sage 9.6 special function translation issue with fricas. elliptic_ec #34058

nasser1 · 2022-06-23T21:45:08Z

Using sagemath 9.6 and fricas 1.3.8.

Fricas solve this integral and returns ellipticF and ellipticE in result, both which take two arguments.

Sagemath seems to translate these to its own elliptic_ec for some reason, which takes only 1 argument and hence gives an exception.

Why did it not translate these to sagemath elliptic_f and elliptic_e? Both which are available in sagemath and take 2 arguments?

Here is an example

>sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.6, Release Date: 2022-05-15                     │
│ Using Python 3.10.4. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘

sage: var('x a b d c e f')
(x, a, b, d, c, e, f)
sage: integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x,algorithm="fricas")
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-11-d0465c613c1a> in <module>
----> 1 integrate((f*x**Integer(3)+e*x**Integer(2)+d*x+c)*(b*x**Integer(4)+a)**(Integer(1)/Integer(2)),x,algorithm="fricas")

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/misc/functional.py in integral(x, *args, **kwds)
    762     """
    763     if hasattr(x, 'integral'):
--> 764         return x.integral(*args, **kwds)
    765     else:
    766         from sage.symbolic.ring import SR

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:95445)()
  13192                     R = SR
  13193             return R(integral(f, v, a, b, **kwds))
> 13194         return integral(self, *args, **kwds)
  13195
  13196     integrate = integral

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/symbolic/integration/integral.py in integrate(expression, v, a, b, algorithm, hold)
   1045         if not integrator:
   1046             raise ValueError("Unknown algorithm: %s" % algorithm)
-> 1047         return integrator(expression, v, a, b)
   1048     if a is None:
   1049         return indefinite_integral(expression, v, hold=hold)

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/symbolic/integration/external.py in fricas_integrator(expression, v, a, b, noPole)
    205             result = e_fricas.integrate(seg)
    206
--> 207     result = result.sage()
    208
    209     if result == "failed":

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/interface.py in sage(self, *args, **kwds)
   1104             [0 0]
   1105         """
-> 1106         return self._sage_(*args, **kwds)
   1107
   1108     def __repr__(self):

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _sage_(self)
   2048             # we treat Expression Integer and Expression Complex
   2049             # Integer just the same
-> 2050             return FriCASElement._sage_expression(P.get_InputForm(self._name))
   2051
   2052         if head == 'DistributedMultivariatePolynomial':

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _sage_expression(fricas_InputForm)
   1730         register_symbol(convert_rootOf, {'fricas': 'rootOf'})
   1731
-> 1732         ex, _ = FriCASElement._parse_and_eval(fricas_InputForm)
   1733         # postprocessing of rootOf
   1734         from sage.rings.all import QQbar, PolynomialRing

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_and_eval(s, start)
   1319
   1320         if s[a] == FriCASElement._LEFTBRACKET:
-> 1321             return FriCASElement._parse_list(s, start=a)
   1322         elif s[a] == FriCASElement._STRINGMARKER:
   1323             return FriCASElement._parse_string(s, start=a)

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_list(s, start)
   1361         args = []
   1362         while s[a] != FriCASElement._RIGHTBRACKET:
-> 1363             e, a = FriCASElement._parse_and_eval(s, start=a)
   1364             args.append(e)
   1365             a += 1

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_and_eval(s, start)
   1319
   1320         if s[a] == FriCASElement._LEFTBRACKET:
-> 1321             return FriCASElement._parse_list(s, start=a)
   1322         elif s[a] == FriCASElement._STRINGMARKER:
   1323             return FriCASElement._parse_string(s, start=a)

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_list(s, start)
   1361         args = []
   1362         while s[a] != FriCASElement._RIGHTBRACKET:
-> 1363             e, a = FriCASElement._parse_and_eval(s, start=a)
   1364             args.append(e)
   1365             a += 1

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_and_eval(s, start)
   1319
   1320         if s[a] == FriCASElement._LEFTBRACKET:
-> 1321             return FriCASElement._parse_list(s, start=a)
   1322         elif s[a] == FriCASElement._STRINGMARKER:
   1323             return FriCASElement._parse_string(s, start=a)

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_list(s, start)
   1361         args = []
   1362         while s[a] != FriCASElement._RIGHTBRACKET:
-> 1363             e, a = FriCASElement._parse_and_eval(s, start=a)
   1364             args.append(e)
   1365             a += 1

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_and_eval(s, start)
   1319
   1320         if s[a] == FriCASElement._LEFTBRACKET:
-> 1321             return FriCASElement._parse_list(s, start=a)
   1322         elif s[a] == FriCASElement._STRINGMARKER:
   1323             return FriCASElement._parse_string(s, start=a)

