yacas | Computer calculations | Math library

The question is asking for something that will extract just the right-hand side "(60 - x)/2" and use it as a function .

We can use package Ryacas (thanks for the hint @Bhas) an interface to the library yacas for symbolic equation solving:

It's hard to fully prove it, but it's most likely that OldSolve is too weak for this system.

A couple of important points from the manual:

This command tries to solve one or more equations.

Hence, no guarantees.

Note that only one solution is found and returned.

Meaning that there surely is no way to get all three solutions that you mentioned.

Again, at most a single solution is returned.

The fact that you got BB == BB and P == P means infinitely many solutions, so possibly we can see it as an evidence of failure to solve the system.

Multiple equations are solved recursively: firstly, an equation is sought in which one of the variables occurs exactly once; then this equation is solved with SuchThat; and finally the solution is substituted in the other equations by Eliminate decreasing the number of equations by one. This suffices for all linear equations and a large group of simple nonlinear equations

So, this kind of explains why OldSolve may fail in your system. First, it's nonlinear, giving no guarantees. Second, each of the variables appears in each of the equations 1-4 times. If I understand the algorithm correctly, after solving one equation (w.r.t. AA, say) and substituting the solution to the other two - we are done. That's because then both BB and P appear in both of the remaining equations more than once (and, as a result, OldSolve fails to solve any of them). You can also try to switch the order of the equations; you will see that then a different variable gets solved for.

There are several problems with the R code in the question:

• it is attempting to assign an S3 object to elements of a logical matrix:

I think you've implemented faithfully, but the algorithm is broken. Asymmetric quadrature can easily give asymmetric results. I get the same kinds of weirdness.

But you can eliminate duplicate points by maintaining them in a sorted set and using the invariant that the endpoints have already been inserted when the recursive analyzer runs.

Here's a simplification using modern Java features more fully: