# Re: [sage-devel] Giving Sage AI-based step-by-step equation solving abilities

```Thierry wrote:

> such a tool could be interesting. However, we are lacking concrete
> examples on PRESS abilities. It would be nice if you could provide some
> examples (and perhaps benchmarks), especially for things that Sage's solve
> command is not able deal with correctely (they are tons, just have a look
> on https://ask.sagemath.org). The only example i could find in the
> testing/ directory on the public reposiroty, is log(x,2) + 4*log(2,x) == 5
> (in Sage's notations), which does not tell much about PRESS abilities.```
```
Most of the research papers on PRESS are available on the following website:

http://www.research.ed.ac.uk/portal/en/persons/alan-bundy%28bfb547ed-a4df-4a6c-b1be-8ecd9b13419f%29/publications.html?pageSize=all&page=0

The paper titled "Solving Symbolic Equations with PRESS" (which is in
the 1982 section of this website) states the following about the kinds
of equations PRESS was designed to solve:

"The equations PRESS has been solving are largely taken from English A-level
examination papers. Such examinations are taken by 18 year olds in
their final year
of high school, and are used to help decide suitability for university entrance.
Particular papers used are those issued by the Associated Examining
Board (A.E.B.),
the University of London, and the University of Oxford. The years
range from 1971 to
1979. Currently the program solves 69 out of 83 single equations and
10 out of 14
sets of simultaneous equations. Some typical problems are

4^(2*x+1) * 5^(x-2) = 6^(1-x)  (A.E.B. November 1971)

cos(x) + cos(3*x) + cos(5*x) = 0  (A.E.B. June 1976)

3*tan(3*x) - tan(x) + 2 = 0  (Oxford Autumn 1978)

log_2 x + 4*log_x 2 = 5  (London January 1978)

3*sech^2(x) + 4*tanh(x) + 1 = 0  (A.E.B. June 1971)

log_e(x+1) + log_e(x-1) = 3

e^(3*x) - 4*e^x + 3*e^(-x) = 0  (London June 1977)

cosh(x) - 3*sinh(y) = O & 2*sinh(x) + 6*cosh(y) = 5  (A.E.B. June 1973)"

Ted

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