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_list(s, start)
   1361         args = []
   1362         while s[a] != FriCASElement._RIGHTBRACKET:
-> 1363             e, a = FriCASElement._parse_and_eval(s, start=a)
   1364             args.append(e)
   1365             a += 1

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_and_eval(s, start)
   1319
   1320         if s[a] == FriCASElement._LEFTBRACKET:
-> 1321             return FriCASElement._parse_list(s, start=a)
   1322         elif s[a] == FriCASElement._STRINGMARKER:
   1323             return FriCASElement._parse_string(s, start=a)

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/interfaces/fricas.py in _parse_list(s, start)
   1364             args.append(e)
   1365             a += 1
-> 1366         return fun(*args), a
   1367
   1368     @staticmethod

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/symbolic/function.pyx in sage.symbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.c:10972)()
   1031             res = self._evalf_try_(*args)
   1032             if res is None:
-> 1033                 res = super(BuiltinFunction, self).__call__(
   1034                         *args, coerce=coerce, hold=hold)
   1035

~/DATA/sage-9.6/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/sage/symbolic/function.pyx in sage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.c:5588)()
    513         """
    514         if self._nargs > 0 and len(args) != self._nargs:
--> 515             raise TypeError("Symbolic function %s takes exactly %s arguments (%s given)" % (self._name, self._nargs, len(args)))
    516
    517         # if the given input is a symbolic expression, we don't convert it back

TypeError: Symbolic function elliptic_ec takes exactly 1 arguments (2 given)

Here is the result using fricas directly

>fricas
FRICAS="/usr/local/lib/fricas/target/x86_64-linux-gnu"
spad-lib="/usr/local/lib/fricas/target/x86_64-linux-gnu/lib/libspad.so"
                       FriCAS Computer Algebra System
                            Version: FriCAS 1.3.8
                   Timestamp: Tue Jun 21 15:11:38 CDT 2022


(22) -> setSimplifyDenomsFlag(true)
(23) -> anti:=integrate((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x);
(24) -> unparse(anti::InputForm)

  "(((-12)*a*e+20*b*c)*x*2^(1/2)*(((-4)*a)/b)^(1/2)*b^(1/2)*((((-4)*a)/b)^(1/2)
  )^(1/2)*ellipticF((((((-4)*a)/b)^(1/2))^(1/2))/(x*2^(1/2)),-1)+(12*a*e*x*2^(1
  /2)*(((-4)*a)/b)^(1/2)*b^(1/2)*((((-4)*a)/b)^(1/2))^(1/2)*ellipticE((((((-4)*
  a)/b)^(1/2))^(1/2))/(x*2^(1/2)),-1)+(15*a*d*x*b^(1/2)*log((-2)*b*x^2*(b*x^4+a
  )^(1/2)+((-2)*b*x^4+(-1)*a)*b^(1/2))+(20*b*f*x^5+24*b*e*x^4+30*b*d*x^3+40*b*c
  *x^2+20*a*f*x+48*a*e)*(b*x^4+a)^(1/2))))/(120*b*x)"

You can see Fricas result do not contain elliptic_ec

Is this a translation problem? Is there something I can do to fix this before running this integral? Right now many integrals are failing using fricas due to this when they should not be failing.

Here is link to sagemath documentation on special functions

Depends on #34062

Component: interfaces

Keywords: FriCAS

Author: Martin Rubey

Branch: 7a172e2

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/34058

The text was updated successfully, but these errors were encountered:

fchapoton · 2022-06-24T15:20:13Z

comment:1

see #34062

mantepse · 2022-06-25T09:30:13Z

comment:2

It seems that FriCAS' ellipticE is different from sage's elliptic_e:

sage: var("y")
y
sage: fricas.ellipticE(x, y).D(x)
 +---------+
 |   2
\|- x y + 1
------------
  +--------+
  |   2
 \|- x  + 1

sage: fricas.ellipticE(x, y).D(y)
- ellipticF(x,y) + ellipticE(x,y)
---------------------------------
               2 y

sage: ascii_art(elliptic_e(x, y).diff(x))
   _________________
  /        2        
\/  - y*sin (x) + 1 

sage: ascii_art(elliptic_e(x, y).diff(y))
E(x|y) - F(x|y)
---------------
      2*y

Do you know the precise relationship?

fchapoton · 2022-06-25T11:45:40Z

comment:3

a reference is 19.2.5 in

https://dlmf.nist.gov/19.2

fchapoton · 2022-06-25T11:49:56Z

comment:4

see also the comment before (53) in

https://mathworld.wolfram.com/EllipticIntegral.html

which explains the different competing notations

EDIT:

see rather https://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html

fchapoton · 2022-06-25T12:06:12Z

comment:5

Fricas : E(z,m) = integrate(sqrt(1-m*t<sup>2)/sqrt(1-t</sup>2), t = 0..z)

Sage : E(phi,m) = integrate(sqrt(1-m*sin(t)^2), t = 0..phi)

So Fricas definition is non-standard but with respect to z !

