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I'm reading the book The Annotated Turing by Charles Petzold. In it he mentions the Diophantine equations - which was a joy to read.

This then lead to Hilbert's 10th problem - finding an algorithm of solving Diophantine in a fixed number of steps to whole numbers. Interestingly enough - Diophantine sets are Turing Machines. (That last one kind of blows my mind).

Now this is what Turing was driving at in his paper in 1936. (On Computable Numbers, with an Application to the Entscheidungsproblem)

Now it seems to me that Macsyma (with some common heritage to Mathematica) is directed at solving Computer Algebra problems.

Now the Entscheidungsproblem (or as we know it the halting problem) has a relationship to Computer Algebra - but was more about the decidability rather than the symbolic mathematics. Can we say Macsyma was directed at both the symbolic mathematics and the halting problem?

My question is: Is there evidence to suggest Macsyma was directed at the Diophantine equations in the Entscheidungsproblem?

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