Ticket #1275: qqbar-sqrt-golden.patch

a/sage/functions/constants.py

@@ -694 +694 @@
-        return R('1.61803398874989484820458683436563811772030917980576286213544862')
-    
-    def _mpfr_(self,R):  #is this OK for _mpfr_ ?
-       
+        
-
-    def _algebraic_(self, field):
-
-
+
-
-golden_ratio = GoldenRatio()
-    

a/sage/rings/complex_interval.pyx

@@ -599 +599 @@
-            [0.00000000000000000 .. 0.00000000000000000]
-            sage: CIF(-2).argument()
-            [3.1415926535897931 .. 3.1415926535897936]
+            sage: CIF(2).argument().is_exact()
+            True
-        """
-        if mpfi_has_zero(self.__re) and mpfi_has_zero(self.__im):
-
@@ -647 +649 @@
-
-            fld = self.parent()._real_field()
-
+            if mpfr_zero_p(&self.__im.left) and mpfr_zero_p(&self.__im.right):
+                if mpfi_is_strictly_pos(self.__re):
+                    return fld(0)
+                else:
+                    return fld.pi()
-            if mpfi_is_strictly_pos(self.__im):
-                return (-self.real() / self.imag()).atan() + fld.pi()/2
-            if mpfi_is_strictly_neg(self.__im):
@@ -738 +745 @@
-        theta = self.argument()
-        rho = abs(self)
-        return ComplexIntervalFieldElement(self._parent, rho.log(), theta)
+        
+    def sqrt(self, bint all=False, **kwds):
+        """
+        The square root function. 
+        
+        Branch cut along negative real axis, with sqrt(-r^2) = i*r for real r. 
+                
+        INPUT:
+            all -- bool (default: False); if True, return a list
+                of all square roots.
+        
+        EXAMPLES: 
+            sage: a = CIF(-1).sqrt()^2; a
+            [-1.0000000000000003 .. -0.99999999999999966] + [-0.00000000000000032162452993532733 .. 0.00000000000000012246467991473533]*I
+            sage: sqrt(CIF(2))
+            [1.4142135623730949 .. 1.4142135623730952]
+            sage: sqrt(CIF(-1))
+            [-0.00000000000000016081226496766367 .. 0.000000000000000061232339957367661] + [0.99999999999999988 .. 1.0000000000000000]*I
+            sage: sqrt(CIF(2-I))^2
+            [1.9999999999999980 .. 2.0000000000000014] - [0.99999999999999877 .. 1.0000000000000012]*I
+            sage: CC(-2-I).sqrt()^2
+            -2.00000000000000 - 1.00000000000000*I
+        """
+        if self.is_zero():
+            return [self] if all else self
+        theta = self.argument()/2
+        rho = abs(self).sqrt()
+        x = ComplexIntervalFieldElement(self._parent, rho*theta.cos(), rho*theta.sin())
+        if all:
+            return [x, -x]
+        else:
+            return x
+
-
-    def is_square(self):
-        """

a/sage/rings/qqbar.py

@@ -4031 +4031 @@
-
-QQbar_hash_offset = AlgebraicNumber(ANExtensionElement(QQbar_I_generator, ~ZZ(123456789) + QQbar_I_nf.gen()/ZZ(987654321)))
-
-ZZX_x = ZZ['x'].gen()
-
-# This is used in the _algebraic_ method of the golden_ratio constant,
-# in sage/functions/constants.py
-AA_golden_ratio = None
-
-def get_AA_golden_ratio():
-    global AA_golden_ratio
-    if AA_golden_ratio is None:
-        AA_golden_ratio_nf = NumberField(ZZX_x**2 - ZZX_x - 1, 'phi')
-        AA_golden_ratio_generator = AlgebraicGenerator(AA_golden_ratio_nf, ANRoot(AAPoly.gen()**2 - AAPoly.gen() - 1, RIF(1.618, 1.6181)))
-        AA_golden_ratio = AlgebraicReal(ANExtensionElement(AA_golden_ratio_generator, AA_golden_ratio_nf.gen()))
-    return AA_golden_ratio