6
$\begingroup$

Can anyone advise a tool that is very convenient for verifying algebraic manipulations step by step as I work. I too often waste hours dealing with a wrong formula because I missed a sign somewhere. I use Mathematica for this by doing things as follow... but have found it awkward.

eq3 := 2 E^((b - d) t) (b - d) == b*E^((b - d) t) - d

eq4 := eq3[[1]]/E^((b - d) t) == eq3[[2]]/E^((b - d) t)

The basic requirement of the tool is to catch trivial mistakes immediately.


Just to make sure I was clear on this, I'm looking for a tool to verify after the fact that steps I took are accurate, not to show me steps for solving something.

I'm actually quite familiar with Mathematica and use it a lot, I'm just looking for something that is oriented more towards convenience for verification rather than solving.

What I really want is something to increase my efficiency when I'm "exploring" on my own, so I don't have to spend so much time double and triple checking my work for trivial errors.

  • 2
    Often useful is just to check some values. Either clearly important ones or "random" ones.2011-06-13
  • 0
    Can you give an example of something you want to verify? The one you have isn't very clear. (For "2 E^((b - d) t) (b - d) == b*E^((b - d) t) - d" to be true, we'd need that bE^((b-d)t) -2dE^((b-d)t) = -d, and it's not at all clear why this should be the case. Or is this what you're trying to solve?2011-06-13
  • 0
    I didn't mean to imply that you were looking for a tool to show you how to solve problems; you were clear about hoping to find a way to verify *your* work... I'm sorry if my answer came across as suggesting otherwise. I was speaking, in part, from experience; I tend to be a perfectionist, and check/double check before, during, after solving problems...But in terms of testing situations, one needs to be able to solve problems/provide solutions in a limited timeframe, without the "luxury" of always being able to "verify". Hence my suggestion to work (even if occasionally) w/o a "safety net."2011-06-14
  • 0
    We physicists also find dimensional analysis to be a good error check. If you are solving a quadratic, $ax^2+bx+c=0$, give $x$ units of length. Then $a$ has units of inverse length^2, etc. Your expression should be consistent at every step, as the final formula is. If you have two variables, give one length and the other time. It doesn't catch sign errors, but it catches many errors in distributing products, substitution, etc.2011-06-15
  • 0
    ShreevatsaR, what the above allows me to do is see what Mathematica gives me when both sides of eq3 are divided by E^((b - d) t) so I can check my own result. This is a very trivial example, but a real one. When doing the work of which this was a part with paper and pencil I missed something which got me off on a wrong track and caused me to waste a bunch of time playing with equations that were completely wrong.2011-06-24

4 Answers 4