16671: swap arguments wrt maxima(_lib); add more documentation

Author: rwst

src/sage/calculus/calculus.py

@@ -1752,6 +1752,8 @@ def _inverse_laplace_latex_(self, *args):
 
 maxima_hyper = re.compile("\%f\[\d+,\d+\]")  # matches %f[m,n]
 
+maxima_harmonic = re.compile("gen_harmonic_number\(([^,]+),([^,]+)\)")
+
 def symbolic_expression_from_maxima_string(x, equals_sub=False, maxima=maxima):
     """
     Given a string representation of a Maxima expression, parse it and
@@ -1888,7 +1890,8 @@ def symbolic_expression_from_maxima_string(x, equals_sub=False, maxima=maxima):
 
     s = polylog_ex.sub('polylog(\\1,', s)
     s = maxima_polygamma.sub('psi(\g<1>,', s) # this replaces psi[n](foo) with psi(n,foo), ensuring that derivatives of the digamma function are parsed properly below
-
+    s = maxima_harmonic.sub('gen_harmonic_number(\\2,\\1)', s) # swap arguments of gen_harmonic_number 
+    
     if equals_sub:
         s = s.replace('=','==')
         # unfortunately, this will turn != into !==, which we correct

src/sage/functions/log.py

@@ -801,11 +801,24 @@ class Function_harmonic_number_generalized(BuiltinFunction):
 
     Evaluation of integer, rational, or complex argument::
     
-        sage:
+        sage: harmonic_number(5)
+        137/60
+        sage: harmonic_number(3,3)
+        251/216
+        sage: harmonic_number(5/2)
+        -2*log(2) + 46/15
+        sage: harmonic_number(5/2,2)
+        -hurwitz_zeta(5/2, 3) + zeta(5/2)
+        sage: harmonic_number(1+I,5)
+        -hurwitz_zeta(I + 1, 6) + zeta(I + 1)
+        sage: harmonic_number(1.+I,5)
+        1.57436810798989 - 1.06194728851357*I
 
     Solutions to certain sums are returned in terms of harmonic numbers::
 
-        sage:
+        sage: k=var('k')
+        sage: sum(1/k^7,k,1,x)
+        harmonic_number(x, 7)
 
     Check the defining integral. at a random integer::
 
@@ -819,6 +832,22 @@ class Function_harmonic_number_generalized(BuiltinFunction):
         0
         sage: harmonic_number(1)
         1
+        sage: harmonic_number(x,1)
+        harmonic_number(x)
+        
+    Arguments are swapped with respect to the same functions in
+    Maxima::
+    
+        sage: maxima(harmonic_number(x,2)) # maxima expect interface
+        gen_harmonic_number(2,x)
+        sage: from sage.calculus.calculus import symbolic_expression_from_maxima_string as sefms
+        sage: sefms('gen_harmonic_number(3,x)')
+        harmonic_number(x, 3)
+        sage: from sage.interfaces.maxima_lib import maxima_lib, max_to_sr
+        sage: c=maxima_lib(harmonic_number(x,2)); c
+        gen_harmonic_number(2,x)
+        sage: max_to_sr(c.ecl())
+        harmonic_number(x, 2)
     """
 
     def __init__(self):
@@ -891,6 +920,8 @@ def _evalf_(self, z, m, parent=None, algorithm=None):
         """
         EXAMPLES::
 
+            sage: harmonic_number(5/2,2)
+            -hurwitz_zeta(5/2, 3) + zeta(5/2)
             sage: harmonic_number(3.,3).n(200)
             1.162037037037036979469917...
             sage: harmonic_number(I,5).n()
@@ -899,6 +930,15 @@ def _evalf_(self, z, m, parent=None, algorithm=None):
         from sage.functions.transcendental import zeta, hurwitz_zeta
         return zeta(z) - hurwitz_zeta(z,m+1)
 
+    def _maxima_init_evaled_(self, n, z):
+        """
+        EXAMPLES:
+
+            sage: maxima(harmonic_number(x,2))
+            gen_harmonic_number(2,x)
+        """
+        return "gen_harmonic_number(%s,%s)" % (z, n) # swap arguments
+
     def _print_(self, z, m):
         """
         EXAMPLES::

src/sage/interfaces/maxima_lib.py

@@ -1267,6 +1267,7 @@ def sage_rat(x,y):
 max_array = EclObject("ARRAY")
 mdiff = EclObject("%DERIVATIVE")
 max_lambert_w = sage_op_dict[sage.functions.log.lambert_w]
+max_harmo = EclObject("$GEN_HARMONIC_NUMBER")
 
 def mrat_to_sage(expr):
     r"""
@@ -1448,21 +1449,37 @@ def dummy_integrate(expr):
         return sage.symbolic.integration.integral.indefinite_integral(*args,
                                                                   hold=True)
 
+def max_harmonic_to_sage(expr):
+    """
+    EXAMPLES::
+
+        sage: from sage.interfaces.maxima_lib import maxima_lib, max_to_sr
+        sage: c=maxima_lib(harmonic_number(x,2))
+        sage: c.ecl()
+        <ECL: (($GEN_HARMONIC_NUMBER SIMP) 2 $X)>
+        sage: max_to_sr(c.ecl())
+        harmonic_number(x, 2)
+    """
+    return sage.functions.log.harmonic_number(max_to_sr(caddr(expr)),
+                                              max_to_sr(cadr(expr)))
+
 ## The dictionaries
 special_max_to_sage={
     mrat : mrat_to_sage,
     mqapply : mqapply_to_sage,
     mdiff : mdiff_to_sage,
     EclObject("%INTEGRATE") : dummy_integrate,
     max_at : max_at_to_sage,
-    mlist : mlist_to_sage
+    mlist : mlist_to_sage,
+    max_harmo : max_harmonic_to_sage
 }
 
 special_sage_to_max={
     sage.functions.log.polylog : lambda N,X : [[mqapply],[[max_li, max_array],N],X],
     sage.functions.other.psi1 : lambda X : [[mqapply],[[max_psi, max_array],0],X],
     sage.functions.other.psi2 : lambda N,X : [[mqapply],[[max_psi, max_array],N],X],
     sage.functions.log.lambert_w : lambda N,X : [[max_lambert_w], X] if N==EclObject(0) else [[mqapply],[[max_lambert_w, max_array],N],X],
+    sage.functions.log.harmonic_number : lambda N,X : [[mqapply],[[max_harmo, max_array],X],N],
     sage.functions.hypergeometric.hypergeometric : lambda A, B, X : [[mqapply],[[max_hyper, max_array],lisp_length(A.cdr()),lisp_length(B.cdr())],A,B,X]
 }