ilmorez - 7 months ago 23

Python Question

Using Sympy package version 1.0 on Python 2.7.11 I found what (to me) is an incongruence. This is the code I'm using:

`import sympy as sy`

from sympy.stats import Normal, density

from sympy.assumptions import assuming, Q, ask

sy.init_printing()

a = sy.symbols('a', real=True)

with assuming(Q.positive(a)):

print ask(Q.positive(a))

N = Normal('N', 0, a)

What I got is

`True`

from the first print as expected but an exception when creating the Normal object

`ValueError: Standard deviation must be positive`

Can anyone, please, explain if it is intended to be like this and why? Thanks!

PS: I'm aware that I could declare the symbols to be positive

Answer

The problem is simple: there are two assumptions systems in SymPy, called the old-style and new-style assumptions. They don't interact quite well, yet.

The old-style assumptions define predicates on symbols, e.g.

```
x = Symbol("x", positive=True)
```

deduction is then performed on generic expressions with methods such as `.is_positive`

```
>>> x.is_positive
True
```

The latest version of SymPy has linked the old-style assumptions to the new-style ones, so you can now query

```
>>> ask(Q.positive(x))
True
```

Older versions of SymPy would return `None`

, as the two assumptions systems were not linked at all.

The problem is that this relation is **not yet** reciprocal: the old-style assumptions system is not aware of assumptions defined with the new-style assumptions system. You can verify it yourself:

```
>>> with assuming(Q.positive(y)):
... print y.is_positive
None
```

The random variable *Normal* requires the standard deviation parameter to be positive, verification is done with the old-style assumptions. Therefore your case fails.

Note that the positivity condition on the standard deviation is likely to get relaxed to a non-negativity condition in the next SymPy version (that is, allow the positivity-indefinite case to be accepted).