Marshall Hampton wrote:
> That definitely looks like a bug. It seems to be in the fast_float
> command, called by setup_for_eval_on_grid. Hopefully someone more
> familiar with fast_float can comment on what is going wrong.
>
First, there is a bug, presumably in setup_for_eval_on_grid, where the
variables are erroneously switched. Here is the call with a bit of
debugging showing the arguments to fast_float. Note that the function
has arguments "y,x", but the variables passed to fast_float are "x,y":
sage: region_plot(2/x + 1/y > 1/x * 1/y, (x,-10,10), (y,-10,10)).show()
[(y, x) |--> -2/x - 1/y + 1/(x*y)] [x, y] {}
I've made this ticket 7809, and posted a patch (please review!). In
practice, this probably does not change anything, but the code should be
cleaner and more correct after the patch is applied.
Second, the issue above appears to be a bug in fast_callable (which
fast_float calls). I've made this
http://trac.sagemath.org/sage_trac/ticket/7810
sage: fast_float(-1/x-1/y+1/(x*y),x,y)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/grout/.sage/temp/tiny/2056/_home_grout__sage_init_sage_0.py in
<module>()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_eval.so
in sage.ext.fast_eval.fast_float (sage/ext/fast_eval.c:8434)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.fast_callable (sage/ext/fast_callable.c:3134)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:24715)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in fast_callable(ex, etb)
1353
1354 """
-> 1355 return FastCallableConverter(ex, etb)()
1356
1357 class RingConverter(Converter):
/home/grout/downloads/sage-4.3/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)
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in <lambda>(x, y)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:4986)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4313)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:24715)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in fast_callable(ex, etb)
1353
1354 """
-> 1355 return FastCallableConverter(ex, etb)()
1356
1357 class RingConverter(Converter):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in __call__(self, ex)
211 if getattr(self, 'use_fake_div', False) and
operator is _operator.mul:
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:
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in <lambda>(x, y)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:4986)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4313)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in _fast_callable_(self, etb)
119 [('load_arg', 0), ('load_arg', 1), 'div', 'return']
120 """
--> 121 return fast_callable(self, etb)
122
123 def _fast_float_(self, *vars):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in fast_callable(ex, etb)
1353
1354 """
-> 1355 return FastCallableConverter(ex, etb)()
1356
1357 class RingConverter(Converter):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in __call__(self, ex)
211 if getattr(self, 'use_fake_div', False) and
operator is _operator.mul:
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:
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
TypeError: reduce() of empty sequence with no initial value
sage: fast_callable(-1/x-1/y+1/(x*y),vars=[x,y])
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/grout/.sage/temp/tiny/2056/_home_grout__sage_init_sage_0.py in
<module>()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.fast_callable (sage/ext/fast_callable.c:3134)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:24715)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in fast_callable(ex, etb)
1353
1354 """
-> 1355 return FastCallableConverter(ex, etb)()
1356
1357 class RingConverter(Converter):
/home/grout/downloads/sage-4.3/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)
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in <lambda>(x, y)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:4986)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4313)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._fast_callable_
(sage/symbolic/expression.cpp:24715)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in fast_callable(ex, etb)
1353
1354 """
-> 1355 return FastCallableConverter(ex, etb)()
1356
1357 class RingConverter(Converter):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in __call__(self, ex)
211 if getattr(self, 'use_fake_div', False) and
operator is _operator.mul:
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:
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in <lambda>(x, y)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.call
(sage/ext/fast_callable.c:4986)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/ext/fast_callable.so
in sage.ext.fast_callable.ExpressionTreeBuilder.__call__
(sage/ext/fast_callable.c:4313)()
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in _fast_callable_(self, etb)
119 [('load_arg', 0), ('load_arg', 1), 'div', 'return']
120 """
--> 121 return fast_callable(self, etb)
122
123 def _fast_float_(self, *vars):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in fast_callable(ex, etb)
1353
1354 """
-> 1355 return FastCallableConverter(ex, etb)()
1356
1357 class RingConverter(Converter):
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in __call__(self, ex)
211 if getattr(self, 'use_fake_div', False) and
operator is _operator.mul:
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:
/home/grout/downloads/sage-4.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1293 elif operator is _operator.neg:
1294 return self.etb.call(operator, operands[0])
-> 1295 return reduce(lambda x,y: self.etb.call(operator, x,y),
operands)
1296
1297 def symbol(self, ex):
TypeError: reduce() of empty sequence with no initial value
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