Opened 8 years ago

# Conversion of power series to symbolic ring

Reported by: Owned by: eviatarbach burcin major sage-6.4 symbolics N/A

Converting a power series to the symbolic ring doesn't work as expected:

```sage: R.<t> = PowerSeriesRing(QQ)
sage: p = R([1,2,3])
sage: SR(p).variables()
()
sage: diff(SR(p))
0
```

Perhaps it could be converted to a polynomial first and then converted to the symbolic ring?

```sage: SR(p.polynomial()).variables()
(t,)
sage: diff(SR(p.polynomial()))
6*t + 2
```

Or maybe just raise an error (as per #13360)?

### comment:1 Changed 8 years ago by eviatarbach

• Description modified (diff)

### comment:2 Changed 8 years ago by jdemeyer

• Milestone changed from sage-5.11 to sage-5.12

### comment:3 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.1 to sage-6.2

### comment:4 Changed 7 years ago by eviatarbach

#15707 is related.

### comment:5 Changed 7 years ago by nbruin

• Description modified (diff)
• Summary changed from Coercion of power series to symbolic ring to Conversion of power series to symbolic ring

The examples here refer to conversion; not coercion. That fact that power series over "basic" ring types such as rationals or integers don't convert into SR is, I think, a shortcoming that can be fixed. The main thing is to find how to represent the relevant "big-Oh" in SR. Maxima does have power series, so there is at least one back-end that provides some support: http://maxima.sourceforge.net/docs/manual/en/maxima_28.html#IDX1221. Linking up maxima's internal format with sage might need some work:

```sage: F=maxima_calculus('taylor(sin(x),x,0,3)')
sage: F
x-x^3/6
sage: F.ecl()
<ECL: ((MRAT SIMP (((%SIN SIMP) \$X) \$X) (#:|sin(x)2136| #:X2137)
((\$X ((3 . 1)) 0 NIL #:X2137 . 2)) TRUNC)
PS (#:X2137 . 2) ((3 . 1)) ((1 . 1) 1 . 1) ((3 . 1) -1 . 6))>
sage: F-x+x^3/6
+0
sage: (F-x+x^3/6).ecl()
<ECL: ((MRAT SIMP (\$X) (#:X2145) ((\$X ((3 . 1)) 0 NIL #:X2145 . 1)) TRUNC) 0 . 1)>
```

(in maxima this prints with dots, so it knows it's a power series)

### comment:6 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.2 to sage-6.3

### comment:7 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:8 Changed 5 years ago by jakobkroeker

• Status changed from new to needs_info

seems fixed?

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