Add more conversions from giac

[Marcelo Forets]

A "conversion" is a dictionary entry which maps object names in an interface (e.g. Maxima, Mathematica, Giac, ...) to corresponding objects with a different name in Sage.

Some conversions relevant to the Giac interface are missing:

• Derivatives of Dirac delta, as in Dirac(t, 1).
• Special function names at /functions/orthogonal_polys.py.

See also:

• In the file: local/share/giac/doc/aide_cas, lines starting by # are keywords followed by synonyms, next lines are for small doc and see also. Full doc can be found in: ​Symbolic algebra and Mathematics with Xcas

• sage.libs.pynac.pynac.register_symbol can be used to register new symbols in the symbols_table, as in register_symbol(heaviside,{'giac':'Heaviside'}).

• for BuiltIn functions which exist in giac with a different name, it is sufficient to update the conversions dictionary for the corresponding __init__ method.

[Han Frederic]

This one doesn't look easy. Any idea to deal with rootof?

sage: giac.simplify((exp(2*i*pi/3)+exp(2*i*pi/15))^3)
((-768*i)*(-1)^(2/15)*sqrt(3)-768*(-1)^(2/15)+768*i*(-1)^(4/15)*sqrt(3)-768*(-1)^(4/15)+rootof([[16-16*i,-16+16*i,-400+528*i,144+240*i],[1,0,-30,-40,5]]))/512

do we need to chose a name for the variable in the extention field? (if yes then how? (or what would be a good name))

[Paul Masson]

I went through the files in sage/functions to add as many conversions for special functions as possible, but could only find ten that were different from Sage.

The Giac exponential integrals Ei, Si and Ci have existing Sage aliases, so there shouldn't be a problem with those.

The orthogonal polynomials hermite and laguerre have the same names in Giac and Sage. Same for erf and a pending erfc, as well as binomial and factorial.

The Giac function Psi has is a different name from Sage psi, but the order of the arguments is reversed so I didn't add it now.

---

New commits:

​0e337ef	Add Giac conversions and cleanup
​ffba36a	Add Giac conversions and cleanup
​e1a63ed	Add Giac conversions and cleanup
​3a3d079	Add Giac conversion
​bdc2807	Add Giac conversions and cleanup

[Paul Masson]

Considering the derivatives of delta functions, I think we'll have to do a string replacement using a regular expression similar to how Maxima conversions are handled starting ​here. Perhaps that should be a separate ticket after #22422 is merged.

The conversions I've entered are not dependent on #22422 and can be merged at any time. If either of you can identify additional functions that can be added easily with this ticket, let me know.

[Ralf Stephan]

Replying to frederichan:

This one doesn't look easy. Any idea to deal with rootof?

sage: giac.simplify((exp(2*i*pi/3)+exp(2*i*pi/15))^3)
((-768*i)*(-1)^(2/15)*sqrt(3)-768*(-1)^(2/15)+768*i*(-1)^(4/15)*sqrt(3)-768*(-1)^(4/15)+rootof([[16-16*i,-16+16*i,-400+528*i,144+240*i],[1,0,-30,-40,5]]))/512

do we need to chose a name for the variable in the extention field? (if yes then how? (or what would be a good name))

This appears to be #22024.

[Marcelo Forets]

Replying to paulmasson:

The Giac function Psi has is a different name from Sage psi, but the order of the arguments is reversed so I didn't add it now.

true and they agree if just 1 argument is passed.

also:

• should Giac's abs be mapped so abs_symbolic? notice that asking for abs_symbolic??, there is already some:

"""GinacFunction.__init__(self, "abs", latex_name=r"\mathrm{abs}",
                               conversions=dict(sympy='Abs'))

• same for binomial, arg, ceil, conjugage (and conj), factorial, frac, imag (and imag_part), real (and real_part).

[Marcelo Forets]

Replying to paulmasson:

Considering the derivatives of delta functions, I think we'll have to do a string replacement using a regular expression similar to how Maxima conversions are handled starting ​here. Perhaps that should be a separate ticket after #22422 is merged.

+1. moreover, it should also fix integration:

sage: integrate(dirac_delta(x-2)*sin(x), x, 0, 4)    # unevaluated??
integrate(dirac_delta(x-2)*sin(x), x, 0, 4)
sage: integrate(dirac_delta(x-2)*sin(x), x, 0, 4, algorithm='sympy')    # ok
sin(2)

[Marcelo Forets]

after this one is done, we could go for "Add giac interface to integrate". what do you think?

[Marcelo Forets]

hi, i've added some simple conversions.

remaining:

• rootof
• psi function
• derivative of delta function.

for the last item is not clear to me if it is required to write a _derivative_ method for FunctionDiracDelta, or to write a new a class FunctionDiracDeltaDerivative, or if it's about passing a dictionary element with some preprocessing (some arguments) so that say Dirac(x, 2) (giac) changes to diff(dirac_delta(x), x, x) in sage and conversely.

