1 | initial version |

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.

2 | No.2 Revision |

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

or ~~RealFeld~~RealField

).~~RealBallFeld~~RealBallField

```
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.

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