Waldek, you are amazing!!! A big thanks for the radicalSolve patch.
Ralf On 5/16/24 15:12, Waldek Hebisch wrote:
On Tue, May 14, 2024 at 03:04:15PM +0200, Ralf Hemmecke wrote:In fact, the value xx is one of radicalRoots(pp) where pp := x^4-2729960418308000*x^3-395258439243352250000*x^2-55499520947716391500000000*x-345363656226658026765625000000 Interestingly, when I put xx into Mathematica, I get a much nicer expressions. In[15]:= p1 = Root[pp, 1] // ToRadicals Out[15]= 250 (2729960418308 + 1930373524352 Sqrt[2] - 23569 Sqrt[2 (13416226688183641 + 9486704869150589 Sqrt[2])]) In[25]:= p3 = Root[pp, 3] // ToRadicals Out[25]= 250 (2729960418308 - 1930373524352 Sqrt[2] - 23569 I Sqrt[2 (-13416226688183641 + 9486704869150589 Sqrt[2])]) Can I somehow "convince" FriCAS to return similarly "simple" radical expresssions?With the attached patch I get: (2) -> radical_solve(univariate(pp)) (2) [ +--------------------------------------------------------------------+ | +-+ \|658730414260118770166403625000 \|2 + 931585485794307216540975125000 + +-+ 482593381088000 \|2 + 682490104577000 , +--------------------------------------------------------------------+ | +-+ - \|658730414260118770166403625000 \|2 + 931585485794307216540975125000 + +-+ 482593381088000 \|2 + 682490104577000 , +---+ \|- 1 * +--------------------------------------------------------------------+ | +-+ \|658730414260118770166403625000 \|2 - 931585485794307216540975125000 + +-+ - 482593381088000 \|2 + 682490104577000 , - +---+ \|- 1 * ROOT +-+ 658730414260118770166403625000 \|2 + - 931585485794307216540975125000 + +-+ - 482593381088000 \|2 + 682490104577000 ] Type: Union(List(Expression(Integer)),...) The result looks more complicated, but this is because FriCAS does not pull squares outside square roots. I would be easy to hook this into 'radicalSolve' so that such result is obtainde by default.
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