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AngouriMath.Functions.PartialFractions

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Classes within the AngouriMath.Functions.PartialFractions namespace

• BeyondTheRadicand

  Summary

  What WhereTheDerivativeHoldsBeyondTheRadicand(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable) shows of an answer where the
  radicand is negative.
  

• ModularElimination

  Summary

  TrySolveOverPolynomials(AngouriMath.Entity[][],AngouriMath.Entity[],AngouriMath.Entity[]@)'s reading and elimination run first on the
  image of the system modulo LiftingPrime, to learn whether the ones over
  Q decline: the same readings, pivots, products and exact divisions, in
  residues that cost a machine multiplication each where the rationals of a minor cost
  a greatest common divisor. The Bareiss intermediates are minors, so each is the image
  of the one over Q and has no monomial that one lacks; a product of more than
  MaxIntermediateTerms terms here, a quotient of
  more, an exponent past MaxDegree, an entry the
  reading refuses or a row that reduces to 0 = c is therefore one there too, and
  the solve over Q refuses it. Anything else -- an image that does not exist, a
  division that does not come out, a remainder too large to hold -- says nothing, and
  the solve over Q runs as it did.
  

  Remarks

  The images follow the elimination over Q as long as no nonzero polynomial of
  it vanishes modulo the prime, every one of its coefficients a multiple of
  2^31 - 1; where one did, a pivot could differ and a system be declined that
  would have been solved, and nothing is ever answered on the strength of the images.
  The Hermite reductions of Rubi's 1/(a + b cosh(x) + c sinh(x))^n under
  u = e^x are systems of twenty rows in three symbols whose minors pass four
  thousand terms by the sixth pivot: the elimination over Q spent seconds on
  each before declining it, eight of them for n = 3, and the rule the
  integrator reaches after the decline answers in milliseconds.
  https://github.com/asc-community/AngouriMath/issues/233