Ticket #12455: trac_12455-symbolic_airy.patch

sage/functions/special.py

@@ -585 +585 @@
 
     return NewMaximaFunction()
 
+class AiryAi(BuiltinFunction):
+    r"""
+    The function `Ai(x)` and the related function `Bi(x)`,
+    which is also called an *Airy function*, are
+    solutions to the differential equation
+    
+    .. math::
+    
+      y'' - xy = 0,
+    
+    known as the *Airy equation*. The initial conditions
+    `Ai(0) = (\Gamma(2/3)3^{2/3})^{-1}`,
+    `Ai'(0) = -(\Gamma(1/3)3^{1/3})^{-1}` define `Ai(x)`.
+    The initial conditions `Bi(0) = 3^{1/2}Ai(0)`,
+    `Bi'(0) = -3^{1/2}Ai'(0)` define `Bi(x)`.
+    
+    They are named after the British astronomer George Biddell Airy.
+    They belong to the class of "Bessel functions of fractional order".
+    
+    EXAMPLES::
 
-def airy_ai(x):
-   r"""
-   The function `Ai(x)` and the related function `Bi(x)`,
-   which is also called an *Airy function*, are
-   solutions to the differential equation
+        sage: var('x')
+        sage: airy_ai(x)
+        airy_ai(x)
+        sage: airy_bi(x)
+        airy_bi(x)
+    
+    REFERENCE:
+    
+    - Abramowitz and Stegun: Handbook of Mathematical Functions,
+     http://www.math.sfu.ca/~cbm/aands/
+    
+    - http://en.wikipedia.org/wiki/Airy_function
+    """
+    def __init__(self):
+        BuiltinFunction.__init__(self, "airy_ai", latex_name=r"\operatorname{Ai}")
 
-   .. math::
+    def _derivative_(self, x, diff_param=None): return airy_ai_prime(x)
+    
+    def _evalf_(self, x, parent=None):
+        r"""
+        EXAMPLES::
 
+            sage: float(airy_ai(1.0))
+            0.135292416313
+        """        
+        _init()
+        return RDF(meval("airy_ai(%s)"%RDF(x)))
+airy_ai=AiryAi()
+
+class AiryBi(BuiltinFunction):
+    r"""
+    The function `Ai(x)` and the related function `Bi(x)`,
+    which is also called an *Airy function*, are
+    solutions to the differential equation
+    
+    .. math::
+    
       y'' - xy = 0,
+    
+    known as the *Airy equation*. The initial conditions
+    `Ai(0) = (\Gamma(2/3)3^{2/3})^{-1}`,
+    `Ai'(0) = -(\Gamma(1/3)3^{1/3})^{-1}` define `Ai(x)`.
+    The initial conditions `Bi(0) = 3^{1/2}Ai(0)`,
+    `Bi'(0) = -3^{1/2}Ai'(0)` define `Bi(x)`.
+    
+    They are named after the British astronomer George Biddell Airy.
+    They belong to the class of "Bessel functions of fractional order".
+    
+    EXAMPLES::
 
-   known as the *Airy equation*. The initial conditions
-   `Ai(0) = (\Gamma(2/3)3^{2/3})^{-1}`,
-   `Ai'(0) = -(\Gamma(1/3)3^{1/3})^{-1}` define `Ai(x)`.
-   The initial conditions `Bi(0) = 3^{1/2}Ai(0)`,
-   `Bi'(0) = -3^{1/2}Ai'(0)` define `Bi(x)`.
+        sage: var('x')
+        sage: airy_ai(x)
+        airy_ai(x)
+        sage: airy_bi(x)
+        airy_bi(x)
+    
+    REFERENCE:
+    
+    - Abramowitz and Stegun: Handbook of Mathematical Functions,
+     http://www.math.sfu.ca/~cbm/aands/
+    
+    - http://en.wikipedia.org/wiki/Airy_function
+    """
+    def __init__(self):
+        BuiltinFunction.__init__(self, "airy_bi", latex_name=r"\operatorname{Bi}")
+    def _derivative_(self, x, diff_param=None): return airy_ai_prime(x)
 
-   They are named after the British astronomer George Biddell Airy.
-   They belong to the class of "Bessel functions of fractional order".
+    def _evalf_(self, x, parent=None):
+        r"""
+        EXAMPLES::
 
-   EXAMPLES::
-   
-       sage: airy_ai(1.0)        # last few digits are random
-       0.135292416312881400
-       sage: airy_bi(1.0)        # last few digits are random
-       1.20742359495287099
+            sage: float(airy_bi(1.0))
+            1.20742359495
+        """
+        _init()
+        return RDF(meval("airy_bi(%s)"%RDF(x)))
+airy_bi=AiryBi()
 
-   REFERENCE:
+class AiryAiPrime(BuiltinFunction):
+    r"""
+    The derivative of the Airy function `Ai(x)`.
+    """
+    def __init__(self):
+        BuiltinFunction.__init__(self, "airy_ai_prime", latex_name=r"\operatorname{Ai}'")
+airy_ai_prime=AiryAiPrime()
 
-   - Abramowitz and Stegun: Handbook of Mathematical Functions,
-     http://www.math.sfu.ca/~cbm/aands/
-
-   - http://en.wikipedia.org/wiki/Airy_function
-   """
-   _init()
-   return RDF(meval("airy_ai(%s)"%RDF(x)))
-
-def airy_bi(x):
-   r"""
-   The function `Ai(x)` and the related function `Bi(x)`,
-   which is also called an *Airy function*, are
-   solutions to the differential equation
-
-   .. math::
-
-      y'' - xy = 0,
-
-   known as the *Airy equation*. The initial conditions
-   `Ai(0) = (\Gamma(2/3)3^{2/3})^{-1}`,
-   `Ai'(0) = -(\Gamma(1/3)3^{1/3})^{-1}` define `Ai(x)`.
-   The initial conditions `Bi(0) = 3^{1/2}Ai(0)`,
-   `Bi'(0) = -3^{1/2}Ai'(0)` define `Bi(x)`.
-
-   They are named after the British astronomer George Biddell Airy.
-   They belong to the class of "Bessel functions of fractional order".
-
-   EXAMPLES::
-   
-       sage: airy_ai(1)        # last few digits are random
-       0.135292416312881400
-       sage: airy_bi(1)        # last few digits are random
-       1.20742359495287099
-
-   REFERENCE:
-
-   - Abramowitz and Stegun: Handbook of Mathematical Functions,
-     http://www.math.sfu.ca/~cbm/aands/
-
-   - http://en.wikipedia.org/wiki/Airy_function
-   """
-   _init()
-   return RDF(meval("airy_bi(%s)"%RDF(x)))
-
+class AiryBiPrime(BuiltinFunction):
+    r"""
+    The derivative of the Airy function `Bi(x)`.
+    """
+    def __init__(self):
+        BuiltinFunction.__init__(self, "airy_bi_prime", latex_name=r"\operatorname{Bi}'")
+airy_bi_prime=AiryBiPrime()
 
 def bessel_I(nu,z,algorithm = "pari",prec=53):
     r"""