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AngouriMath

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WithoutWhatTheExpressionImplies​(AngouriMath.​Entity,​AngouriMath.​Entity)

 Method (no overloads)

Summary

predicate with every conjunct that expression implies on its own taken off: a condition not e = 0 says nothing where the
expression has no value at the zeros of e anyway. True where nothing is left.

Remarks

(1 + ln(x)) x^x provided not x = 0 is (1 + ln(x)) x^x: 0^0 has no
value, so the condition excludes a point the expression does not reach, and a reader
is told twice what the expression says once.
https://github.com/asc-community/AngouriMath/issues/1394
Decided by the expression's own domain condition, under the codomain. A
provided says where the expression has a value, so a condition is redundant
exactly where the expression has none in the codomain the question is asked in --
and what an expression accepts under a codomain is what
DomainConditionIn(AngouriMath.Core.Domain) already says: a quotient accepts a nonzero
divisor, a power a nonzero base or a positive exponent, a logarithm a nonzero
antilogarithm over the complex plane and a positive one over the reals, and so on
through every node. The condition is redundant where that domain condition already
excludes the zeros of e: a conjunct not d = 0 or d > 0 with
d vanishing at them -- d being e itself, a positive power of it, a
product holding it, a sine, tangent, arcsine or arctangent of such a thing, or a
polynomial in the variable e is with no constant term -- or a disjunction every
side of which does. Nothing here decides what a node accepts; that stays with the
node, and when a complex infinity is written
(https://github.com/asc-community/AngouriMath/issues/217) and a quotient's domain
condition changes under the codomains that admit it, this follows. Anything not
proven keeps its condition: a false negative is a redundant clause, a false positive
would claim a value at a point.
 Decided on the expression as it stands, which matters: x/x provided not x = 0 simplifies to 1, and 1 says nothing about zero, so the condition on the
simplified body is not redundant and stays.

























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