# Revision history [back]

You can turn your symbolic expression into a polynomial over a well-defined ring. Given the coefficients, i presume that they are floating-point numbers. Given the precision, the best "field" for that is RDF (if they had more digits of precision, you shoud have a look at RealFeld or RealBallFeld).

sage: e = pp^5 + 4.61469389524440*pp^4 - 12795.2676889452*pp^3 - 22752.9358658338*pp^2 + 4.19349202517816e7*pp - 8.10593457285525e7
sage: e.parent()
Symbolic Ring

sage: e.plot(-100,100)
Launched png viewer for Graphics object consisting of 1 graphics primitive

sage: P = e.polynomial(RDF)
sage: P
pp^5 + 4.6146938952444*pp^4 - 12795.2676889452*pp^3 - 22752.9358658338*pp^2 + 41934920.2517816*pp - 81059345.7285525
sage: P.parent()
Univariate Polynomial Ring in pp over Real Double Field

sage: P.roots()
[(1.9372319190989842, 1)]
sage: P.roots(multiplicities=False)
[1.9372319190989842]

sage: e.plot(1,2)


Just in case, if the coefficients could be described as rational or algebraic numbers, i would suggest to use them as coefficients within the correct polynomial ring so that you will get exact solutions.

You can turn your symbolic expression into a polynomial over a well-defined ring. Given the coefficients, i presume that they are floating-point numbers. Given the precision, the best "field" for that is RDF (if they had more digits of precision, you shoud have a look at RealFeldRealField or RealBallFeldRealBallField).

sage: e = pp^5 + 4.61469389524440*pp^4 - 12795.2676889452*pp^3 - 22752.9358658338*pp^2 + 4.19349202517816e7*pp - 8.10593457285525e7
sage: e.parent()
Symbolic Ring

sage: e.plot(-100,100)
Launched png viewer for Graphics object consisting of 1 graphics primitive

sage: P = e.polynomial(RDF)
sage: P
pp^5 + 4.6146938952444*pp^4 - 12795.2676889452*pp^3 - 22752.9358658338*pp^2 + 41934920.2517816*pp - 81059345.7285525
sage: P.parent()
Univariate Polynomial Ring in pp over Real Double Field

sage: P.roots()
[(1.9372319190989842, 1)]
sage: P.roots(multiplicities=False)
[1.9372319190989842]

sage: e.plot(1,2)


Just in case, if the coefficients could be described as rational or algebraic numbers, i would suggest to use them as coefficients within the correct polynomial ring so that you will get exact solutions.