[sage-support] Re: laplace_transform hypergeometric?

[Ralf Stephan]

I confirm conversion of hypergeometric 2F1 to SymPy is broken---but 2F2 is 
not so the workaround would be to give an additional 1 argument in the 
second slot. 

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[sage-support] laplace_transform hypergeometric?

[Ralf Stephan]

The transform is implemented via calling of SymPy but apparently something went 
wrong in the conversion to SymPy. I cannot say more as I'm not at my box but 
you can try to use SymPy directly as a workaround.

Regards,

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[sage-support] laplace_transform hypergeometric?

[Raymond Rogers]

Is the Laplace transform of hypergeometric functions implemented?  If 
not can I have a pointer to how to implement it?

Here is an example under notebook(); jupyter throws the same error.
"TypeError: 'Integer' object is not iterable" , I tried various 
alterations of the parameters; to no avail.
Since the error seems irrelevant, should I try to look at the source 
(since it seems to try)?


Ray

from sympy import *
from sage.calculus import *
from sympy.integrals import laplace_transform
from sympy.abc import t, s
#from sympy.holonomic.holonomic import *
#from sympy.holonomic import DifferentialOperators,  from_meijerg, 
from_hyper

#from sympy.abc import x
from sympy import ZZ
#R, D = DifferentialOperators(ZZ.old_poly_ring(x), 'D')
#HolonomicFunction(D**2 + 1, x, 0, [0, 1])
#HolonomicFunction((1) + (1)*D**2, x, 0, [0, 1])

x, y,b,a= symbols('x y b a  ')

k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)
init_printing(use_unicode=True)

--- code
eq= hypergeometric([1,2-a], [2], t)
print(eq)
print("")
eq3l=laplace_transform(eq,t,s)
print("")
eq3l

---
response from sagemath
---
hypergeometric((1, -a + 2), (2,), t)
Traceback (most recent call last):
  File "", line 1, in 
  File "_sage_input_23.py", line 10, in 
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 
-*-\\n" + 
_support_.preparse_worksheet_cell(base64.b64decode("ZXFhPSBoeXBlcmdlb21ldHJpYyhbMSwyLWFdLCBbMl0sIHQpCnByaW50KGVxYSkKZXEzbD1sYXBsYWNlX3RyYW5zZm9ybShlcWEsdCxzLHBsYW5lPU5vbmUpCmVxM2w="),globals())+"\\n"); 
execfile(os.path.abspath("___code___.py"))

  File "", line 1, in 

  File "/tmp/tmpO9ZqR1/___code___.py", line 5, in 
    eq3l=laplace_transform(eqa,t,s,plane=None)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/integrals/transforms.py", 
line 1122, in laplace_transform

    return LaplaceTransform(f, t, s).doit(**hints)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/core/cache.py", 
line 95, in wrapper

    retval = func(*args, **kwargs)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/core/function.py", 
line 427, in __new__

    result = super(Function, cls).__new__(cls, *args, **options)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/core/cache.py", 
line 95, in wrapper

    retval = func(*args, **kwargs)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/core/function.py", 
line 240, in __new__

    args = list(map(sympify, args))
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/core/sympify.py", 
line 291, in sympify

    return a._sympy_()
  File "sage/symbolic/expression.pyx", line 1445, in 
sage.symbolic.expression.Expression._sympy_ 
(build/cythonized/sage/symbolic/expression.cpp:11968)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py", 
line 226, in __call__

    return self.composition(ex, operator)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py", 
line 794, in composition

    return f_sympy(*sympy.sympify(g, evaluate=False))
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/functions/special/hyper.py", 
line 182, in __new__

    return Function.__new__(cls, _prep_tuple(ap), _prep_tuple(bq), z)
  File 
"/media/rrogers/Data/opt/SageMath/local/lib/python2.7/site-packages/sympy/functions/special/hyper.py", 
line 44, in _prep_tuple

    return TupleArg(*[unpolarify(x) for x in v])
TypeError: 'Integer' object is not iterable

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[sage-support] Re: points on a Fermat curve

[slelievre]

Fri 2018-04-13 10:56:17 UTC, David Joyner:
>
> PS: About 3 years ago, a related question was posted: 
>
> https://groups.google.com/forum/#!topic/sage-support/s59iDjhu2zU
>
> For some reason, the method described there is no longer implemented.

