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It is quite possible to get what you want with formal power series:

sage: R.<a,b> = PowerSeriesRing(ZZ); R
Multivariate Power Series Ring in a, b over Integer Ring
sage: exp(a+b)==exp(a)*exp(b)
True
sage: exp(a-b)==exp(a)/exp(b)
True

Read

  • https://en.wikipedia.org/wiki/Formal_power_series
  • http://sagemath.org/doc/reference/power_series/index.html

It is quite possible to get what you want with formal power series:

sage: R.<a,b> = PowerSeriesRing(ZZ); PowerSeriesRing(QQ); R
Multivariate Power Series Ring in a, b over Integer Ring
Rational Field
sage: exp(a+b)==exp(a)*exp(b)
True
sage: exp(a-b)==exp(a)/exp(b)
True

Read

  • https://en.wikipedia.org/wiki/Formal_power_series
  • http://sagemath.org/doc/reference/power_series/index.html