charpoly error on matrices with pi

[eviatarbach]

Sage returns an error when attempting to calculate the characteristic polynomial of a matrix with pi:

sage: matrix([[sqrt(2), -1], [1, e^2]]).charpoly()    
x^2 + (-sqrt(2) - e^2)*x + sqrt(2)*e^2 + 1
sage: matrix([[sqrt(2), -1], [pi, e^2]]).charpoly()
TypeError

This is fixed in sage-6.6. The branch just add a doctest to the method charpoly of symbolic matrices.

[eviatarbach]

Okay, I think I found the source of the error; Sage tries to coerce the pyobjects of the symbolic constants into the Symbolic Ring, which doesn't work:

sage: SR(pi.pyobject())
TypeError
sage: SR(euler_gamma.pyobject())
TypeError

What would be the best way to fix this? It seems to be quite a major problem, since characteristic polynomials cannot at the moment be computed for any matrices with symbolic constants (it does work for e, since it is defined differently, and golden_ratio, since it is replaced with its numerical value before running into this error).

[nbruin]

The right way of turning a constant into an expression is apparently via the expression method. The element constructor for SR tests for the presence of a _symbolic_ method on its argument. If we add a method to sage.symbolic.constants.Constant:

    def _symbolic_(self,SR):
        """
        doctest:
            sage: SR(sage.symbolic.constants.Constant('a'))
            a
            sage: SR(sage.symbolic.constants.Constant('a')).subs(a=10)
            a
        """
        return SR(self.expression())

the system picks up the conversion. The double conversion that's happening here is a little sad, but the interface for _symbolic_ is that the ring in question is given as a parameter. I guess our design does not rule out the existence of multiple symbolic rings, whereas expression will return a member of whatever symbolic ring is considered "home" by pynac.

One solution would be to give sage.symbolic.constants_c.PynacConstant.expression an optional argument SR to specify in which ring the expression should lie (defaulting to what SR is there now). This routine now just reads:

    def expression(self):
       return new_Expression_from_GEx(SR, <GEx>(self.pointer[0]))

so making that def expression(self, SR=SR) shouldn't make too much difference. With that in place we can just alias _symbolic_ to expression.

[nbruin]

ensure that SymbolicConstant? object convert into SR

[nbruin]

Note that once you get a characteristic polynomial, it's likely wrong. See #14403

[eviatarbach]

Great! The patch works for me, and all tests pass on constants_c.pyx and constants.py.

[eviatarbach]

Maybe it would be good to add doctests for matrix([pi]).charpoly() and SR(pi.pyobject())?

[kcrisman]

Maybe it would be good to add doctests for matrix([pi]).charpoly() and SR(pi.pyobject())?

Agreed.

[vdelecroix]

Just works fine on 6.6-rc2

sage: sage: matrix([[sqrt(2), -1], [pi, e^2]]).charpoly()
x^2 + (-sqrt(2) - e^2)*x + pi + sqrt(2)*e^2

Migt be because symbolic constants are now element of the symbolic ring:

sage: type(pi)
<type 'sage.symbolic.expression.Expression'>
sage: pi.pyobject()
pi
sage: type(_)
<class 'sage.symbolic.constants.Pi'>

Vincent

[vdelecroix]

New commits:

​005cd02

Trac 13711: add a doctest to the method charpoly