sympy arbitrary function range

Question

I want to define the arbitrary function f. I know that f always returns a positive number. I want sympy to be able to use this knowledge when running simplifications (especially the three power rules mentioned in the simplify documentation). Is there a way to do this? I'm looking for something like the below:

f = Function("f", positive = True)
g = Function("g", positive = True)
x = symbols("x")
y = symbols("y")
n = symbols("n", real = True)

test = ( f(x) * g(y) ) ** n
# This should work but doesn't
expand_power_base(test)

I don't understand your question. Do you just want a function that returns a random positive number? — AbrahamB, Oct 28 '16 at 05:23
I've added some code to help clarify. Let me know if it's still unclear — bramtayl, Oct 28 '16 at 07:31

score 0 · Answer 1 · answered Oct 28 '16 at 08:46

Here is a not-so-great way of going about things:

alphabet = list(string.ascii_lowercase)

def assert_positive(value, args):
    result = value
    for i in range( len(args) ):
        a_symbol = symbols( alphabet[i], positive = True)
        result = result.subs(args[i], a_symbol)

    result = simplify(result)

    for i in range( len(args) ):
        a_symbol = symbols( alphabet[i], positive = True)
        result = result.subs(a_symbol, args[i])

    return(result)

score 0 · Answer 2 · answered Oct 28 '16 at 08:51

0

One workaround is to call expand_power_base with the force=True option. This forces sympy to perform power simplifications, irrespective of assumptions.

import sympy as sp

f = sp.Function("f")
g = sp.Function("g")
x, y, n = sp.symbols("x, y, n")

test = ( f(x) * g(y) ) ** n
sp.expand_power_base(test, force=True)

f(x)**n*g(y)**n

answered Oct 28 '16 at 08:51

Stelios

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This won't work for me. My actual expressions are iterative and very complicated, and I need to be able to use all three rules at once. – bramtayl Oct 28 '16 at 09:05

score 0 · Accepted Answer · answered Nov 01 '16 at 19:01

0

Functions defined like Function('f') do not support assumptions at this time. You'll need to create a subclass explicitly, like

class f(Function):
    is_positive = True

answered Nov 01 '16 at 19:01

asmeurer

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Wow, thanks for the answer! Will an object of class f then be able to be used in any way a regular function would? Or is there anything else I'd need to add? – bramtayl Nov 03 '16 at 17:00
It will work in the same way. `f = Function('f')` is (roughly) equivalent to `class f(Function): pass`. – asmeurer Nov 03 '16 at 17:26

sympy arbitrary function range

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