Regarding the example in the discussion you point to,
a minor change gets it to work: instead of

sage: C.cardinality()

you can use

sage: C.point_set().cardinality()

Illustration below:

Sage version:

$ sage -v
SageMath version 8.2.rc1, Release Date: 2018-03-31


Define the finite field F:

sage: F. = GF(13^2)
sage: F
Finite Field in q of size 13^2

The projective plane over F: 

sage: P2. = toric_varieties.P2(base_ring=F)
sage: P2
2-d CPR-Fano toric variety covered by 3 affine patches

The curve (as a scheme):

sage: C = P2.subscheme(x^8 + y^8 + z^8)
sage: C
Closed subscheme of 2-d CPR-Fano toric variety covered by 3 affine 
patches defined by:
  x^8 + y^8 + z^8

Trying to get the cardinality fails for this scheme:

sage: C.cardinality()
Traceback (most recent call last)
...
AttributeError: 'AlgebraicScheme_subscheme_toric_with_category' object 
has no attribute 'cardinality'

We need to go through the point set:

sage: P = C.point_set()
sage: P
Set of rational points of Closed subscheme of 2-d CPR-Fano toric 
variety covered by 3 affine patches defined by:
  x^8 + y^8 + z^8

Now we can get the cardinality:

sage: c = P.cardinality()
sage: c
512

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Re: [sage-support] points on a Fermat curve

[David Joyner]

On Fri, Apr 13, 2018 at 7:26 AM, John Cremona  wrote:
> This looks like a bug to me:
>
> sage: F=GF(3)
> sage: R.=F[]
> sage: C=Curve(X^8+Y^8-Z^8)
> sage: C.count_points(1) # correct count over GF(3^1)
> [4]
> sage: C.count_points(8) # should give counts over GF(3^n) for n=1..8 but it
> crashes
>
> TypeError: F (=[X^8 + Y^8 - Z^8]) must be a list or tuple of polynomials of
> the coordinate ring of A  (=Projective Space of dimension 2 over Finite
> Field in z2 of size 3^2)
>
> -- note that the error message looks suspicious.
>
> Also the more naive
>
> sage: F=GF(3^8)
> sage: R.=F[]
> sage: C=Curve(X^8+Y^8-Z^8)
> sage: C.count_points(1)
> [4696]
>
> works but is so slow it must be doing something very basic such as testing
> every point in the plane (of which there are 3^16+3^8+1...)
>
> John
>

Agreed.

Moreover, according to
http://doc.sagemath.org/html/en/constructions/algebraic_geometry.html,
"The option algorithm="bn uses Sage’s Singular interface and calls the
brnoeth package."
However, when I look at the doc string in C.rational_points? it says the option
algorithm is ignored. Times seem to bear this out:

sage: x,y,z = PolynomialRing(GF(3^7), 3, 'xyz').gens()
sage: C = Curve(z^8 - y^8 - x^8)
sage: time Cpts = C.rational_points()
CPU times: user 10.9 s, sys: 243 ms, total: 11.1 s
Wall time: 10.9 s
sage: time Cpts = C.rational_points(algorithm="bn")
CPU times: user 10.8 s, sys: 182 ms, total: 11 s
Wall time: 10.8 s
sage: x,y,z = PolynomialRing(GF(3^8), 3, 'xyz').gens()
sage: C = Curve(z^8 - y^8 - x^8)
sage: time Cpts = C.rational_points()
CPU times: user 22.8 s, sys: 97.2 ms, total: 22.9 s
Wall time: 22.8 s
sage: time Cpts = C.rational_points(algorithm="bn")
CPU times: user 22.8 s, sys: 97.2 ms, total: 22.9 s
Wall time: 22.9 s


>
> On 13 April 2018 at 11:55, David Joyner  wrote:
>>
>> Hi:
>>
>> The question below is posted for Gary McGuire, who is not a subscriber
>> to this list:
>>
>> "I would like to know the number of rational points on the (projective)
>> curve
>> x^8+y^8=z^8
>> over the field of order 3^{18}.
>>
>> My question is, can Sage do this calculation, and how?"
>>
>> - David
>>
>> PS: About 3 years ago, a related question was posted:
>> https://groups.google.com/forum/#!topic/sage-support/s59iDjhu2zU
>> For some reason, the method described there is no longer implemented.
>>
>> --
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>
>
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Re: [sage-support] Re: simple?--from_meijer in jupyter

[Raymond Rogers]

Sigh:   Yes...

Thanks!

