Trac #19948: Upgrade to pynac-0.6.1

Brand new pynac has:
* Stieltjes constant function (#19834)
* `zeta` expansion at 1 using `stieltjes()` (#19836, thanks Benjamin
Hackl)
* fix hashing of infinities (#19928)
* fix `exp` and `atan` of `oo` (#19918)
* fix `pseries` print order
* speedups and fixes from GiNaC

'''Tarball''': https://github.com/pynac/pynac/releases/download/pynac-0.
6.1/pynac-0.6.1.tar.bz2

URL: http://trac.sagemath.org/19948
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Benjamin Hackl

Author: Release Manager

build/pkgs/pynac/checksums.ini

@@ -1,4 +1,4 @@
 tarball=pynac-VERSION.tar.bz2
-sha1=1c955b11dd52b6eefb43d5ebf00c3a735140faec
-md5=4cdac770128d41e230b06e3c82d928e0
-cksum=2890824965
+sha1=8de4355307261c4012922560b4257e07606aabea
+md5=551c7a8b07d8b5dbc7bf9adb8f710362
+cksum=226559555

build/pkgs/pynac/package-version.txt

@@ -1 +1 @@
-0.6.0
+0.6.1

src/sage/functions/transcendental.py

@@ -83,7 +83,7 @@ def __init__(self):
         Check that :trac:`15846` is resolved::
 
             sage: zeta(x).series(x==1, 1)
-            1*(x - 1)^(-1) + (euler_gamma + log(2) + log(pi) + 2*zetaderiv(1, 0)) + Order(x - 1)
+            1*(x - 1)^(-1) + (euler_gamma) + Order(x - 1)
             sage: zeta(x).residue(x==1)
             1
 

src/sage/symbolic/ginac.pxd

@@ -367,6 +367,7 @@ cdef extern from "sage/symbolic/ginac_wrap.h":
     GEx g_H "GiNaC::H" (GEx m, GEx x)                   except + # harmonic polylogarithm
     GEx g_zeta "GiNaC::zeta" (GEx m)                    except + # Riemann's zeta function as well as multiple zeta value
     GEx g_zeta2 "GiNaC::zeta" (GEx m, GEx s)            except + # alternating Euler sum
+    GEx g_stieltjes "GiNaC::stieltjes" (GEx m)          except + # Stieltjes constants
     GEx g_zetaderiv "GiNaC::zetaderiv" (GEx n, GEx x)   except + # derivatives of Riemann's zeta function
     GEx g_tgamma "GiNaC::tgamma" (GEx x)                except + # gamma function
     GEx g_lgamma "GiNaC::lgamma" (GEx x)                except + # logarithm of gamma function
@@ -473,6 +474,7 @@ cdef extern from "sage/symbolic/ginac_wrap.h":
     unsigned H_serial "GiNaC::H_SERIAL::serial" # harmonic polylogarithm
     unsigned zeta1_serial "GiNaC::zeta1_SERIAL::serial" # Riemann's zeta function as well as multiple zeta value
     unsigned zeta2_serial "GiNaC::zeta2_SERIAL::serial" # alternating Euler sum
+    unsigned stieltjes1_serial "GiNaC::stieltjes1_SERIAL::serial" # Stieltjes constants
     unsigned zetaderiv_serial "GiNaC::zetaderiv_SERIAL::serial" # derivatives of Riemann's zeta function
     unsigned tgamma_serial "GiNaC::tgamma_SERIAL::serial" # gamma function
     unsigned lgamma_serial "GiNaC::lgamma_SERIAL::serial" # logarithm of gamma function
@@ -527,6 +529,7 @@ cdef extern from "sage/symbolic/ginac_wrap.h":
         object (*py_bernoulli)(object x) except +
         object (*py_sin)(object x) except +
         object (*py_cos)(object x) except +
+        object (*py_stieltjes)(object x) except +
         object (*py_zeta)(object x) except +
         object (*py_exp)(object x) except +
         object (*py_log)(object x) except +

src/sage/symbolic/pynac.pyx

@@ -1457,6 +1457,48 @@ cdef object py_cos(object x) except +:
     except (TypeError, ValueError):
         return CC(x).cos()
 
+cdef object py_stieltjes(object x) except +:
+    """
+    Return the Stieltjes constant of the given index.
+
+    The value is expected to be a non-negative integer.
+
+    TESTS::
+
+        sage: from sage.symbolic.pynac import py_stieltjes_for_doctests as py_stieltjes
+        sage: py_stieltjes(0)
+        0.577215664901533
+        sage: py_stieltjes(1.0)
+        -0.0728158454836767
+        sage: py_stieltjes(RealField(100)(5))
+        0.00079332381730106270175333487744
+        sage: py_stieltjes(-1)
+        Traceback (most recent call last):
+        ...
+        ValueError: Stieltjes constant of negative index
+    """
+    n = ZZ(x)
+    if n < 0:
+        raise ValueError("Stieltjes constant of negative index")
+    import mpmath
+    if isinstance(x, Element) and hasattr((<Element>x)._parent, 'prec'):
+        prec = (<Element>x)._parent.prec()
+    else:
+        prec = 53
+    return mpmath_utils.call(mpmath.stieltjes, n, prec=prec)
+
+def py_stieltjes_for_doctests(x):
+    """
+    This function is for testing py_stieltjes().
+
+    EXAMPLES::
+
+        sage: from sage.symbolic.pynac import py_stieltjes_for_doctests
+        sage: py_stieltjes_for_doctests(0.0)
+        0.577215664901533
+    """
+    return py_stieltjes(x)
+
 cdef object py_zeta(object x) except +:
     """
     Return the value of the zeta function at the given value.
@@ -2264,6 +2306,7 @@ def init_function_table():
     py_funcs.py_bernoulli = &py_bernoulli
     py_funcs.py_sin = &py_sin
     py_funcs.py_cos = &py_cos
+    py_funcs.py_stieltjes = &py_stieltjes
     py_funcs.py_zeta = &py_zeta
     py_funcs.py_exp = &py_exp
     py_funcs.py_log = &py_log