Say I want to get Mathematica to compute some function that Sage can't
compute for me. What is the best way to pipe the arguments into
Mathematica, and then get the answer back into the world of sage?
Here's what I tried:
sage: def math_bessel_K(nu,x):
... m=mathematica('N[BesselK['+str(mathematica(nu))
+','+str(mathematica(x))+'],20]')
... return m.sage()
...
This seems to work: See the appended output.
But I wonder if it's really necessary to do the conversion to a string
and then the string concatenations. Maybe there is a more direct way
to get the arguments into Mathematica?
Also, I wonder about the type when the result is a complex number: Do
I really want the result to have type
<class 'sage.calculus.calculus.SymbolicArithmetic'>? I presume I want
to get the result into a standard
Sage type, rather than having it maintain its connection with
Mathematica. But would I be better off converting
it to some other format, e.g. some kind of complex number that takes
account of the the precision that the
result carries?
But, maybe there is already a general way of subcontracting a
computation like this to Mathematica, or Maple, or Matlab, or
whatever?
Finally, note that Sage's bessel_K gets very close to computing the
result for me.
Cheers,
Peter
------------
sage: def bessel_comp(nu,x):
... m=math_bessel_K(nu,x)
... print m
... print type(m)
... print
... p=pari(nu).besselk(x)
... print p
... print type(p)
... print
... s=bessel_K(nu,x,100)
... print
... print type(s)
sage: bessel_comp(2,3)
0.061510458471742037657
<type 'sage.rings.real_mpfr.RealNumber'>
0.06151045847174203765682007145288
<type 'sage.libs.pari.gen.gen'>
0.061510458471742037656820071453
<type 'sage.rings.real_mpfr.RealNumber'>
sage: bessel_comp(2,I)
0.180489972066962 I - 2.592886175491197
<class 'sage.calculus.calculus.SymbolicArithmetic'>
-2.592886175491196978167660649170 +
0.1804899720669620266296208813982*I
<type 'sage.libs.pari.gen.gen'>
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
88.py", line 4, in <module>
exec compile(ur'bessel_comp(Integer(2),I)' + '\n', '', 'single')
File "/usr/local/sage-2.8.15-ubuntu32bit-i686-Linux/data/extcode/
sage/", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
86.py", line 16, in bessel_comp
s=bessel_K(nu,x,Integer(100))
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/
functions/special.py", line 526, in bessel_K
b = RR(pari(nu).besselk(z))
File "real_mpfr.pyx", line 244, in
sage.rings.real_mpfr.RealField.__call__
File "real_mpfr.pyx", line 673, in
sage.rings.real_mpfr.RealNumber._set
TypeError: Unable to convert x
(='-2.592886175491196978167660649170+0.1804899720669620266296208813982*I')
to real number.
sage: bessel_comp(2,3+I)
0.0152759650615147 - 0.0554717495270565 I
<class 'sage.calculus.calculus.SymbolicArithmetic'>
0.01527596506151469555940906153650 -
0.05547174952705649444323133156426*I
<type 'sage.libs.pari.gen.gen'>
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
89.py", line 4, in <module>
exec compile(ur'bessel_comp(Integer(2),Integer(3)+I)' + '\n', '',
'single')
File "/usr/local/sage-2.8.15-ubuntu32bit-i686-Linux/data/extcode/
sage/", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
86.py", line 16, in bessel_comp
s=bessel_K(nu,x,Integer(100))
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/
functions/special.py", line 526, in bessel_K
b = RR(pari(nu).besselk(z))
File "real_mpfr.pyx", line 244, in
sage.rings.real_mpfr.RealField.__call__
File "real_mpfr.pyx", line 673, in
sage.rings.real_mpfr.RealNumber._set
TypeError: Unable to convert x
(='0.01527596506151469555940906153650-0.05547174952705649444323133156426*I')
to real number.
sage: bessel_comp(2+I,3)
0.0289192946582081 I + 0.0455907718407551
<class 'sage.calculus.calculus.SymbolicArithmetic'>
0.04559077184075505871203211093879 +
0.02891929465820812820828883525761*I
<type 'sage.libs.pari.gen.gen'>
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
90.py", line 4, in <module>
exec compile(ur'bessel_comp(Integer(2)+I,Integer(3))' + '\n', '',
'single')
File "/usr/local/sage-2.8.15-ubuntu32bit-i686-Linux/data/extcode/
sage/", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
86.py", line 16, in bessel_comp
s=bessel_K(nu,x,Integer(100))
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/
functions/special.py", line 526, in bessel_K
b = RR(pari(nu).besselk(z))
File "real_mpfr.pyx", line 244, in
sage.rings.real_mpfr.RealField.__call__
File "real_mpfr.pyx", line 673, in
sage.rings.real_mpfr.RealNumber._set
TypeError: Unable to convert x
(='0.04559077184075505871203211093879+0.02891929465820812820828883525761*I')
to real number.
sage: bessel_comp(2+I,3+I)
0.0431928272695873 - 0.0400595380665329 I
<class 'sage.calculus.calculus.SymbolicArithmetic'>
0.04319282726958726692927951697209 -
0.04005953806653287581272798713877*I
<type 'sage.libs.pari.gen.gen'>
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
91.py", line 4, in <module>
exec compile(ur'bessel_comp(Integer(2)+I,Integer(3)+I)' + '\n',
'', 'single')
File "/usr/local/sage-2.8.15-ubuntu32bit-i686-Linux/data/extcode/
sage/", line 1, in <module>
File "/home/doyle/.sage/sage_notebook/worksheets/admin/5/code/
86.py", line 16, in bessel_comp
s=bessel_K(nu,x,Integer(100))
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/
functions/special.py", line 526, in bessel_K
b = RR(pari(nu).besselk(z))
File "real_mpfr.pyx", line 244, in
sage.rings.real_mpfr.RealField.__call__
File "real_mpfr.pyx", line 673, in
sage.rings.real_mpfr.RealNumber._set
TypeError: Unable to convert x
(='0.04319282726958726692927951697209-0.04005953806653287581272798713877*I')
to real number.
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/
-~----------~----~----~----~------~----~------~--~---
