You might want to search the sage devel archives for an email from John Perry
called "implicit_diff".
On Mon, Oct 19, 2009 at 10:35 PM, Alex Raichev <tortoise.s...@gmail.com> wrote:
>
> Hi all:
>
> I'm trying to differentiate implicitly and solve for the derivative
> but get an error. Does anyone know what's wrong?
>
> Alex
>
> ----------------------------------------------------------------------
> | Sage Version 4.1.2, Release Date: 2009-10-13 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
>
> sage: var('x,y')
> (x, y)
> sage: H= function('H',x,y)
> sage: h= function('h',x)
> sage: e= diff(H.subs(y=h),x); e
> D[0](h)(x)*D[1](H)(x, h(x)) + D[0](H)(x, h(x))
> sage: solve(e==0,diff(h,x))
> ---------------------------------------------------------------------------
> IndexError Traceback (most recent call
> last)
>
> /Users/arai021/<ipython console> in <module>()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> relation.pyc in solve(f, *args, **kwds)
> 489 """
> 490 try:
> --> 491 return f.solve(*args,**kwds)
> 492 except AttributeError:
> 493 from sage.symbolic.ring import is_SymbolicVariable
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression.solve (sage/
> symbolic/expression.cpp:22187)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression._maxima_ (sage/
> symbolic/expression.cpp:3480)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> sage_object.so in sage.structure.sage_object.SageObject._interface_
> (sage/structure/sage_object.c:3409)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/structure/
> sage_object.so in sage.structure.sage_object.SageObject._maxima_init_
> (sage/structure/sage_object.c:5090)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression.so in sage.symbolic.expression.Expression._interface_init_
> (sage/symbolic/expression.cpp:3609)()
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in __call__(self, ex)
> 214 return self.arithmetic(ex, operator)
> 215 elif operator in relation_operators:
> --> 216 return self.relation(ex, operator)
> 217 elif isinstance(operator, FDerivativeOperator):
> 218 return self.derivative(ex, operator)
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in relation(self, ex, operator)
> 449 'x < 3'
> 450 """
> --> 451 return "%s %s %s"%(self(ex.lhs()),
> self.relation_symbols[operator],
> 452 self(ex.rhs()))
> 453
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in __call__(self, ex)
> 212 div = self.get_fake_div(ex)
> 213 return self.arithmetic(div, div.operator())
> --> 214 return self.arithmetic(ex, operator)
> 215 elif operator in relation_operators:
> 216 return self.relation(ex, operator)
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in arithmetic(self, ex, operator)
> 495 '(x)+(2)'
> 496 """
> --> 497 args = ["(%s)"%self(op) for op in ex.operands()]
> 498 return arithmetic_operators[operator].join(args)
> 499
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in __call__(self, ex)
> 212 div = self.get_fake_div(ex)
> 213 return self.arithmetic(div, div.operator())
> --> 214 return self.arithmetic(ex, operator)
> 215 elif operator in relation_operators:
> 216 return self.relation(ex, operator)
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in arithmetic(self, ex, operator)
> 495 '(x)+(2)'
> 496 """
> --> 497 args = ["(%s)"%self(op) for op in ex.operands()]
> 498 return arithmetic_operators[operator].join(args)
> 499
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in __call__(self, ex)
> 216 return self.relation(ex, operator)
> 217 elif isinstance(operator, FDerivativeOperator):
> --> 218 return self.derivative(ex, operator)
> 219 else:
> 220 return self.composition(ex, operator)
>
> /Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/
> expression_conversions.pyc in derivative(self, ex, operator)
> 479 f = operator.function()
> 480 params = operator.parameter_set()
> --> 481 params = ["%s, %s"%(args[i], params.count(i)) for i in
> set(params)]
> 482
> 483 return "diff('%s(%s), %s)"%(f.name(),
>
> IndexError: tuple index out of range
>
> >
>
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