Changeset 7386:9a74afabd367

Timestamp:

11/20/07 07:30:58 (6 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Message:

Fix trac #215 and add asinh, acosh, atanh.

Location:

sage/calculus

Files:

• all.py (modified) (1 diff)
• calculus.py (modified) (5 diffs)

sage/calculus/all.py

@@ -11 +11 @@
                       sin, cos, sec, csc, cot, tan, log, erf, sqrt, asin, acos, atan,
                       tanh, sinh, cosh, coth, sech, csch, ln,
+                      asinh, acosh, atanh,
                       ceil, floor,
                       polylog,

sage/calculus/calculus.py

@@ -129 +129 @@
         sage: f.diff(x)
         1/(3*sqrt(x^2/9 + 1))
+
+    We compute the length of the parabola from 0 to 2:
+        sage: x = var('x')
+        sage: y = x^2
+        sage: dy = diff(y,x)
+        sage: z = integral(sqrt(1 + dy^2), x, 0, 2)
+        sage: print z
+                             asinh(4) + 4 sqrt(17)
+                             ---------------------
+                                       4
+        sage: n(z,200)
+        4.6467837624329358733826155674904591885104869874232887508703
+        sage: float(z)
+        4.6467837624329356
 
 COERCION EXAMPLES:
@@ -4377 +4391 @@
 _syms['asin'] = asin
 
+class Function_asinh(PrimitiveFunction):
+    """
+    The inverse of the hyperbolic sine function.
+
+    EXAMPLES:
+        sage: asinh(0.5)
+        0.481211825059603
+        sage: asinh(1/2)
+        asinh(1/2)
+        sage: asinh(1 + I*1.0)
+        0.6662394324925153*I + 1.061275061905036
+    """
+    def _repr_(self, simplify=True):
+        return "asinh"
+
+    def _latex_(self):
+        return "\\sinh^{-1}"
+
+    def _approx_(self, x):
+        return float(pari(float(x)).asinh())
+
+asinh = Function_asinh()
+_syms['asinh'] = asinh
+
+class Function_acosh(PrimitiveFunction):
+    """
+    The inverse of the hyperbolic cose function.
+
+    EXAMPLES:
+        sage: acosh(1/2)
+        acosh(1/2)
+        sage: acosh(1 + I*1.0)
+        0.9045568943023813*I + 1.061275061905036
+
+    Warning: If the input is real the output will be real or NaN:
+        sage: acosh(0.5)
+        NaN
+
+    But evaluate where the input is in the complex field yields a complex output:
+        sage: acosh(CC(0.5))
+        1.04719755119660*I
+        
+    """
+    def _repr_(self, simplify=True):
+        return "acosh"
+
+    def _latex_(self):
+        return "\\cosh^{-1}"
+
+    def _approx_(self, x):
+        return float(pari(float(x)).acosh())
+
+acosh = Function_acosh()
+_syms['acosh'] = acosh
+
+class Function_atanh(PrimitiveFunction):
+    """
+    The inverse of the hyperbolic tane function.
+
+    EXAMPLES:
+        sage: atanh(0.5)
+        0.549306144334055
+        sage: atanh(1/2)
+        atanh(1/2)
+        sage: atanh(1 + I*1.0)
+        1.017221967897851*I + 0.4023594781085251
+    """
+    def _repr_(self, simplify=True):
+        return "atanh"
+
+    def _latex_(self):
+        return "\\tanh^{-1}"
+
+    def _approx_(self, x):
+        return float(pari(float(x)).atanh())
+
+atanh = Function_atanh()
+_syms['atanh'] = atanh
+
 class Function_acos(PrimitiveFunction):
     """
@@ -4932 +5025 @@
         self._kwds = kwds
 
+    def __float__(self):
+        return float(maxima(self))
+    
     def _is_atomic(self):
         return True
@@ -4940 +5036 @@
     def keyword_arguments(self):
         return self._kwds
-    
+
     def _repr_(self, simplify=True):
         if simplify:
@@ -5234 +5330 @@
                 nm = msg[i+1:j]
 
-                res = re.match(nm + '\s*\(.*\)', s)
+                res = re.match('.*' + nm + '\s*\(.*\)', s)
                 if res:
                     syms[nm] = function(nm)