There are 5 objects provided by the program:
`Rate`, `Ratekurz`, `Rateeins`, `Rateint`,
`Ratepol`.

`Rate` tries to find a closed form for a
sequence within the hierarchy of expressions of the form <rational
function>, <product of rational function>, <product of product of
rational function>, etc. It may give several answers.

`Ratekurz` tries to find a closed form for a
sequence within the hierarchy of expressions of the form <rational
function>, <product of rational function>, <product of product of
rational function>. (I.e., it searches only within the first 3 levels
of the search that is done by `Rate`.)

`Rateeins` does the same thing as `Ratekurz`, with the
difference that it immediately exits if one answer is found.

`Rateint` just tries rational interpolation.

`Ratepol` just tries (polynomial) interpolation.

You may want to try the examples

`
Rate[1, 2, 3]
Rate[1, 4, 9, 16]
Rate[1, 3, 6, 10]
Rate[1, 2, 6, 24]
Rate[1, 2, 7, 42, 429, 7436, 218348, 10850216]` (alternating sign matrices)

`Rateeins`, `Ratekurz`, `Rateint`, and
`Ratepol` work in the same way.

For users of rate2.m:
The function `PProduct` that features in guessed results
stands for "product".
Having obtained a result, in case you are interested to see what
the simplification procedures of Mathematica do, you enter

`%/.PProduct->Product
`

`
General Hint/Warning:
It is (most of the time) wise to first enter just a moderate number of terms.
The formula that you are looking forward may not be so complicated,
and therefore this moderate number of terms may already suffice to
guess the formula.
The more terms you enter, Rate* will try to find higher and
higher order formulae, and that may require more time.
`

If you are looking for something similar within the "*q*-world",
then the file rate.q is exactly the right thing
for you. It contains the analogous objects `Rateq`,
`Ratekurzq`, `Rateeinsq`, `Rateintq` und
`Ratepolq`.

Here you may want to try

`
Rateq[1, 1+q, 1+q+q^2, 1+q+q^2+q^3, q]`

which explains the syntax. It is the same for `Ratekurzq`,
`Rateeinsq`, `Rateintq`, and `Ratepolq`.

Back to Christian Krattenthaler's home page.