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IsIdentity(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity.Set,System.Boolean)

Method (no overloads)

Summary

True where the two sides differ by a polynomial that expands to nothing,
True provided P where they do once quotients are put over one denominator
and P says the denominator's factors in the free names are not zero, and
null otherwise. A factor in the quantified name has to be decided
non-zero over the set, or the identity is not claimed.

Remarks

Binomial coefficients are read twice more where they are atoms that do not cancel as
written. Those whose upper indices are one another plus whole numbers are each written
over the lowest by Vandermonde's identity,
binomial(m + d, r) = sum_j binomial(d, j) binomial(m, r - j), which holds for
every m and whole r and so needs no condition: Sullivan and Mackey's
Prob 8.9.20, binomial(n, k) - binomial(n - 2, k) = 2 binomial(n - 2, k - 1) +
binomial(n - 2, k - 2), is then the same atoms on both sides. And a product of them
is written in factorials, where the trinomial revision of §8.4.5,
binomial(n, k) binomial(k, l) = binomial(n, l) binomial(n - l, k - l), cancels factor
by factor. https://github.com/asc-community/AngouriMath/issues/1409

AngouriMath

Table of contents

AngouriMath

IsIdentity​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity.​Set,​System.​Boolean)

IsIdentity(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity.Set,System.Boolean)