Hi Guys
was just wondering whether the "algebraic" coercion QQbar --> SR had been
implemented in any form yet? I certainly cannot trick it into happening! ...
eg I have a matrix in SR and I need its (diagonalization and) normalized
eigenmatrix - that doesn't seem to work in SR (not that I expected it to!)
so I change rings to QQbar and it works fine - but then I have a matrix
over QQbar and I need to recognise the algebraic numbers, and they are not
very nice ... so it would be great to be able to see them in the usual SR
format. But if I coerce them explicitly to SR via SR(x?) they remain in the
format x? and I do not seem to be able to trick them back into their
original format. I would love any suggestions as to how to do this (other
than Wolfram Alpha, which abandons ship too quickly ...)
Many thanks
Gary
On Thursday, April 8, 2010 12:05:09 AM UTC+1, Alex Raichev wrote:
>
> Hi all:
>
> I ran into an error trying to evaluate the exponential function at an
> algebraic number. Looks like there's a bug in substituting algebraic
> numbers for variables; see below. While i was at it, i tried creating
> the expression QQbar(sqrt(2))*x and got a not implemented error.
> Wasn't symbolics with QQbar working in previous versions of Sage, or
> am i mistaken?
>
> Alex
>
> ----------------------------------------------------------------------
> | Sage Version 4.3.5, Release Date: 2010-03-28 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: exp(QQbar(sqrt(2)))
> 4.11325037878293
> sage: exp(x).subs({x:QQbar(sqrt(2))})
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
>
> /Users/arai021/Dropbox/sage_work/<ipython console> in <module>()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression.substitute (sage/
> symbolic/expression.cpp:14851)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression.coerce_in (sage/
> symbolic/expression.cpp:10246)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> parent_old.so in sage.structure.parent_old.Parent._coerce_ (sage/
> structure/parent_old.c:3289)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> parent.so in sage.structure.parent.Parent.coerce (sage/structure/
> parent.c:6826)()
>
> TypeError: no canonical coercion from Algebraic Field to Symbolic Ring
> sage: x.subs({x:QQbar(sqrt(2))})
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
>
> /Users/arai021/Dropbox/sage_work/<ipython console> in <module>()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression.substitute (sage/
> symbolic/expression.cpp:14851)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression.coerce_in (sage/
> symbolic/expression.cpp:10246)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> parent_old.so in sage.structure.parent_old.Parent._coerce_ (sage/
> structure/parent_old.c:3289)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> parent.so in sage.structure.parent.Parent.coerce (sage/structure/
> parent.c:6826)()
>
> TypeError: no canonical coercion from Algebraic Field to Symbolic Ring
> sage: QQbar(sqrt(2))*x
> ---------------------------------------------------------------------------
> NotImplementedError Traceback (most recent call
> last)
>
> /Users/arai021/Dropbox/sage_work/<ipython console> in <module>()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> element.so in sage.structure.element.RingElement.__mul__ (sage/
> structure/element.c:11337)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op
> (sage/structure/coerce.c:6137)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> coerce.so in
> sage.structure.coerce.CoercionModel_cache_maps.canonical_coercion
> (sage/structure/coerce.c:7358)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/categories/
> morphism.so in sage.categories.morphism.CallMorphism._call_ (sage/
> categories/morphism.c:2758)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/rings/
> qqbar.pyc in __call__(self, x)
> 779 return AlgebraicNumber(x._descr)
> 780 elif hasattr(x, '_algebraic_'):
> --> 781 return x._algebraic_(QQbar)
> 782 return AlgebraicNumber(x)
> 783
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression._algebraic_ (sage/
> symbolic/expression.cpp:5544)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in algebraic(ex, field)
> 807 0
> 808 """
> --> 809 return AlgebraicConverter(field)(ex)
> 810
> 811 ##############
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in __call__(self, ex)
> 206 operator = ex.operator()
> 207 if operator is None:
> --> 208 return self.symbol(ex)
> 209
> 210 if operator in arithmetic_operators:
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in symbol(self, ex)
> 312 NotImplementedError: symbol
> 313 """
> --> 314 raise NotImplementedError, "symbol"
> 315
> 316 def relation(self, ex, operator):
>
> NotImplementedError: symbol
>
>
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