Hi Chris,
thanks for your quick reply.
If I understand you correctly, this works only for this specific case (and on
top of that I had a typo, I have multiple, here 2, equations). But this was
just an example, it also should work for a more general case, like
print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 +
y*2+z*3=5,x*10-y-z=5,x <= 1, x >= 0, y <= 1, y >= 0,z <= 1, z >= 0]],
[x,y,z]))
Thanks again,
Rainer
Am Dienstag, 16. August 2022, 04:48:14 CEST schrieb Chris Smith:
> Ignore your equality `5*x + 2*y+3*z=5` and see if a solution exists for the
>
> condition you specify:
> >>> LP(
>
> ... x*2-y-z-5,[x <= 1, y <= 1,z <= 1,x>0,y>0,z>0],[x,y,z])
> (-3, {x: 1, y: 0, z: 0}, _y0 + _y1 + _y2 - 5, [_y0 - _y3 - 2 >= 0, _y1 -
> _y4 + 1 >= 0, _y2 - _y5 + 1 >= 0], {_y0: 2, _y1: 0, _y2: 0, _y3: 0, _y4: 0,
> _y5: 0})
>
> The maximum that 2*x - y - z - 5 can be is -3 but you want it to be greater
> than 0. So there is no solution, is there?
>
> /c
>
> On Monday, August 15, 2022 at 3:30:43 AM UTC-5 [email protected] wrote:
> > Hi Chris,
> >
> > many thanks for the link to the stack overflow answer and in particular
> > the PR
> > and also the elegant suggestion on how to address the problem with linear
> > programming.
> >
> > I realized that I oversimplified the example though:
> >
> > The problem I want to solve is a vector equation:
> >
> > f_vec+a*x_vec+b*y_vec+n*s_vec=sh_vec+c*xsh_vec+d*ysh_vec
> >
> > and I am looking for a solution with
> >
> > 0<=a,b,c,d<=1
> >
> > I.e. there is more than one equation which need to be satisfied for the
> > same x
> > and y:
> >
> > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 + y*2
> > +z*3=5,x*2-y-z>5,x <= 1, x >= 0, y <= 1, y >= 0,z <= 1, z >= 0]],
> > [x,y,z]))
> >
> > I see no obvious way to apply your method to a set of multiple equations,
> > but
> > it might due to my lack of experience with linear programming.
> >
> > Thanks again
> > Rainer
> >
> > Am Mittwoch, 10. August 2022, 23:03:29 CEST schrieb Chris Smith:
> > > You can't enter your expressions with `=` to create and Equality. You
> >
> > would
> >
> > > have to reenter as Eq(5*x+2*y,10) or
> > > `parse_expr('5*x+2*y=10',transformations=T[1,9]')` (see
> > > [here](https://stackoverflow.com/a/73307040/1089161)).
> > >
> > > Past that, there is no SymPy function that will solve this, but in
> > > PR https://github.com/sympy/sympy/pull/22389 I added code today that
> >
> > will
> >
> > > do so.
> > >
> > > Your equality will be treated like a function to maximize under the
> > >
> > > constrains that x<=1 and y<=1 (and both are nonnegative):
> > > >>> func = 5*x+2*y-10
> > > >>> cond = [x<=1, y<=1]
> > > >>> LP(func, cond, [x,y])[:2]
> > >
> > > (-3, {x: 1, y: 1})
> > >
> > > So that function has a maximum value of -3 when x and y are 1. Now
> > > negate
> > > the function and repeat
> > >
> > > >>> LP(-func, cond, [x,y])[:2]
> > >
> > > (10, {x: 0, y: 0})
> > >
> > > The max of the negated function is 10 when x and y are 0. So the min of
> >
> > the
> >
> > > function is -10. You are interested in the case when the function is 0.
> > > Since the function is linear and has as bounds [-10, -3] which does not
> > > contain 0, it seems to me that this proves there is no solution.
> > >
> > > /c
> > >
> > > On Tuesday, August 9, 2022 at 10:46:55 AM UTC-5 [email protected] wrote:
> > > > Hi Jeremy,
> > > >
> > > > thanks for sharing your link and thanks for compiling the
> >
> > documentation.
> >
> > > > And
> > > > indeed it helped, with the information I could easily fix it:
> > > >
> > > > rd@h370:~/tmp.nobackup$ cat test-sympy.py
> > > > import sympy
> > > >
> > > > x, y, z = sympy.symbols('x y z')
> > > > sympy.init_printing(use_unicode=True)
> > > >
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2
> > > > >
> > > > 0]],
> > > > x))
> > > >
> > > >
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2
> > > > >
> > > > 0,x <
> > > > 5]], x))
> > > > rd@h370:~/tmp.nobackup$ python3 test-sympy.py
> > > > (-2 < x) & (x < oo)
> > > > (-2 < x) & (x < 5)
> > > > rd@h370:~/tmp.nobackup$
> > > >
> > > > I read through your page and posted some feedback at
> > > >
> > > > https://github.com/sympy/sympy/pull/23768
> > > >
> > > > My real problem is somewhat more complex though:
> > > >
> > > > I want to find out if
> > > >
> > > > f_vec+a*x_vec+b*y_vec+n*s_vec=sh_vec+c*xsh_vec+d*ysh_vec
> > > >
> > > > has a solution with
> > > >
> > > > 0<=a,b,c,d<=1
> > > >
> > > > All quantities with _vec are 3 dimensional vectors. I want to to find
> >
> > out
> >
> > > > if
> > > > for a given set of vectors a solution exists or not.
