# Tips on finessing Reduce[] with inequalities

Reduce[] sometimes solves inequalities I give it, sometimes it doesn't. Is there some general principles I'm missing or some common pitfalls I'm falling into?

For example, here is easy problem I can't seem to make MMa solve.

Reduce[{4*Abs[p + p^2] < 1, c == 1 - p - p^2}, p]


The hand-derived solution is just $|c-1|<\frac{1}{4}$ but MMa gets stuck.

Any pointers?

• Sometimes it depends on the domain. If you add the option Reals, i.e. Reduce[{4*Abs[p + p^2] < 1, c == 1 - p - p^2}, p, Reals], it spits back an answer practically instantaneously. It is likely more difficult to solve that problem in the complex plane, which is what it assumes and probably why it gets stuck. – march Nov 27 '15 at 21:36
• Or Reduce[{4*Abs[p + p^2] < 1, c == 1 - p - p^2, {c, p} \[Element] Reals}, {c}, {p}]... – Michael E2 Nov 27 '15 at 21:59