Ray


On 04/13/2018 08:01 AM, Eric Gourgoulhon wrote:

Hi,

There is a typo in your code: it should be "from_meijerg" instead of 
"from_meijer":


|
sage:fromsympy.holonomic.holonomic importfrom_meijerg
sage:from_meijerg?
Signature:from_meijerg(func,x0=0,evalf=False,initcond=True,domain=QQ)
Docstring:
Convertsa MeijerG-functionto Holonomic."func"isthe G-Function
and"x0"isthe point at which initial conditions are required.

>>>fromsympy.holonomic.holonomic importfrom_meijerg,DifferentialOperators
>>>fromsympy importsymbols,meijerg,S
>>>x =symbols('x')
>>>from_meijerg(meijerg(([],[]),([S(1)/2],[0]),x**2/4))
HolonomicFunction((1)+(1)*Dx**2,x,0,[0,1/sqrt(pi)])
Initdocstring:x.__init__(...)initializes x;see help(type(x))forsignature
File:~/sage/8.1/local/lib/python2.7/site-packages/sympy/holonomic/holonomic.py
Type:function
|

Best wishes,

Eric.

Le vendredi 13 avril 2018 00:06:17 UTC+2, Raymond Rogers a écrit :

The sympy documentation
http://docs.sympy.org/latest/modules/holonomic/convert.html

 has the function from_meiljer and I do
from sympy import *
from sympy.holonomic.holonomic import from_hyper, from_meijer,
DifferentialOperators
(I think redundant)
I get: "ImportError: cannot import name from_meijer"
Is this a versioning error or what?

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[sage-support] Re: simple?--from_meijer in jupyter

[Eric Gourgoulhon]

Hi, 

There is a typo in your code: it should be "from_meijerg" instead of 
"from_meijer":

sage: from sympy.holonomic.holonomic import from_meijerg
sage: from_meijerg?
Signature: from_meijerg(func, x0=0, evalf=False, initcond=True, domain=QQ)
Docstring: 
 Converts a Meijer G-function to Holonomic. "func" is the G-Function
 and "x0" is the point at which initial conditions are required.

 >>> from sympy.holonomic.holonomic import from_meijerg, 
DifferentialOperators
 >>> from sympy import symbols, meijerg, S
 >>> x = symbols('x')
 >>> from_meijerg(meijerg(([], []), ([S(1)/2], [0]), x**2/4))
 HolonomicFunction((1) + (1)*Dx**2, x, 0, [0, 1/sqrt(pi)])
Init docstring: x.__init__(...) initializes x; see help(type(x)) for 
signature
File: ~/sage/8.1/local/lib/python2.7/site-packages/sympy/holonomic/holonomic
.py
Type: function

Best wishes,

Eric. 

Le vendredi 13 avril 2018 00:06:17 UTC+2, Raymond Rogers a écrit :
>
> The sympy documentation
> http://docs.sympy.org/latest/modules/holonomic/convert.html
>  has the function from_meiljer and I do 
> from sympy import *
> from sympy.holonomic.holonomic import from_hyper, from_meijer, 
> DifferentialOperators
> (I think redundant)
> I get: "ImportError: cannot import name from_meijer" 
> Is this a versioning error or what?
>
>

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Re: [sage-support] simple?--from_meijer in jupyter

[Raymond Rogers]

Yes I had that; I thought the whole thing was too redundant.

Here is a complete entry and response:
from sympy import *
from sympy.holonomic.holonomic import from_hyper, from_meijer, 
DifferentialOperators

from sympy.holonomic.holonomic import *
from sympy.integrals import laplace_transform
from sympy.abc import z, t,s,a
from sympy.holonomic.holonomic import *

x, y= symbols('x y   ')
k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)
init_printing(use_unicode=True)
--
--Response

ImportError   Traceback (most recent call last)
 in ()
  1 from sympy import *
> 2 from sympy.holonomic.holonomic import from_hyper, from_meijer, 
DifferentialOperators

  3 from sympy.holonomic.holonomic import *
  4 from sympy.integrals import laplace_transform
  5 from sympy.abc import z, t,s,a

ImportError: cannot import name from_meijer
--
And the suggestion in your following message works; or at least doesn't 
error out.

But the attempt to:

from sympy.holonomic import DifferentialOperators,  from_meijer, from_hyper

continues to fail irrespective of the ordering of from_meijer and 
from_hyper.
I will check and see if that statement can be removed; perhaps it's not 
needed?


