chore: import upstream snapshot with attribution

2026-07-13 12:32:53 +08:00
commit 2a16f2f53b
247 changed files with 69150 additions and 0 deletions
@@ -0,0 +1,31 @@
+Number identification
+=====================
+
+Most function in mpmath are concerned with producing approximations from exact mathematical formulas. It is also useful to consider the inverse problem: given only a decimal approximation for a number, such as 0.7320508075688772935274463, is it possible to find an exact formula?
+
+Subject to certain restrictions, such "reverse engineering" is indeed possible thanks to the existence of *integer relation algorithms*. Mpmath implements the PSLQ algorithm (developed by H. Ferguson), which is one such algorithm.
+
+Automated number recognition based on PSLQ is not a silver bullet. Any occurring transcendental constants (`\pi`, `e`, etc) must be guessed by the user, and the relation between those constants in the formula must be linear (such as `x = 3 \pi + 4 e`). More complex formulas can be found by combining PSLQ with functional transformations; however, this is only feasible to a limited extent since the computation time grows exponentially with the number of operations that need to be combined.
+
+The number identification facilities in mpmath are inspired by the `Inverse Symbolic Calculator <http://wayback.cecm.sfu.ca/projects/ISC/ISCmain.html>`_ (ISC). The ISC is more powerful than mpmath, as it uses a lookup table of millions of precomputed constants (thereby mitigating the problem with exponential complexity).
+
+Constant recognition
+-----------------------------------
+
+:func:`~mpmath.identify`
+^^^^^^^^^^^^^^^^^^^^^^^^^
+.. autofunction:: mpmath.identify
+
+Algebraic identification
+---------------------------------------
+
+:func:`~mpmath.findpoly`
+^^^^^^^^^^^^^^^^^^^^^^^^^
+.. autofunction:: mpmath.findpoly
+
+Integer relations (PSLQ)
+----------------------------
+
+:func:`~mpmath.pslq`
+^^^^^^^^^^^^^^^^^^^^^
+.. autofunction:: mpmath.pslq