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IntegrateOverBlocksInAPowerOfX​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean,​System.​Boolean,​System.​Boolean)

 Method (no overloads)

Summary

N/(B_1 ... B_m) where every block B_i is a polynomial in x^n for one
n >= 2, linear or quadratic in it, with a symbol among them: split in
u = x^n by TrySplitOverWrittenFactors(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity@,System.Boolean),
one residue of the numerator's powers modulo n at a time, each fraction then
over one block in x. With besideAPowerOfX, a power of x beside two
blocks or more as well, and only then.

Remarks

1/((a + b x^3)(c + d x^3)) was declined: over the rationals it does not factor,
and the split over written factors reads a block of the third degree as nothing. In
u = x^3 it is 1/((a + b u)(c + d u)), two linear factors. A numerator
term x^r M(x^n) keeps its x^r outside the split, which is exact since
the blocks are polynomials in x^n alone.
A power of x beside the blocks stays outside the split: 1/(x^7 (a + b x^3)(c + d x^3)) is (b/(x^7 (a + b x^3)) - d/(x^7 (c + d x^3)))/(b c - a d), a power of x over one
block twice. Split at the power of x first, the rest over both blocks had coefficients
that were pages of symbols, and the answer came to 265,499 characters.
 https://github.com/asc-community/AngouriMath/issues/718

























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