Set Tools
Browse all available set tools.
Available tools
- Atom Membership Bit Signature Tool Encode ordered set-membership flags as a left-to-right signature and an exact atom index, with the first set occupying the least significant bit.
- Bounded Set Cardinality Uncertainty Pair Tool Compute bounded set cardinality uncertainty pair from explicit bounded inputs.
- Cartesian Product Empty Factor Flag Tool Calculate cartesian product empty factor flag from explicit caller-supplied inputs.
- Cartesian Product Single Pair Membership Tool Compute cartesian product single pair membership from explicit bounded inputs.
- Family Union Support Count Tool Count union membership from explicit member/family incidences, ignoring duplicate incidences.
- Finite Set Cardinality Update Tool Update finite-set cardinality for one insertion or deletion given an explicit pre-operation membership flag.
- Finite Set Complement Cardinality Pair Tool Compute finite set complement cardinality pair from explicit bounded inputs.
- Finite Set Prefix Cover Count Gap Tool Calculate finite set prefix cover count gap from explicit caller-supplied inputs.
- Finite Set Rank After One Insertion Tool Calculate finite set rank after one insertion from explicit caller-supplied inputs.
- Finite Set Two Witness Equality Status Tool Compute finite set two witness equality status from explicit bounded inputs.
- Integer Set One Residue Class Membership Tool Calculate integer set one residue class membership from explicit caller-supplied inputs.
- Intersection Emptiness Witness Size Tool Calculate intersection emptiness witness size from explicit caller-supplied inputs.
- Interval Set Touching Endpoint Policy Tool Calculate interval set touching endpoint policy from explicit caller-supplied inputs.
- Interval Touch Point Isolated Flag Tool Touch behavior of two ordered nonoverlapping interval interiors with explicit adjacent endpoint closure.
- List Difference Tool Return unique values from the first string list that are absent from the second.
- List Intersection Tool Return unique strings shared by two lists.
- List Symmetric Difference Tool Return unique strings found in exactly one of two lists.
- List Union Tool Return unique strings from two lists in first-occurrence order.
- Multiset Count Map Negative Entry Flag Tool Compute multiset count map negative entry flag from explicit bounded inputs.
- Multiset Count Signed Update Underflow Tool Calculate multiset count signed update underflow from explicit caller-supplied inputs.
- Multiset Count Zero Removal Policy Tool Compute multiset count zero removal policy from explicit bounded inputs.
- Multiset Item Count Delta Tool Describe the multiplicity change of one multiset item, separating inserted and removed occurrence counts.
- Multiset Key Capacity Slack Tool Calculate multiset key capacity slack from explicit caller-supplied inputs.
- Multiset Overdraw Single Item Check Tool Compute multiset overdraw single item check from explicit bounded inputs.
- Multiset Quotient Remainder One Key Tool Calculate multiset quotient remainder one key from explicit caller-supplied inputs.
- Multiset Subtraction Truncated One Key Tool Calculate multiset subtraction truncated one key from explicit caller-supplied inputs.
- Multiset Symmetric Difference One Count Tool Calculate multiset symmetric difference one count from explicit caller-supplied inputs.
- Nested Set Element Versus Subset Label Tool Distinguish finite-set membership from subset inclusion using JSON scalar atoms and nested arrays, ignoring set order and duplicate elements.
- Ordered Set Exclusive Rank Gap Tool Compute ordered set exclusive rank gap from explicit bounded inputs.
- Ordered Set Insertion Neighbor Label Tool Compute ordered set insertion neighbor label from explicit bounded inputs.
- Ordered Set Neighbor Insertion Rank Tool Calculate ordered set neighbor insertion rank from explicit caller-supplied inputs.
- Partition Block Count Change Tool Compare declared partition block counts without constructing or validating the partitions.
- Partition Block Size Residual Tool Check cardinality balance of supplied partition block sizes without claiming their disjointness.
- Power Set Member Complement Index Tool Calculate power set member complement index from explicit caller-supplied inputs.
- Set Atom Bit Count Tool Count true membership bits in an explicit set-atom mask.
