refine with multiple variables

[Joseph Nasser]

Hello,

I would like to check whether an inequality with multiple variables is satisfied under certain assumptions on the variables. Is this supported? Using refine seems to work with one variable but not a multi-variable expression. I am using Sympy 1.11.1 

from sympy import Q
var('z w', real=True)
refine(z**2 > 0, Q.positive(z)) # Returns BooleanTrue, expected behavior
refine(z**2 + w**2 > 0, Q.positive(z) & Q.positive(w)) #does not return a Boolean type

Thanks

[Oscar Benjamin]

Ideally things like this would work but support for multivariate
systems of inequalities is practically nonexistent in refine right
now.

Oscar

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[Aaron Meurer]

This is currently only implemented in ask(), and you have to use
Q.positive(x) instead of x > 0 (ask does not yet know how to deal with
inequalities directly):

>>> ask(Q.positive(z**2), Q.positive(z))
True
>>> ask(Q.positive(z**2 + w**2), Q.positive(z) & Q.positive(w))
True

Aaron Meurer

[Jeremy Monat]

Perhaps relevant: A new page on reducing ("solving") sets of inequalities has recently been published to the dev version of the documentation.

Jeremy Monat

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[Joseph Nasser]

Thanks to all for the comments - much appreciated. Aaron's suggestion to use ask() is sufficient for me at the moment. It would be great to support relational inequalities between variables (eg, z > w) in the future. 

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[Chris Smith]

For simple domains like this, the old assumptions work. Just define `var('z w', positive=True)` and then the inequalities evaluate.

You might try AccumBounds for more complicated expressions

B = AccumBounds

(z**2 - w**2).subs(z,B(0,1)).subs(w,B(0,2))

AccumBounds(-4,1)

/c