Changes between Initial Version and Version 11 of Ticket #11143


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Timestamp:
06/13/11 02:10:22 (10 years ago)
Author:
benjaminfjones
Comment:

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  • Ticket #11143

    • Property Cc benjaminfjones added
    • Property Keywords special function maxima added
  • Ticket #11143 – Description

    initial v11  
    77}}}
    88See [http://ask.sagemath.org/question/488/calculating-integral this ask.sagemath post] for some details.
     9
     10== Current symbol conversion table ==
     11From `sage.symbolic.pynac.symbol_table['maxima']` as of Sage-4.7
    912{{{
    10 sage: sage.symbolic.pynac.symbol_table['maxima']
    11 {'elliptic_e': elliptic_e, 'imagpart': imag_part, 'acsch': arccsch, 'glaisher': glaisher, 'asinh': arcsinh, 'minf': -Infinity, 'elliptic_f': elliptic_f, '(1+sqrt(5))/2': golden_ratio, 'inf': +Infinity, 'log(2)': log2, 'kron_delta': kronecker_delta, 'asin': arcsin, 'log': log, 'atanh': arctanh, 'brun': brun, '%pi': pi, 'acosh': arccosh, 'sin': sin, 'mertens': mertens, 'ceiling': ceil, 'infinity': Infinity, 'elliptic_ec': elliptic_ec, 'atan': arctan, 'factorial': factorial, 'twinprime': twinprime, 'khinchin': khinchin, 'catalan': catalan, 'signum': sgn, 'binomial': binomial, 'delta': dirac_delta, 'asec': arcsec, 'elliptic_kc': elliptic_kc, '%gamma': euler_gamma, 'realpart': real_part, 'elliptic_eu': elliptic_eu, 'cos': cos, 'acoth': arccoth, 'gamma_incomplete': gamma, 'li[2]': dilog, 'atan2': arctan2, 'exp': exp, 'psi[0]': psi, 'asech': arcsech, 'acos': arccos, 'acot': arccot, 'acsc': arccsc, 'elliptic_pi': elliptic_pi}
     13Maxima ---> Sage
     14
     15%gamma ---> euler_gamma
     16%pi ---> pi
     17(1+sqrt(5))/2 ---> golden_ratio
     18acos ---> arccos
     19acosh ---> arccosh
     20acot ---> arccot
     21acoth ---> arccoth
     22acsc ---> arccsc
     23acsch ---> arccsch
     24asec ---> arcsec
     25asech ---> arcsech
     26asin ---> arcsin
     27asinh ---> arcsinh
     28atan ---> arctan
     29atan2 ---> arctan2
     30atanh ---> arctanh
     31binomial ---> binomial
     32brun ---> brun
     33catalan ---> catalan
     34ceiling ---> ceil
     35cos ---> cos
     36delta ---> dirac_delta
     37elliptic_e ---> elliptic_e
     38elliptic_ec ---> elliptic_ec
     39elliptic_eu ---> elliptic_eu
     40elliptic_f ---> elliptic_f
     41elliptic_kc ---> elliptic_kc
     42elliptic_pi ---> elliptic_pi
     43exp ---> exp
     44expintegral_e ---> En
     45factorial ---> factorial
     46gamma_incomplete ---> gamma
     47glaisher ---> glaisher
     48imagpart ---> imag_part
     49inf ---> +Infinity
     50infinity ---> Infinity
     51khinchin ---> khinchin
     52kron_delta ---> kronecker_delta
     53li[2] ---> dilog
     54log ---> log
     55log(2) ---> log2
     56mertens ---> mertens
     57minf ---> -Infinity
     58psi[0] ---> psi
     59realpart ---> real_part
     60signum ---> sgn
     61sin ---> sin
     62twinprime ---> twinprime
    1263}}}
     64
     65= Summary of missing conversions =
     66
     67== Special functions defined in Maxima ==
     68(http://maxima.sourceforge.net/docs/manual/en/maxima_16.html#SEC56)
     69
     70{{{
     71bessel_j (index, expr)         Bessel function, 1st kind
     72bessel_y (index, expr)         Bessel function, 2nd kind
     73bessel_i (index, expr)         Modified Bessel function, 1st kind
     74bessel_k (index, expr)         Modified Bessel function, 2nd kind
     75}}}
     76
     77 * Notes: bessel_I, bessel_J, etc. are functions in Sage for numerical evaluation. There is also the `Bessel` class, but no conversions from Maxima's bessel_i etc. to Sage.
     78
     79{{{
     80hankel_1 (v,z)                 Hankel function of the 1st kind
     81hankel_2 (v,z)                 Hankel function of the 2nd kind
     82struve_h (v,z)                 Struve H function
     83struve_l (v,z)                 Struve L function
     84}}}
     85
     86 * Notes: None of these functions are currently exposed at the top level in Sage. Evaluation is possible using mpmath.
     87
     88{{{
     89assoc_legendre_p[v,u] (z)      Legendre function of degree v and order u
     90assoc_legendre_q[v,u] (z)      Legendre function, 2nd kind
     91}}}
     92
     93 * Notes: In Sage we have `legendre_P(n, x)` and `legendre_Q(n, x)` both described as Legendre functions. It's not clear to me how there are related to Maxima's versions since the number of arguments differs.
     94
     95{{{
     96%f[p,q] ([], [], expr)         Generalized Hypergeometric function
     97hypergeometric(l1, l2, z)      Hypergeometric function
     98slommel
     99%m[u,k] (z)                    Whittaker function, 1st kind
     100%w[u,k] (z)                    Whittaker function, 2nd kind
     101}}}
     102
     103 * Notes: `hypergeometric(l1, l2, z)` needs a conversion to Sage's `hypergeometric_U`. The others can be evaluated using mpmath. `slommel` is presumably mpmath's `lommels1()` or `lommels2()` (or both?). This isn't well documented in Maxima.
     104
     105{{{
     106expintegral_e (v,z)            Exponential integral E
     107expintegral_e1 (z)             Exponential integral E1
     108expintegral_ei (z)             Exponential integral Ei
     109expintegral_li (z)             Logarithmic integral Li
     110expintegral_si (z)             Exponential integral Si
     111expintegral_ci (z)             Exponential integral Ci
     112expintegral_shi (z)            Exponential integral Shi
     113expintegral_chi (z)            Exponential integral Chi
     114erfc (z)                       Complement of the erf function
     115}}}
     116
     117 * Notes: The exponential integral functions `expintegral_e1` and `expintegral_ei (z)` are called `exponential_integral_1` and `Ei` resp. in Sage. They both need conversions. The rest need `BuiltinFunction` classes defined for them with evaluation handled by mpmath and the symbol table conversion added. Also, `erfc` is called `error_fcn`, so also needs a conversion.
     118
     119{{{
     120kelliptic (z)                  Complete elliptic integral of the first
     121                               kind (K)
     122parabolic_cylinder_d (v,z)     Parabolic cylinder D function
     123}}}
     124
     125 * Notes: `kelliptic(z)` needs a conversion to `elliptic_kc` in Sage and `parabolic_cylinder_d (v,z)` does not seem to be exposed at top level. It can be evaluated by mpmath.