On 3/22/24 17:14, Waldek Hebisch wrote:
You asked almost the same thing on 6 Jul 2023.
Do you see a problem?
I have at least 2.
(1) your solution was too complicated, i.e. hard to remember by heart,
(2) it involves InnerTrigonometricManipulations.
I consider an "Inner..." package as something hidden for a user.
(3) if a user does not know how to achieve
Expression(Complex(Integer))->AlgebraicNumber,
then what function name he would search for? "FG2F"?
I much more like Qian's suggestion to add this special case to
"retractIfCan".
PS: That is one of the situations where things that look simple are
hard for users to actually perform.
Well, internally Expression(Complex(Integer)) and Expression(Integer)
are represented in quite different way, so there is notrivial
calculation to convert between the two forms.
Why shouldn't FriCAS help the user by basically exporting the
functionality of "FG2F" via "retractIfCan"?
Would you accept such a patch?
And at least one reason for types is that we want to do calculations
in a single type, without "useless" convertions. So, start from
'sqrt(-1)' and you will consistently get Expression(Integer) or
AlgebraicNumber. OTOH if you want Expression(Complex(Integer)) then
stay there...
Good suggestion. ;-)
You know that I like FriCAS, because it has types. However, I hate it to
waste time if I first have to dig deep into the internals until I can do
seemingly simple transformations.
My actual problem was to denest that expresssion.
%%% (1) -> z :=
sqrt(184726398605281*sqrt(-163)+14962838287027761)/(17502080*sqrt(20010))
+--------------------------------------------+
+-----+ | +-----+
\|20010 \|184726398605281 \|- 163 + 14962838287027761
(1) -------------------------------------------------------
350216620800
Type: AlgebraicNumber
%%% (2) -> rsimp(z)$RootSimplification
(2) "failed"
Type: Union("failed",...)
So I wrote a function that simply solves "x^2-radicand=0". I would have
to do it over complex numbers otherwise it wouldn't factorize. So I
ended in Expression Complex Integer.
While writing this mail, I have found out, that meanwhile
rsimp$RootSimplification can do the trick via ...(see below).
BTW, I am not sure whether I can trust the result, because there is
sqrt(-163) so it's over complex numbers and the docstring of rsimp
http://fricas.github.io/api/RootSimplification.html doesn't say anything
about how to interpret the result. Is there a particular preference over
the two possible solutions?
I still think that "retractIfCan" in Expression(Complex Integer) should
be able to yield an AlgebraicNumber if possible.
Ralf
%%% (57) -> z :=
sqrt(184726398605281*sqrt(-163)+14962838287027761)/(17502080*sqrt(20010))::Expression(Integer)
+--------------------------------------------+
| +-----+
\|184726398605281 \|- 163 + 14962838287027761
(57) -----------------------------------------------
+-----+
17502080 \|20010
Type: Expression(Integer)
%%% (58) -> rsimp(numer z)$RootSimplification
+---------------+
+-----+ |184726398605281
(58) (\|- 163 + 163) |---------------
\| 326
Type: Union(Expression(Integer),...)
%%% (59) -> rootSplit rsimp(numer z)$RootSimplification
+-----+
13591409 \|- 163 + 2215399667
(59) ------------------------------
+---+
\|326
Type: Expression(Integer)
%%% (60) -> rootSplit rsimp(numer z)$RootSimplification / denom z
+-----+
13591409 \|- 163 + 2215399667
(60) ------------------------------
+---+ +-----+
17502080 \|326 \|20010
Type: Expression(Integer)
%%% (61) -> % :: AlgebraicNumber
+-----+ +---+ +-----+
(13591409 \|- 163 + 2215399667)\|326 \|20010
(61) ----------------------------------------------
114170618380800
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