Ugly conversion : z = sin(phi)

mantepse · 2022-06-25T13:08:24Z

comment:6

For the complete elliptic integral, we are fine?

fchapoton · 2022-06-25T16:32:11Z

comment:7

yes, and there is already a doctest for that in

src/sage/functions/special.py

mantepse · 2022-06-25T17:48:03Z

Branch: u/mantepse/sage_9_6_special_function_translation_issue_with_fricas__elliptic_ec

mantepse · 2022-06-25T17:48:18Z

Commit: 24b6495

mantepse · 2022-06-25T17:48:18Z

comment:9

doctest will be provided tomorrow or so

New commits:

`71528ac`	`first try at enhanced conversion system`
`b4a8566`	`adding wish of doctest`
`f81a1cc`	`maple conversion of zeta derivatives`
`c76dbda`	`detail in fricas interface`
`c0bbbe4`	`fix Fricas back conversion`
`24b6495`	`provide conversion to incomplete elliptic integral`

mantepse · 2022-06-25T17:48:37Z

Dependencies: #34062

fchapoton · 2022-06-25T18:44:56Z

comment:11

not sure that it's a good idea to build upon #34062, which may be in a very unstable state

any idea why Fricas does not use the standard definitions ? already for dilog..

mantepse · 2022-06-26T08:00:34Z

comment:12

I'm not sure, but I think without #34062 it won't work, because fricas.ellipticE accepts one or two arguments.

nasser1 · 2022-06-26T08:04:14Z

comment:13

Fyi, list of Fricas special functions and their signatures at

https://fricas.github.io/api/SpecialFunctionCategory.html

From the above:

ellipticE(m) is the complete elliptic integral of the second kind: ellipticE(m) = integrate(sqrt(1-m*t^2)/sqrt(1-t^2), t = 0..1).

ellipticE(z, m) is the incomplete elliptic integral of the second kind: ellipticE(z, m) = integrate(sqrt(1-m*t^2)/sqrt(1-t^2), t = 0..z).

mantepse · 2022-06-26T21:18:44Z

comment:14

Should we somehow deal that the conversion is only valid for phi between -pi/2 and pi/2?

mantepse · 2022-06-26T21:21:00Z

comment:15

re comment:11: I don't think it's nonstandard, see https://en.wikipedia.org/wiki/Elliptic_integral

mantepse · 2022-06-26T21:22:45Z

Changed keywords from fricas intergate symbolic to FriCAS

sagetrac-git · 2022-06-27T06:18:08Z

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

`3916cdb`	`add doctest`

sagetrac-git · 2022-06-27T06:18:08Z

Changed commit from 24b6495 to 3916cdb

fchapoton · 2022-06-27T06:29:50Z

comment:18

Replying to @mantepse:

re comment:11: I don't think it's nonstandard, see https://en.wikipedia.org/wiki/Elliptic_integral

Wikipedia is not a valid reference for scientific purposes. It uses a confusing notation with functions E(*,*) and E(*;*).

mantepse · 2022-07-05T08:50:41Z

comment:19

Ping? (especially comment:14)

fchapoton · 2022-07-05T09:40:50Z

comment:20

the doctest in /src/sage/functions/special.py is missing the # optional - fricas tag

and the doctest there must now start with r"""

sagetrac-git · 2022-07-05T11:49:06Z

Changed commit from 3916cdb to 7a172e2

sagetrac-git · 2022-07-05T11:49:06Z

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

`7a172e2`	`add missing optional - fricas tag`

fchapoton · 2022-07-06T12:31:44Z

Author: Martin Rubey

fchapoton · 2022-07-06T12:31:44Z

comment:22

ok, let's go

note that the correct dilog function exists in fricas under then name li2. We should fix the forward conversion in another ticket.

fchapoton · 2022-07-06T12:31:44Z

Reviewer: Frédéric Chapoton

vbraun · 2022-07-10T22:34:57Z

Changed branch from u/mantepse/sage_9_6_special_function_translation_issue_with_fricas__elliptic_ec to 7a172e2

nasser1 · 2022-07-15T02:27:10Z

Changed commit from 7a172e2 to none

nasser1 · 2022-07-15T02:27:10Z

comment:25

I tested this in sagemath 9.7 beta 5 on Linux.

But it is still not correct.

Even though there is no exception now, which is good, but the result from Fricas 1.3.8 returns ellipticF but there is no ellipticF in sagemath.

It should have been translated to sagemath elliptic_f ?