---

New commits:

​9143bd2

add more /functions conversions

[Marcelo Forets]

we may want to ensure a symbolic integral wrapper, for instance with (cf. #22138):

sage: n = var('n')
sage: integral(x^n*sin(x), x, algorithm='giac')
...
NotImplementedError: Unable to parse Giac output: integrate(x^n*sin(x),x)

but in other cases it already returns unevaluted:

sage: integrate(log(1+x)/x, x, 0, 1, algorithm='giac')
integrate(ln(x + 1)/x, x, 0, 1)

[Frédéric Chapoton]

something related:

sage: integrate(exp(x^3), (x, 1, 2), algorithm='giac') 
1/3*igamma(1/3, -1) - 1/3*igamma(1/3, -8)

where igamma is giac's name for the incomplete gamma function.

[Marcelo Forets]

Replying to chapoton:

something related:

sage: integrate(exp(x^3), (x, 1, 2), algorithm='giac') 
1/3*igamma(1/3, -1) - 1/3*igamma(1/3, -8)

where igamma is giac's name for the incomplete gamma function.

interesting. it seems that giac's igamma corresponds to gamma_inc_lower in Sage (lower incomplete Gamma). moreover, giac's ugamma corresponds to gamma_inc in Sage (upper incomplete Gamma). i'll add these conversions asap.

[Marcelo Forets]

in this case there is also a difference in their numerical evaluations:

actual value of the integral:

sage: numerical_integral(exp(x^3), 1, 2)
(275.51098376331174, 3.0587863771115636e-12)

giac:

sage: giac('1/3*igamma(1./3, -1) - 1/3*igamma(1./3, -8)')
275.510983763
sage: giac('igamma(1./3, -1)')
-4.02571325393
sage: giac('igamma(1./3, -8)') 
-830.558664544
sage: giac('igamma(1./3, 1)') 
2.42253354642
sage: giac('igamma(1./3, 8)') 
2.67886054288

sage:

sage: 1/3*gamma_inc_lower(1./3, -1) - 1/3*gamma_inc_lower(1./3, -8)
-137.755491881656 - 238.599510960670*I
sage: gamma_inc_lower(1./3, -1)    # values don't match. imag part => t^(-2/3) ? 
2.01285662696613 + 3.48636994625705*I
sage: gamma_inc_lower(1./3, -8)    # values don't match
415.279332271934 + 719.284902828267*I    
sage: gamma_inc_lower(1./3, 1)    # values match
2.42253354641901
sage: gamma_inc_lower(1./3, 8)    # values match
2.67886054288163

[Marcelo Forets]

however,

sage: integrate(exp(x^3), x, 1, 2, algorithm='maxima') # OK
-1/3*(-1)^(2/3)*gamma(1/3, -1) + 1/3*(-1)^(2/3)*gamma(1/3, -8)
sage: _.n()
275.510983763312 - 7.21644966006352e-14*I
sage: giac('integrate(exp(x^3), x, 1, 2)')  # OK
1/3*igamma(1/3,-1)-1/3*igamma(1/3,-8)

what's going on? is there a problem on the numerical eval of gamma_inc_lower or the conversion is not accurate?

[Frédéric Chapoton]

branch looks good to me and bot is green, but is this in "needs review" state ?

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​4b9bfda	Merge branch 'develop' into t/mforets/22706
​6e5e3e2	incomplete gamma conversions

[Marcelo Forets]

Replying to chapoton:

branch looks good to me and bot is green, but is this in "needs review" state ?

Thanks for the feedback -- not yet but close! I'd like to handle the psi function conversion. Have to figure out how to reverse the arguments in the function call. I haven't seen examples of that sort..

For the other tasks discussed in this thread, i've separated them into smaller chunks, see ​giac interface wiki section.

[Frédéric Chapoton]

branch does not apply

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​666c2f3	resolve merge conflicts with v.8.0.beta8
​71bc336	add error functions conversions

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b2f4261

fix missing ) in giac erfc

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6592c61

register swap psi

[Marcelo Forets]

partial progress: with the last commit one has

sage: giac('Psi(x,1)')._sage_()
psi(1, x)

as desired. however the other way round doesn't work get swapped:

sage: psi(1, x)._giac_() 
psi(1, x)   # Psi(x, 1) is expected

[Ralf Stephan]

It works if you give a giac conversion in the psi2 init as well.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​350316f

add Psi conversion in psi2

[Marcelo Forets]

Replying to rws:

It works if you give a giac conversion in the psi2 init as well.

It does!! Thanks.

[Frédéric Chapoton]

ok, let it be

[Marcelo Forets]

Replying to chapoton:

ok, let it be

great, thanks for the review and to all participants of this ticket!

w.r.t ​giac symbolics tickets i think i'll go on with #23016...