mentioned `{exp(x): x}` ) with some other f2 (say linear function, you mentioned `{exp(x): x}`  ) in your expression ?

[Aaron Meurer]

xreplace only does exact structural replacement (the "x" stands for "exact"). To get mathematical replacement, use subs:

>>> print(exp(5*x).subs(exp(x), sin(x)))

sin(x)**5

Aaron Meurer

On Fri, Aug 14, 2015 at 5:17 AM, AMiT Kumar <dtu....@gmail.com> wrote:

I am also Interested in getting the solution for this.

AMiT Kumar

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[Adrián Ashley]

Hi, 

Thanks for the workaround, but

subs doesn't work here:

>>> sin(exp(a*x)).subs({exp(x): x})
>>> sin(exp(a*x))

Best,

Adrian

[Aaron Meurer]

subs is limited on how smart it is. I think it only works for numerical coefficients.

Also note that exp(a*x) != exp(x)**a in general (take x = 2*pi*I and a = 1/2). It should be true if a is an integer, though (but subs doesn't handle it if you set a = Symbol('a', integer=True)).

If you know what form of expression you want to replace, you can use the replace() method with Wilds, like

In [26]: b = Wild('b', exclude=[x])

In [27]: print(exp(a*x).replace(exp(b*x), sin(x)**b))

sin(x)**a

Aaron Meurer

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[Richard Fateman]

You could look at Maxima's  ratsubst command for ideas about what could be

done.

ratsubst(y, exp(x), exp(5*x))  returns y^5.

RJF