first sketch of MZV function

src/sage/functions/multizeta.py

@@ -0,0 +1,95 @@
+"""
+Multiple zeta values
+"""
+from __future__ import print_function
+
+from sage.symbolic.function import BuiltinFunction
+from sage.rings.all import Integer
+from sage.misc.latex import latex
+from sage.symbolic.ring import SR
+from sage.libs.all import pari
+
+
+class MultipleZetaValue(BuiltinFunction):
+    def __init__(self):
+        """
+        Initialize class.
+
+        EXAMPLES::
+
+            sage: maxima(hypergeometric)
+            hypergeometric
+        """
+        BuiltinFunction.__init__(self, 'multizeta', nargs=1,
+                                 conversions={'pari': 'zetamult'})
+
+    def __call__(self, a):
+        r"""
+        Return the multiple zeta value of `n_1,n_2,...,n_k`.
+
+        INPUT:
+
+        - ``a`` -- a list or tuple of parameters
+
+        EXAMPLES::
+
+            sage: from sage.functions.multizeta import multizeta
+            sage: multizeta((4,2))
+            multizeta((4, 2))
+        """
+        return BuiltinFunction.__call__(self, SR._force_pyobject(a))
+
+    def _print_latex_(self, a):
+        r"""
+        TESTS::
+
+            sage: from sage.functions.multizeta import multizeta
+            sage: latex(multizeta([2, 2]))
+            \zeta(2,2)
+        """
+        aa = ",".join(latex(c) for c in a)
+        return r"\zeta(" + aa + ")"
+
+    def _eval_(self, a):
+        """
+        Evaluate the multiple zeta value.
+
+        EXAMPLES::
+
+            sage: from sage.functions.multizeta import multizeta
+            sage: multizeta((3,3,2))
+            multizeta((3, 3, 2))
+        """
+        if not isinstance(a, tuple):
+            raise TypeError("The parameters must be of type tuple")
+        if not all(isinstance(y, Integer) for y in a):
+            raise TypeError('arguments must be integers')
+        if not all(y >= 1 for y in a):
+            raise TypeError('arguments must be positive integers')
+        if a[0] == 1:
+            raise ValueError('divergence')
+
+    def _evalf_(self, a, parent, algorithm=None):
+        """
+        TESTS::
+
+            sage: from sage.functions.multizeta import multizeta
+            sage: M = multizeta((3,))
+            sage: pari(M)
+            1.20205690315959
+            sage: M = multizeta((2,1))
+            sage: pari(M)
+            1.20205690315959
+        """
+        if not isinstance(a, tuple):
+            raise TypeError("The first parameters must be of type tuple")
+
+        if algorithm is None:
+            algorithm = "pari"
+        if algorithm == "pari":
+            return pari(a).zetamult()
+
+        raise ValueError("unknown algorithm")
+
+
+multizeta = MultipleZetaValue()