1 | initial version |

I don't know if 1 and 4 can be done, but 2 and 3 can.

See the documentation on

- Power Series Rings, Power Series, Power Series Methods,
- Multivariate Power Series Rings, Multivariate Power Series.

For instance

```
sage: R.<x,y> = PowerSeriesRing(QQ); R
Multivariate Power Series Ring in x, y over Rational Field
sage: h = (exp(x) - 1)*(1/(1-4*y))
sage: H = h(x,exp(x*y)*y)
```

If you feel ready to write your own software, why not instead write a class in Sage for multivariate power series with coefficients expressed as symbolic expressions in the exponents? You could then use all the simplification tools already in Sage.

2 | No.2 Revision |

I don't know if 1 and 4 can be done, but 2 and 3 can.

See the documentation ~~on~~

- on
Power Series Rings,
Power Series,
Power Series Methods
~~,~~ - ,
Multivariate Power Series Rings,
Multivariate Power Series.

For instance

```
sage: R.<x,y> = PowerSeriesRing(QQ); R
Multivariate Power Series Ring in x, y over Rational Field
sage: h = (exp(x) - 1)*(1/(1-4*y))
sage: H = h(x,exp(x*y)*y)
```

If you feel ready to write your own software, why not instead write a class in Sage for multivariate power series with coefficients expressed as symbolic expressions in the exponents? You could then use all the simplification tools already in Sage.

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