>./sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7.beta5, Release Date: 2022-07-10               │
│ Using Python 3.10.5. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: var('a b c x d')
(a, b, c, x, d)
sage: integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2),x, algorithm="fricas")
1/3*((b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)*sqrt(-c/d) - (b^2*c^3 + a*b*c^2*d + 2*a*b*c*d^2)*x*ellipticF(sqrt(-c/d)/x, a*d/(b*c)) + (b^2*c^3 + a*b*c^2*d)*x*elliptic_e(arcsin(sqrt(-c/d)/x), a*d/(b*c)))/(sqrt(b*d)*b*d^2*x*sqrt(-c/d))
sage: ?ellipticF
Object `ellipticF` not found.

--Nasser

nasser1 · 2022-07-15T05:27:59Z

comment:26

Should I open a new ticket on this new issues since this ticket is closed?

mantepse · 2022-07-15T08:44:20Z

comment:27

Yes, please!

nasser1 · 2022-07-15T08:52:00Z

comment:28

OK. Created new ticket. Here is the link to it

#34186

Thanks

nasser1 added this to the sage-9.7 milestone Jun 23, 2022

nasser1 added c: interfaces labels Jun 23, 2022

fchapoton added s: needs review and removed s: needs review labels Jul 6, 2022

vbraun removed the s: positive review label Jul 10, 2022

vbraun closed this as completed in 38b2bf7 Jul 10, 2022

nasser1 mentioned this issue Aug 30, 2022

Problem translating Fricas special function ellipticF to Sagemath #34186

Closed

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

sage 9.6 special function translation issue with fricas. elliptic_ec #34058

sage 9.6 special function translation issue with fricas. elliptic_ec #34058

nasser1 commented Jun 23, 2022

fchapoton commented Jun 24, 2022

mantepse commented Jun 25, 2022

fchapoton commented Jun 25, 2022

fchapoton commented Jun 25, 2022

fchapoton commented Jun 25, 2022

mantepse commented Jun 25, 2022

fchapoton commented Jun 25, 2022

mantepse commented Jun 25, 2022

mantepse commented Jun 25, 2022

mantepse commented Jun 25, 2022

mantepse commented Jun 25, 2022

fchapoton commented Jun 25, 2022

mantepse commented Jun 26, 2022

nasser1 commented Jun 26, 2022

mantepse commented Jun 26, 2022

mantepse commented Jun 26, 2022

mantepse commented Jun 26, 2022

sagetrac-git mannequin commented Jun 27, 2022

sagetrac-git mannequin commented Jun 27, 2022

fchapoton commented Jun 27, 2022

mantepse commented Jul 5, 2022

fchapoton commented Jul 5, 2022

sagetrac-git mannequin commented Jul 5, 2022

sagetrac-git mannequin commented Jul 5, 2022

fchapoton commented Jul 6, 2022

fchapoton commented Jul 6, 2022

fchapoton commented Jul 6, 2022

vbraun commented Jul 10, 2022

nasser1 commented Jul 15, 2022

nasser1 commented Jul 15, 2022

nasser1 commented Jul 15, 2022

mantepse commented Jul 15, 2022

nasser1 commented Jul 15, 2022

sage 9.6 special function translation issue with fricas. elliptic_ec #34058

sage 9.6 special function translation issue with fricas. elliptic_ec #34058

Comments

nasser1 commented Jun 23, 2022

fchapoton commented Jun 24, 2022

mantepse commented Jun 25, 2022

fchapoton commented Jun 25, 2022

fchapoton commented Jun 25, 2022

fchapoton commented Jun 25, 2022

mantepse commented Jun 25, 2022

fchapoton commented Jun 25, 2022

mantepse commented Jun 25, 2022

mantepse commented Jun 25, 2022

mantepse commented Jun 25, 2022

mantepse commented Jun 25, 2022

fchapoton commented Jun 25, 2022

mantepse commented Jun 26, 2022

nasser1 commented Jun 26, 2022

mantepse commented Jun 26, 2022

mantepse commented Jun 26, 2022

mantepse commented Jun 26, 2022

sagetrac-git mannequin commented Jun 27, 2022

sagetrac-git mannequin commented Jun 27, 2022

fchapoton commented Jun 27, 2022

mantepse commented Jul 5, 2022

fchapoton commented Jul 5, 2022

sagetrac-git mannequin commented Jul 5, 2022

sagetrac-git mannequin commented Jul 5, 2022

fchapoton commented Jul 6, 2022

fchapoton commented Jul 6, 2022

fchapoton commented Jul 6, 2022

vbraun commented Jul 10, 2022

nasser1 commented Jul 15, 2022

nasser1 commented Jul 15, 2022

nasser1 commented Jul 15, 2022

mantepse commented Jul 15, 2022

nasser1 commented Jul 15, 2022