On Thu, May 15, 2025 at 07:40:39PM +0200, Grégory Vanuxem wrote:
> Hello here,
>
> Can you explain me this:
I am not sure what you want explained? Algorithms then Nemo uses
to give possible symbolic values of floating pint results? Or
maybe why FriCAS outputs specific things?
If you wander why FriCAS leaves asin(sin(x)) unsimplified, this
is due to branches, sin(x) = sin(x + 2*%pi), applaying asin
to both sides and using unsound transformation of asin(sin(x))
to x would give false equality x = x + 2*%pi. Similarly,
pulling %i before square roots leads to nonsense like the last
result in the following mail.
> ==
>
> └─$ jlfricas
> Checking for foreign routines
> FRICAS="/usr/local/lib/fricas/target/x86_64-linux-gnu"
> spad-lib="/usr/local/lib/fricas/target/x86_64-linux-gnu/lib/libspad.so"
> foreign routines found
> openServer result 0
> FriCAS Computer Algebra System
> Version: jlFriCAS 1.3.12-dev built with SBCL 2.5.2.debian
> Timestamp: Wed Apr 16 09:50:54 AM CEST 2025
> -----------------------------------------------------------------------------
> Issue )copyright to view copyright notices.
> Issue )summary for a summary of useful system commands.
> Issue )quit to leave FriCAS and return to shell.
> -----------------------------------------------------------------------------
>
>
> (1) -> jnecf (-2/3)
>
> (1) -0.666667 {-2/3}
>
> Type: NMExactCalciumField
>
> Time: 0.13 (EV) + 3.88 (OT) = 4.01 sec
> (2) -> sqrt %
>
> (2) 0.816497*I {(a)/3 where a = 2.44949*I [a^2+6=0]}
>
> Type: NMExactCalciumField
>
> Time: 0.01 sec
> (3) -> sin %
>
> (3)
> 0.910291*I {(-a^2*c+c)/(2*a) where a = 0.441977 [Exp(-0.816497
> {(b*c)/3})], b = 2.44949*I [b^2+6=0], c = I [c^
> 2+1=0]}
>
> Type: NMExactCalciumField
>
> Time: 0.02 (EV) = 0.02 sec
>
> (4) -> asin %
>
> (4) 0.816497*I {(a)/3 where a = 2.44949*I [a^2+6=0]}
>
> Type: NMExactCalciumField
>
> Time: 0.02 (EV) = 0.02 sec
> (5) -> %^2
>
> (5) -0.666667 {-2/3}
>
> Type: NMExactCalciumField
>
> Time: 0.02 sec
> (6) -> -2/3
>
> 2
> (6) - -
> 3
>
> Type: Fraction(Integer)
>
> Time: 0 sec
> (7) -> sqrt %
>
> +---+
> | 2
> (7) |- -
> \| 3
>
> Type: AlgebraicNumber
>
> Time: 0.03 (OT) = 0.03 sec
> (8) -> sin %
>
> +---+
> | 2
> (8) sin( |- - )
> \| 3
>
> Type: Expression(Integer)
>
> Time: 0 sec
> (9) -> asin %
>
> +---+
> | 2
> (9) asin(sin( |- - ))
> \| 3
>
> Type: Expression(Integer)
>
> Time: 0 sec
> (10) -> %^2
>
> +---+ 2
> | 2
> (10) asin(sin( |- - ))
> \| 3
>
> Type: Expression(Integer)
>
> Time: 0 sec
> (11) ->
>
> Is it related to complex number handling or the fact that EXPR(INT) is used
> a lot (algebraic number for example). Or I am totally wrong.
>
> Greg
>
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--
Waldek Hebisch
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