> > > >
> > > > Extending my testcase in this direction does not work though:
> > > >
> > > > rd@h370:~/tmp.nobackup$ cat test-sympy.py
> > > > import sympy
> > > >
> > > > x, y, z = sympy.symbols('x y z')
> > > > sympy.init_printing(use_unicode=True)
> > > >
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2
> > > > >
> > > > 0]],
> > > > x))
> > > >
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 +
> >
> > y*2
> >
> > > > =
> > > > 10,x <= 1, x >= 0, y <= 1, y >= 0]], x))
> > > > rd@h370:~/tmp.nobackup$ python3 test-sympy.py
> > > > File "/home/rd/tmp.nobackup/test-sympy.py", line 9
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 +
> >
> > y*2
> >
> > > > = 10,x <= 1, x >= 0, y <= 1, y >= 0]], x))
> > > > ^
> > > > SyntaxError: invalid syntax
> > > > rd@h370:~/tmp.nobackup$
> > > >
> > > > I suspect that reduce_rational_inequalities is the wrong approach
> > > > here,
> > > > but
> > > > what would the the right functions to use?
> > > >
> > > > Any hint is welcome :-)
> > > >
> > > > Many thanks
> > > > Rainer
> > > >
> > > > PS: Also thanks for hint towards less-verbose function calls. I
> >
> > typically
> >
> > > > write it verbose, since I am not writing Python code too frequently,
> >
> > and
> >
> > > > for
> > > > me the verbose version is something like a documentation, since I see
> > > > where
> > > > the functions come from.
> > > >
> > > > Am Samstag, 6. August 2022, 17:19:45 CEST schrieb Jeremy Monat:
> > > > > Hi Ranier,
> > > > >
> > > > > Here's a way to do it:
> > > > > >>> import sympy
> > > > > >>> x, y, z = sympy.symbols('x y z')
> > > > > >>> sympy.solvers.inequalities.reduce_inequalities([x + 2 > 0, x <
> >
> > 5],
> >
> > > > > >>> x)
> > > > >
> > > > > (-2 < x) & (x < 5)
> > > > >
> > > > > reduce_inequalities is the top-level inequality reducer, which will
> >
> > call
> >
> > > > > other lower-level functions (such as reduce_rational_inequalities)
> > > > > as
> > > > > needed. reduce_inequalities takes a simple list, rather than a
> > > > > nested
> > > >
> > > > list,
> > > >
> > > > > of inequalities.
> > > > >
> > > > > I'm actually drafting a guide page on this topic now; glad to know
> >
> > it's
> >
> > > > of
> > > >
> > > > > interest! You can access the draft
> > > > > <
> >
> > https://output.circle-artifacts.com/output/job/a1f8297d-6be8-4627-9f47-a96
> >
> > > > 9
> >
> > 709f9293/artifacts/0/doc/_build/html/guides/solving/solve-system-of-inequa
> >
> > > > li>
> > > >
> > > > > ties-algebraically.html>, and I'd appreciate any feedback (either
> >
> > here
> >
> > > > or on
> > > >
> > > > > the pull request <https://github.com/sympy/sympy/pull/23768> on
> >
> > GitHub).
> >
> > > > > Best,
> > > > > Jeremy
> > > > >
> > > > > P.S. If you like, you can use less-verbose function calls by
> >
> > importing
> >
> > > > > reduce_inequalities and symbols from SymPy:
> > > > > >>> from sympy import reduce_inequalities, symbols
> > > > > >>> x, y, z = symbols('x y z')
> > > > > >>> reduce_inequalities([x + 2 > 0, x < 5], x)
> > > > >
> > > > > (-2 < x) & (x < 5)
> > > > >
> > > > > On Sat, Aug 6, 2022 at 3:31 AM 'Rainer Dorsch' via sympy <
> > > > >
> > > > > [email protected]> wrote:
> > > > > > Hi,
> > > > > >
> > > > > > I just started with sympy, and try to understand how to tell
> > > > > > sympy,
> > > >
> > > > what I
> > > >
> > > > > > want. I tried
> > > > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x
> >
> > + 2
> >
> > > > > > 0],[x
> > > > > > < 5]], x))
> > > > > > and expected
> > > > > > (-2 < x) & (x < 5)
> > > > > > but got
> > > > > > (-oo < x) & (x < oo)
> > > > > > Can anybody tell how I can tell sympy that x should satisfy both
> > > > > > inequalities
> > > > > > the same time?
> > > > > > For me it seems sympy rather interprets the set of equations
> >
> > rather as
> >
> > > > an
> > > >
> > > > > > "or"
> > > > > > and not an "and"
> > > > > >
> > > > > > Here is the full example
> > > > > >
> > > > > > rd@h370:~/tmp.nobackup$ cat test-sympy.py
> > > > > > import sympy
> > > > > >
> > > > > > x, y, z = sympy.symbols('x y z')
> > > > > > sympy.init_printing(use_unicode=True)
> > > > > >
> > > > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x
> >
> > + 2
> >
> > > > > > 0]],
> > > > > > x))
> > > > > >
> > > > > >
> > > > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x
> >
> > + 2
> >
> > > > > > 0],[x
> > > > > > < 5]], x))
> > > > > > rd@h370:~/tmp.nobackup$ python3 test-sympy.py
> > > > > > (-2 < x) & (x < oo)
> > > > > > (-oo < x) & (x < oo)
> > > > > > rd@h370:~/tmp.nobackup$
> > > > > >
> > > > > >
> > > > > > Any hint is welcome.
> > > > > >
> > > > > > Thanks
> > > > > > Rainer
> > > > > >
> > > > > >
> > > > > > --
> > > > > > Rainer Dorsch
> > > > > > http://bokomoko.de/
> > > > > >
> > > > > >
> > > > > > --
> > > > > > You received this message because you are subscribed to the Google
> > > >
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> >
> > send
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--
Rainer Dorsch
http://bokomoko.de/
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