Re: [sage-devel] Introduction to differentiable manifolds in SageMath
Hi,
Proxying of URL's from github, etc., is now live in cocalc share
server. See the comment here about how it works:
https://github.com/sagemathinc/cocalc/issues/6015#issuecomment-1172967091
For example
https://cocalc.com/github/sagemanifolds/IntroToManifolds
is now actually proxying exactly what is on github directly. Also,
you can easily click "Edit" and in about 25 seconds you're running a
notebook with Sage!
William
On Sun, Jun 26, 2022 at 11:42 AM William Stein wrote:
>
> On Sun, Jun 26, 2022 at 1:42 AM Eric Gourgoulhon
> wrote:
> >
> > Le samedi 25 juin 2022 à 17:31:10 UTC+2, wst...@gmail.com a écrit :
> >>
> >> > There is some issue in the latex display of manifold maps:
> >> > ParseError: KaTeX parse error: Undefined control sequence: \mbox at
> >> > position 96: …thbb{E}^{2} \\ \̲m̲b̲o̲x̲{on}\ A : & \ph…
> >>
> >> Thanks -- I've created this issue in case you're curious about the
> >> situation:
> >>
> >> https://github.com/sagemathinc/cocalc/issues/6019
> >>
> >> In particular, I think it would be better if the latex representation
> >> output by sage manifolds used "\text{on}" instead of "\mbox{on}";
> >> however, I'll add a workaround in CoCalc so that isn't necessary.
> >
> >
> > IIRC, I used \mbox instead of \text because \mbox is plain LaTeX, while
> > \text requires the package amstext, so I naively thought that \mbox was
> > more robust. The katex example shows that it is rather the converse. So
> > yes, we may change \mbox to \text. Note that \mbox is quite heavily used in
> > all Sage: running
>
> I think what happened is that the problem \mbox tries to solve is
> solved in a slightly better way by other commands like \text. As a
> result katex only implemented the better solution. Your reasoning to
> use \mbox instead \of text might be a reasonable argument for keeping
> the current behavior in Sage, despite this annoying katex situation.
> Regarding CoCalc, yesterday I added an alias so that now our katex
> rendering works with \mbox (it just sets \mbox to \text), so these
> sage manifolds notebooks all look fine now.
>
> William
>
> > grep -r '\\mbox'
> > from src/sage returns 206 lines, among which 34 in src/sage/manifolds.
>
> >
> > Eric.
> >
> > --
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>
>
>
> --
> William (http://wstein.org)
--
William (http://wstein.org)
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[sage-devel] Re: Request for advice : extend exponentialize ?
BTW, (too ?) simple check :
sage: all(map(lambda
u,v:bool(u(v(x)._sympy_().rewrite("log")._sage_()).exponentialize().simplify_full()==x),
: (sin, cos, tan, csc, sec, cot, sinh, cosh, tanh, csch, sech,
coth),
: (arcsin, arccos, arctan, arccsc, arcsec, arccot, arcsinh,
arccosh, arctanh, arccsch, arcsech, arccoth)))
True
Le samedi 2 juillet 2022 à 10:32:30 UTC+2, Emmanuel Charpentier a écrit :
> The SR.exponentialize method implements :
>
> sage: [u(x)==u(x)._sympy_().rewrite("exp")._sage_()
> : for u in (sin, cos, tan, csc, sec, cot, sinh, cosh, tanh, csch, sech,
> coth)]
> [sin(x) == -1/2*I*e^(I*x) + 1/2*I*e^(-I*x),
> cos(x) == 1/2*e^(I*x) + 1/2*e^(-I*x),
> tan(x) == -I*(e^(I*x) - e^(-I*x))/(e^(I*x) + e^(-I*x)),
> csc(x) == 2*I/(e^(I*x) - e^(-I*x)),
> sec(x) == 2/(e^(I*x) + e^(-I*x)),
> cot(x) == I*(e^(I*x) + e^(-I*x))/(e^(I*x) - e^(-I*x)),
> sinh(x) == -1/2*e^(-x) + 1/2*e^x,
> cosh(x) == 1/2*e^(-x) + 1/2*e^x,
> tanh(x) == -(e^(-x) - e^x)/(e^(-x) + e^x),
> csch(x) == -2/(e^(-x) - e^x),
> sech(x) == 2/(e^(-x) + e^x),
> coth(x) == -(e^(-x) + e^x)/(e^(-x) - e^x)]
>
> However, we also have :
>
> sage: [u(x)==u(x)._sympy_().rewrite("log")._sage_()
> : for u in (arcsin, arccos, arctan, arccsc, arcsec, arccot, arcsinh,
> arccosh, arctanh, arccsch, arcsech, arccoth)]
> [arcsin(x) == -I*log(I*x + sqrt(-x^2 + 1)),
> arccos(x) == 1/2*pi + I*log(I*x + sqrt(-x^2 + 1)),
> arctan(x) == -1/2*I*log(I*x + 1) + 1/2*I*log(-I*x + 1),
> arccsc(x) == -I*log(sqrt(-1/x^2 + 1) + I/x),
> arcsec(x) == 1/2*pi + I*log(sqrt(-1/x^2 + 1) + I/x),
> arccot(x) == -1/2*I*log(I/x + 1) + 1/2*I*log(-I/x + 1),
> arcsinh(x) == log(x + sqrt(x^2 + 1)),
> arccosh(x) == log(sqrt(x + 1)*sqrt(x - 1) + x),
> arctanh(x) == 1/2*log(x + 1) - 1/2*log(-x + 1),
> arccsch(x) == log(sqrt(1/x^2 + 1) + 1/x),
> arcsech(x) == log(sqrt(1/x + 1)*sqrt(1/x - 1) + 1/x),
> arccoth(x) == 1/2*log(1/x + 1) - 1/2*log(-1/x + 1)]
>
> Hence two questions :
>
>-
>
>Is it worth implementing it (for the benefit of
>high-school/undergrads/engineering math) ?
