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expansions

Field

Summary

The expansions the polynomial passes made inside the outermost
Simplify(AngouriMath.Entity,System.Int32) on this thread, by the tree expanded, each with the
settings it was made under.

Remarks

Alternate(AngouriMath.Entity,System.Int32) expands each candidate and reads the expansion as a polynomial
in every variable in turn, and then factors it in every variable, which expands it
again; and nested simplifications meet the same candidate again, since a sum of
fractions simplifies the product of its denominators afresh at each pass that meets
it. t^4/((b t^2 + a + a t^2)^2 (1 + t^2)), the tangent's integrand for Rubi's
4.1.7 sin(c + d x)^4/(a + b sin(c + d x)^2)^2, expanded one product of 342
terms 72 times, 24 trees of it three variables each, at 145 MB a time: 11 GB of
the 12 GB its simplification cost. Under u = sqrt((a x + 1)/(a x - 1)) Rubi's
7.4.2 e^(arcoth(a x)) (c - c/(a^2 x^2))^4 asked to factor 200 polynomials in
1 - u^2 2145 times, most of them past the degree the factoring takes and
expanded to be told so: 5.4 GB.
The expansion of a tree of numbers, variables, arithmetic and the elementary functions
is a function of the tree and the settings, so one kept is the one the pass would make
again: a tree is looked up by its value, and an expansion is used only while every
setting reads as it did when it was made. Nothing else is kept -- a piecewise, a
calculus operator or a statement simplifies through scopes of its own, an integral by
integrating -- and nothing at all where a derivation is being recorded, whose steps the
expansion writes down each time it runs.
https://github.com/asc-community/AngouriMath/issues/746

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expansions