#7155: Allow solving of inequalities
---------------------------+------------------------------------------------
Reporter: kcrisman | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.1.3
Component: symbolics | Keywords: solve, inequality, Maxima
Work_issues: | Author:
Reviewer: | Merged:
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From a Maxima FAQ:
{{{
(%i1) load(fourier_elim)$
(%i2) fourier_elim([abs(x - abs(5-x)) < 1],[x]);
(%o2) [2<x,x<3]
(%i3) fourier_elim([x + y < 1, x - y > 9],[x,y]);
(%o3) [y+9<x,x<1-y,y<-4]
(%i4) fourier_elim([max(-x,x) < 7 * x + 1],[x]);
(%o4) [-1/8<x]
}}}
From pre-release codebase:
{{{
(%i79) to_poly_solve((x-1)*(x-6) < 0,x);
(%o79) %union([1 < x,x < 6])
(%i80) to_poly_solve(min(x,1) < max(-5,x),x);
(%o80) %union([1 < x],[x < -5])
(%i81) to_poly_solve(min(x,1) # max(x,4),x);
(%o81) %union([1 < x,x < 4],[4 < x],[x = 1],[x < 1],[x = 4])
(%i82) to_poly_solve((x+1)/(x-1) < 4,x);
(%o82) %union([5/3 < x],[x < 1])
}}}
So it should not be too hard to wrap this, checking input/output for < or
> or something. This is one of those basic things people want, but which
we assume it's too hard to write from scratch (which it probably is!).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7155>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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