>-
>
>Should it be implemented by SR.exponentialize or by a distinct method
>? (My preference is for the former, notwithstanding the apparent
>discrepancy in names…).
>
> Your advice is welcome.
>
>
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[sage-devel] Request for advice : extend exponentialize ?
The SR.exponentialize method implements :
sage: [u(x)==u(x)._sympy_().rewrite("exp")._sage_()
: for u in (sin, cos, tan, csc, sec, cot, sinh, cosh, tanh, csch, sech,
coth)]
[sin(x) == -1/2*I*e^(I*x) + 1/2*I*e^(-I*x),
cos(x) == 1/2*e^(I*x) + 1/2*e^(-I*x),
tan(x) == -I*(e^(I*x) - e^(-I*x))/(e^(I*x) + e^(-I*x)),
csc(x) == 2*I/(e^(I*x) - e^(-I*x)),
sec(x) == 2/(e^(I*x) + e^(-I*x)),
cot(x) == I*(e^(I*x) + e^(-I*x))/(e^(I*x) - e^(-I*x)),
sinh(x) == -1/2*e^(-x) + 1/2*e^x,
cosh(x) == 1/2*e^(-x) + 1/2*e^x,
tanh(x) == -(e^(-x) - e^x)/(e^(-x) + e^x),
csch(x) == -2/(e^(-x) - e^x),
sech(x) == 2/(e^(-x) + e^x),
coth(x) == -(e^(-x) + e^x)/(e^(-x) - e^x)]
However, we also have :
sage: [u(x)==u(x)._sympy_().rewrite("log")._sage_()
: for u in (arcsin, arccos, arctan, arccsc, arcsec, arccot, arcsinh,
arccosh, arctanh, arccsch, arcsech, arccoth)]
[arcsin(x) == -I*log(I*x + sqrt(-x^2 + 1)),
arccos(x) == 1/2*pi + I*log(I*x + sqrt(-x^2 + 1)),
arctan(x) == -1/2*I*log(I*x + 1) + 1/2*I*log(-I*x + 1),
arccsc(x) == -I*log(sqrt(-1/x^2 + 1) + I/x),
arcsec(x) == 1/2*pi + I*log(sqrt(-1/x^2 + 1) + I/x),
arccot(x) == -1/2*I*log(I/x + 1) + 1/2*I*log(-I/x + 1),
arcsinh(x) == log(x + sqrt(x^2 + 1)),
arccosh(x) == log(sqrt(x + 1)*sqrt(x - 1) + x),
arctanh(x) == 1/2*log(x + 1) - 1/2*log(-x + 1),
arccsch(x) == log(sqrt(1/x^2 + 1) + 1/x),
arcsech(x) == log(sqrt(1/x + 1)*sqrt(1/x - 1) + 1/x),
arccoth(x) == 1/2*log(1/x + 1) - 1/2*log(-1/x + 1)]
Hence two questions :
-
Is it worth implementing it (for the benefit of
high-school/undergrads/engineering math) ?
-
Should it be implemented by SR.exponentialize or by a distinct method ?
(My preference is for the former, notwithstanding the apparent discrepancy
in names…).
Your advice is welcome.
--
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Re: [sage-devel] closed tickets
On Saturday, July 2, 2022 at 12:33:38 PM UTC+9 Kwankyu Lee wrote: > ... I think this should be explained somewhere, perhaps in the notice > itself. > Added to https://trac.sagemath.org/ticket/33849 which needs review. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/24363201-699d-4301-a80e-7a16a91afd43n%40googlegroups.com.
