1 | initial version |

There is no general algorithm able to decide whether a symbolically defined function is positive. Note that, when Sage outputs `False`

it means `False or Unknown`

. When Sage is able to prove `(f1>f2)`

, it outputs True, otherwise, it will output `False`

.

2 | No.2 Revision |

There is no general algorithm able to decide whether a symbolically defined function is ~~positive. ~~positive, see for example this paper. Note that, when Sage outputs `False`

it means `False or Unknown`

. When Sage is able to prove `(f1>f2)`

, it outputs True, otherwise, it will output `False`

.

3 | No.3 Revision |

There is no general algorithm able to decide whether a symbolically defined function is ~~positive, ~~positive even in a single variable, see for example this paper. Note that, when Sage outputs `False`

it means `False or Unknown`

. When Sage is able to prove `(f1>f2)`

, it outputs True, otherwise, it will output `False`

.

4 | No.4 Revision |

There is no general algorithm able to decide whether a symbolically defined function is positive even in a single variable, and using only `log2, exp(x), pi, sin(x), x, +, - , *, o`

, see for example this paper.

Note that, when ~~Sage outputs ~~Sage is able to prove `False`

it means `False or Unknown`

. When `(f1>f2)`

, it outputs ~~True, ~~`True`

, otherwise, it will output `False`

~~.~~. This means that when Sage outputs "`False`

", it means "`False or Unknown`

".

Now, if you have a concrete example, someone may help you to decide in that particular case.

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