Its not linear algebra but comes from the symbolic ring stuff:
sage: var('x,y')
(x, y)
sage: (y - sqrt(x)).polynomial(None, ring=SR[y])
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-75-0227d66cfcfd> in <module>()
----> 1 (y - sqrt(x)).polynomial(None, ring=SR[y])
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression.polynomial
(sage/symbolic/expression.cpp:23610)()
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc
in polynomial(ex, base_ring, ring)
1054 """
1055 converter = PolynomialConverter(ex, base_ring=base_ring,
ring=ring)
-> 1056 res = converter()
1057 return converter.ring(res)
1058
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/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/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1008 return self(base)**Integer(exp)
1009 else:
-> 1010 ops = [self(a) for a in ex.operands()]
1011 return reduce(operator, ops)
1012
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/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/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1008 return self(base)**Integer(exp)
1009 else:
-> 1010 ops = [self(a) for a in ex.operands()]
1011 return reduce(operator, ops)
1012
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/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/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc
in arithmetic(self, ex, operator)
1006 from sage.rings.all import Integer
1007 base, exp = ex.operands()
-> 1008 return self(base)**Integer(exp)
1009 else:
1010 ops = [self(a) for a in ex.operands()]
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/rings/integer.so
in sage.rings.integer.Integer.__init__ (sage/rings/integer.c:7335)()
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/symbolic/expression.so
in sage.symbolic.expression.Expression._integer_
(sage/symbolic/expression.cpp:5340)()
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/rings/integer.so
in sage.rings.integer.Integer.__init__ (sage/rings/integer.c:7335)()
/home/vbraun/opt/sage-5.9.beta2/local/lib/python2.7/site-packages/sage/rings/rational.so
in sage.rings.rational.Rational._integer_ (sage/rings/rational.c:20598)()
TypeError: no conversion of this rational to integer
On Saturday, March 30, 2013 5:14:35 PM UTC, Eric Gourgoulhon wrote:
>
> Hello,
>
> I've noticed this strange behavior (bug ?) on the following elementary
> computation:
>
> sage: a = matrix([[sqrt(x),0,0,0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0,
> 1]])
> sage: det(a)
> ...
> TypeError: no conversion of this rational to integer
>
> If the matrix is smaller, it is fine:
>
> sage: a = matrix([[sqrt(x),0,0], [0, 1, 0], [0, 0, 1]])
> sage: det(a)
> sqrt(x)
>
> If sqrt(x) is replaced by another function, e.g. exp(x), it is fine as
> well:
>
> sage: a = matrix([[exp(x),0,0,0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0,
> 1]])
> sage: det(a)
> e^x
>
> The problem seems to be connected with the non-integer power of x:
>
> sage: a = matrix([[x^(1/2),0,0,0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0,
> 1]])
> sage: det(a)
> ...
> TypeError: no conversion of this rational to integer
>
> I've reproduced it in Sage 5.8, 5.7 and 5.4.
>
> Is this a known issue ?
>
> Eric.
>
>
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