AngouriMath
Semiring
Description
Summary
The arithmetic the coefficients of a SparseTerms`1 obey.
Remarks
Coefficients are always Entity; what changes between features is what
adding and multiplying two of them means. A polynomial adds them in a field, a boolean
expression joins them in a lattice, and everything else about the representation is the
same.
delegates.**a or a = a holds in the boolean semiring and fails in the complex
one, where|x> + |x> is 2|x> -- and that single difference is
what separates *covering* from *superposition*. Quine-McCluskey's merge step is
absorption, and it is sound only because a minterm may be covered twice for free; a
procedure that assumed the same of amplitudes would double them. Anything reading this
flag is asking whether it may cover the same basis element more than once.
adding and multiplying two of them means. A polynomial adds them in a field, a boolean
expression joins them in a lattice, and everything else about the representation is the
same.
delegates.**
one, where
what separates *covering* from *superposition*. Quine-McCluskey's merge step is
absorption, and it is sound only because a minterm may be covered twice for free; a
procedure that assumed the same of amplitudes would double them. Anything reading this
flag is asking whether it may cover the same basis element more than once.
Members
Boolean
PropertyField
PropertyIsIdempotent
PropertyOne
PropertyZero
Property
Angouri © 2019-2023 · Project's repo · Site's repo · Octicons · Transparency · 1953 pages online