- Set Complement Explicit Universe Boundary Tool Calculate set complement explicit universe boundary from explicit caller-supplied inputs.
- Set Containment Slack Tool Inspect cardinality witnesses for finite-set containment without materializing elements.
- Set Difference Counterexample Role Label Tool Calculate set difference counterexample role label from explicit caller-supplied inputs.
- Set Difference Parenthesis Membership Truth Tool Calculate set difference parenthesis membership truth from explicit caller-supplied inputs.
- Set Disjoint Union Tagged Element Key Tool Calculate set disjoint union tagged element key from explicit caller-supplied inputs.
- Set Element Canonical Key Type Tag Tool Compute set element canonical key type tag from explicit bounded inputs.
- Set Element Power Weight Tool Return the exact binary subset-encoding weight 2^index for one zero-based set element, capped at index 4096.
- Set Equality Single Element Obstruction Tool Calculate set equality single element obstruction from explicit caller-supplied inputs.
- Set Image Preimage Multiplicity Tag Tool Preimage and multiplicity of one supplied target under a finite explicitly tabulated map.
- Set Inclusion Counterexample Tool Return exact string witnesses disproving finite-set inclusion, in the subset's first-occurrence order.
- Set Inclusion Exclusion One Region Term Tool Calculate set inclusion exclusion one region term from explicit caller-supplied inputs.
- Set Interval Boundary Member Policy Tool Compute set interval boundary member policy from explicit bounded inputs.
- Set Literal Single Element Quoting Policy Tool Compute set literal single element quoting policy from explicit bounded inputs.
- Set Membership Four Way Label Tool Classify one element into the four Boolean membership regions of two sets.
- Set Membership Negation Universe Guard Tool Compute set membership negation universe guard from explicit bounded inputs.
- Set Membership Unknown Universe Code Tool Calculate set membership unknown universe code from explicit caller-supplied inputs.
- Set Pair Disjointness Single Element Witness Tool Compute set pair disjointness single element witness from explicit bounded inputs.
- Set Partition Block Disjointness Pair Tool Calculate set partition block disjointness pair from explicit caller-supplied inputs.
- Set Partition One Block Coverage Budget Tool Audit one proposed partition block for unique coverage, outside elements and repeated entries.
- Set Partition Single Pair Coassignment Tool Compute set partition single pair coassignment from explicit bounded inputs.
- Set Single Element Insertion Flag Tool Insert one string into a finite set while preserving first-occurrence order and reporting whether membership changed.
- Set Single Element Removal Flag Tool Remove one exact string member from a finite set, deduplicating the result in first-occurrence order.
- Set Singleton Subset Witness Tool Compute set singleton subset witness from explicit bounded inputs.
- Set Threeway Membership Region Token Tool Compute set threeway membership region token from explicit bounded inputs.
- Set Union One Element Cardinality Delta Tool Calculate set union one element cardinality delta from explicit caller-supplied inputs.
- Set Universe Size Residual Compare an explicit unique-item count with declared universe size without asserting actual set membership.
- Singleton Empty Set Brace Formatter Tool Format either the empty set or a singleton string set using a quoted JSON string to avoid delimiter ambiguity.
- Subset Checker Case-sensitiveexactstring-set inclusion,duplicatesignored,emptycandidatevalid. Explicitboundedofflineconvention,not authoritative external identity,eligibility,clinical or safe-use determination.
- Subset Counterexample Single Witness Tool Calculate subset counterexample single witness from explicit caller-supplied inputs.
- Symmetric Difference Parity Tool Evaluate membership in the symmetric difference of an explicitly supplied finite tuple of set-membership bits.
- Symmetric Difference Single Element Toggle Tool Calculate symmetric difference single element toggle from explicit caller-supplied inputs.
- Symmetric Difference Three Membership Parity Tool Calculate symmetric difference three membership parity from explicit caller-supplied inputs.
- Three Set Venn Region Cardinality Term Tool Calculate three set venn region cardinality term from explicit caller-supplied inputs.