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How to Use FullSimplify to breakdown algebraic expression

James Parkus, JHU/APL
Posted 24 days ago

Hello,

I am not very good with Mathematica in general. I typically use it to breakdown and solve complex algebraic equations to support hand-calculation, numeric solutions, etc. I am trying to solve for the points of intersection between two circles that are not located on the origin, call them Circle A and Circle B. So I solved one equation by hand for x, then tried to use Solve[-,-] to have Mathematica write out the expression for me. I can make use of what's given, but there are some easy "gimmie's" that I wish I knew how to tell Mathematica to do because it could greatly simplify the expression. See the attached notebook.

Can someone please help me figure out how to make better use of Mathematica and/or the FullSimplify function so I can tell it to assume x1-x2 = x3, y1-y2 = y3, etc? I tried looking through the "assumptions" documentation but I kept getting errors from what I tried to do there.

Thanks, James
POSTED BY: James Parkus
2 Replies
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This is one way:

FullSimplify[Solve[(x - x2)^2 + (f1 - y2)^2 == L2^2, x],
 {x1 == x3 + x2, y1 == y2 + y3}]

The assumptions are added as second argument for Simplify or FullSimplify.

Another way can be to use replacement rules:

FullSimplify[Solve[(x - x2)^2 + (f1 - y2)^2 == L2^2, x]] /.
 {x1 -> x3 + x2, y1 -> y2 + y3}
POSTED BY: Gianluca Gorni

Fantastic, thank you so much! This worked well.

POSTED BY: James Parkus
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