Ray


On 04/13/2018 03:25 AM, Henri Girard wrote:


Sorry if I spam :

I did this is it of any help as it works in sage-8.1

from sympy import *
from sympy.holonomic.holonomic import *
from sympy.holonomic import DifferentialOperators
from sympy.abc import x
from sympy import ZZ
R, D = DifferentialOperators(ZZ.old_poly_ring(x), 'D')
HolonomicFunction(D**2 + 1, x, 0, [0, 1])
HolonomicFunction((1) + (1)*D**2, x, 0, [0, 1])



Le 13/04/2018 à 00:06, Raymond Rogers a écrit :

The sympy documentation
http://docs.sympy.org/latest/modules/holonomic/convert.html
 has the function from_meiljer and I do
from sympy import *
from sympy.holonomic.holonomic import from_hyper, from_meijer, 
DifferentialOperators

(I think redundant)
I get: "ImportError: cannot import name from_meijer"
Is this a versioning error or what?
As a side issue: I am trying to go from generalized hypergeometric 
<-> meijerg

Is there a better way than through holomorphic?
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Re: [sage-support] points on a Fermat curve

[John Cremona]

This looks like a bug to me:

sage: F=GF(3)
sage: R.=F[]
sage: C=Curve(X^8+Y^8-Z^8)
sage: C.count_points(1) # correct count over GF(3^1)
[4]
sage: C.count_points(8) # should give counts over GF(3^n) for n=1..8 but it
crashes

TypeError: F (=[X^8 + Y^8 - Z^8]) must be a list or tuple of polynomials of
the coordinate ring of A  (=Projective Space of dimension 2 over Finite
Field in z2 of size 3^2)

-- note that the error message looks suspicious.

Also the more naive

sage: F=GF(3^8)
sage: R.=F[]
sage: C=Curve(X^8+Y^8-Z^8)
sage: C.count_points(1)
[4696]

works but is so slow it must be doing something very basic such as testing
every point in the plane (of which there are 3^16+3^8+1...)

John


On 13 April 2018 at 11:55, David Joyner  wrote:

> Hi:
>
> The question below is posted for Gary McGuire, who is not a subscriber
> to this list:
>
> "I would like to know the number of rational points on the (projective)
> curve
> x^8+y^8=z^8
> over the field of order 3^{18}.
>
> My question is, can Sage do this calculation, and how?"
>
> - David
>
> PS: About 3 years ago, a related question was posted:
> https://groups.google.com/forum/#!topic/sage-support/s59iDjhu2zU
> For some reason, the method described there is no longer implemented.
>
> --
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>

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[sage-support] points on a Fermat curve

[David Joyner]

Hi:

The question below is posted for Gary McGuire, who is not a subscriber
to this list:

"I would like to know the number of rational points on the (projective) curve
x^8+y^8=z^8
over the field of order 3^{18}.

My question is, can Sage do this calculation, and how?"

- David

PS: About 3 years ago, a related question was posted:
https://groups.google.com/forum/#!topic/sage-support/s59iDjhu2zU
For some reason, the method described there is no longer implemented.

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Re: [sage-support] simple?--from_meijer in jupyter

[Henri Girard]

Sorry if I spam :

I did this is it of any help as it works in sage-8.1

from sympy import *
from sympy.holonomic.holonomic import *
from sympy.holonomic import DifferentialOperators
from sympy.abc import x
from sympy import ZZ
R, D = DifferentialOperators(ZZ.old_poly_ring(x), 'D')
HolonomicFunction(D**2 + 1, x, 0, [0, 1])
HolonomicFunction((1) + (1)*D**2, x, 0, [0, 1])



Le 13/04/2018 à 00:06, Raymond Rogers a écrit :

The sympy documentation
http://docs.sympy.org/latest/modules/holonomic/convert.html
 has the function from_meiljer and I do
from sympy import *
from sympy.holonomic.holonomic import from_hyper, from_meijer, 
DifferentialOperators

(I think redundant)
I get: "ImportError: cannot import name from_meijer"
Is this a versioning error or what?
As a side issue: I am trying to go from generalized hypergeometric <-> 
meijerg

Is there a better way than through holomorphic?
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Re: [sage-support] simple?--from_meijer in jupyter

[Henri Girard]

from sympy.holonomic.holonomic import *

Have you tried this ?


Le 13/04/2018 à 00:06, Raymond Rogers a écrit :

The sympy documentation
http://docs.sympy.org/latest/modules/holonomic/convert.html
 has the function from_meiljer and I do
from sympy import *
from sympy.holonomic.holonomic import from_hyper, from_meijer, 
DifferentialOperators

(I think redundant)
I get: "ImportError: cannot import name from_meijer"
Is this a versioning error or what?
As a side issue: I am trying to go from generalized hypergeometric <-> 
meijerg

Is there a better way than through holomorphic?
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