Solve goes into infinite loop, when solving a quadratic equation system

Questions
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1

I have written a program for the principal axis transformation of quadrics in matrix form with homogeneous coordinates. The Solve command goes into an infinite loop in the third function call of “principalAxisMat” with matrix “A3”. It fails to solve a system of quadratic equations in exact form. Is this a failure of Wolfram Mathematica or is this my fault?

Open in Wolfram Cloud ↗

principalAxis-03.nb (20 KB)
principalAxisMat.wl (1.77 KB)

2

Try with:

 A3 = Transpose[T30] . A30 . T30 // FullSimplify

I don’t know why it works with FullSimplify.

I tried with Mathematica 13.0.

3

Not that I would go about it in this way, but if I did, I would change this construct:

Solve[Thread[Chop[Flatten[Transpose[T1s] . As . T1s -
                   B1s]]==ConstantArray[0,n*n]],...]

Since T1s is constructed to be orthogonal, you can make the system linear by multiplying through by Transpose[T1s].