Hello,
Apologies if I'm missing something trivial here...
I have the function y= sqrt(4*x**2 - 9) for which I want to know the real
domain of definition. I.e. the answer should be: y is defined for x <= -3/2
and x >= 3/2.
If I try solve(y >= 0) I get a PolynomialError. I could do solve(y**2 >= 0)
to get the "right" answer but it feels like a hack and I'm wondering
whether there is a better strategy to solve this inequality. Any idea?
I.m using sympy 0.7.5 and this below is the bit of code to reproduce my
question above.
Many thanks!
Dario
isympy
x= symbols('x')
y= sqrt(4*x**2 - 9)
## That's Ok:
solve(y**2 >= 0) ## im(x) = 0 ∧ (re(x) ≥ 3/2 ∨ re(x) ≤ -3/2)
## Or even better:
x= symbols('x', real= True)
y= sqrt(4*x**2 - 9)
solve(y**2 >= 0) ## x ≥ 3/2 ∨ x ≤ -3/2
## This doesn't work:
x= symbols('x')
y= sqrt(4*x**2 - 9)
solve(y >= 0)
---------------------------------------------------------------------------
PolynomialError Traceback (most recent call last)
<ipython-input-14-8865cc4d86ab> in <module>()
----> 1 solve(y >= 0)
/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/sympy/solvers/solvers.pyc
in solve(f, *symbols, **flags)
686 elif isinstance(fi, (bool, C.BooleanAtom)) or
fi.is_Relational:
687 return reduce_inequalities(f,
assume=flags.get('assume'),
--> 688 symbols=symbols)
689
690 # Any embedded piecewise functions need to be brought out
to the
/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/sympy/solvers/inequalities.pyc
in reduce_inequalities(inequalities, assume, symbols)
514
515 for gen, exprs in poly_part.items():
--> 516 poly_reduced.append(reduce_rational_inequalities([exprs],
gen, assume))
517
518 for gen, exprs in abs_part.items():
/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/sympy/solvers/inequalities.pyc
in reduce_rational_inequalities(exprs, gen, assume, relational)
219 expr.together().as_numer_denom(), gen)
220 except PolynomialError:
--> 221 raise PolynomialError("only polynomials and "
222 "rational functions are supported in this
context")
223
PolynomialError: only polynomials and rational functions are supported in
this context
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