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rational root theorem

Relationships observed in Wikidata. Connections do not establish verification or source support.

Release: sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Provider: Wikidata · graph projection only.

OBSERVED · GRAPH-PROJECTION · NOT ADMITTED · NOT VERIFIED · NOT SUPPORT

Edge identity is the provider property id (for example P31). It is not a Counterpedia predicate.

Development requests are not available on this deployment. The observed entity and its graph links remain readable.

Relationships of rational root theorem

Show relationship types (drawing only; the text lists are unaffected)
Relationship label not yet available (Observed provider relationships)instance of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)instance of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)studied by (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)part of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)rational root theorem — Wikidata entity (Q180345)rational roottheoremWIKIDATA ENTITYWikiProject Mathematics — Wikidata entity (Q8487137)WikiProjectMathematicsWIKIDATA ENTITYtheorem — Wikidata entity (Q65943)theoremWIKIDATA ENTITY\text{gcd} — Literal value (wikidata:literal:2:\text{gcd})\text{gcd}LITERAL VALUEroot-finding algorithm — Wikidata entity (Q1085860)root-findingalgorithmWIKIDATA ENTITY\mid — Literal value (wikidata:literal:4:\mid)\midLITERAL VALUEalgebra — Wikidata entity (Q3968)algebraWIKIDATA ENTITYa_i — Literal value (wikidata:literal:6:a_i)a_iLITERAL VALUEx — Literal value (wikidata:literal:7:x)xLITERAL VALUEa_0,a_n \neq 0 \implies \exists p,q\in\mathbb Z,\ (x=\frac{p}{q} \land \gcd\{p,q\}=1 \land p \mid a_0 \land q \mid a_n) — Literal value (wikidata:literal:8:a_0,a_n \neq 0 \implies \exists p,q\in\mathbb Z,\ (x=\frac{p}{q} \land \gcd\{p,q\}=1 \land p \mid a_0 \land q \mid a_n))a_0,a_n \neq 0\implies \exist…LITERAL VALUElist of theorems — Wikidata entity (Q944443)list of theoremsWIKIDATA ENTITYn — Literal value (wikidata:literal:10:n)nLITERAL VALUE

Legend

  • Governed record relationships (solid)
  • Countergraph traversal (dashed)
  • Countergraph evidence (dotted)
  • Observed provider relationships (dash-dot)
  • Structurally derived (sparse dots)

Node shape identifies node kind only. Size, color, and position carry no meaning beyond hop distance from the root.

A line means a supported artifact carried an explicit structured relation. It does not mean the relation is true, admitted, verified, or authoritative.

Graph as text

Nodes (12)

  • rational root theorem — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q180345
    stable_ref
    Q180345
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q180345
    provider
    wikidata
    entity_href
    /entries/wikidata/Q180345
  • WikiProject Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q8487137
    stable_ref
    Q8487137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q8487137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q8487137
  • theorem — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q65943
    stable_ref
    Q65943
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q65943
    provider
    wikidata
    entity_href
    /entries/wikidata/Q65943
  • \text{gcd} — Literal value
    Technical details
    node_id
    wikidata:literal:2:\text{gcd}
    stable_ref
    wikidata:literal:2:\text{gcd}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • root-finding algorithm — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q1085860
    stable_ref
    Q1085860
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q1085860
    provider
    wikidata
    entity_href
    /entries/wikidata/Q1085860
  • \mid — Literal value
    Technical details
    node_id
    wikidata:literal:4:\mid
    stable_ref
    wikidata:literal:4:\mid
    node_kind
    wikidata_literal
    plane
    provider_observed
  • algebra — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q3968
    stable_ref
    Q3968
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q3968
    provider
    wikidata
    entity_href
    /entries/wikidata/Q3968
  • a_i — Literal value
    Technical details
    node_id
    wikidata:literal:6:a_i
    stable_ref
    wikidata:literal:6:a_i
    node_kind
    wikidata_literal
    plane
    provider_observed
  • x — Literal value
    Technical details
    node_id
    wikidata:literal:7:x
    stable_ref
    wikidata:literal:7:x
    node_kind
    wikidata_literal
    plane
    provider_observed
  • a_0,a_n \neq 0 \implies \exists p,q\in\mathbb Z,\ (x=\frac{p}{q} \land \gcd\{p,q\}=1 \land p \mid a_0 \land q \mid a_n) — Literal value
    Technical details
    node_id
    wikidata:literal:8:a_0,a_n \neq 0 \implies \exists p,q\in\mathbb Z,\ (x=\frac{p}{q} \land \gcd\{p,q\}=1 \land p \mid a_0 \land q \mid a_n)
    stable_ref
    wikidata:literal:8:a_0,a_n \neq 0 \implies \exists p,q\in\mathbb Z,\ (x=\frac{p}{q} \land \gcd\{p,q\}=1 \land p \mid a_0 \land q \mid a_n)
    node_kind
    wikidata_literal
    plane
    provider_observed
  • list of theorems — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q944443
    stable_ref
    Q944443
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q944443
    provider
    wikidata
    entity_href
    /entries/wikidata/Q944443
  • n — Literal value
    Technical details
    node_id
    wikidata:literal:10:n
    stable_ref
    wikidata:literal:10:n
    node_kind
    wikidata_literal
    plane
    provider_observed

Edges (11)

  • rational root theorem — Relationship label not yet available → WikiProject Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P6104
    predicate_ref
    wikidata:property:P6104
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:0:P6104
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — instance of → theorem — Observed provider relationships
    Technical details
    machine_predicate
    P31
    predicate_ref
    wikidata:property:P31
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:1:P31
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — Relationship label not yet available → \text{gcd} — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:2:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — instance of → root-finding algorithm — Observed provider relationships
    Technical details
    machine_predicate
    P31
    predicate_ref
    wikidata:property:P31
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:3:P31
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — Relationship label not yet available → \mid — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:4:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — studied by → algebra — Observed provider relationships
    Technical details
    machine_predicate
    P2579
    predicate_ref
    wikidata:property:P2579
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:5:P2579
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — Relationship label not yet available → a_i — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:6:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — Relationship label not yet available → x — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:7:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — Relationship label not yet available → a_0,a_n \neq 0 \implies \exists p,q\in\mathbb Z,\ (x=\frac{p}{q} \land \gcd\{p,q\}=1 \land p \mid a_0 \land q \mid a_n) — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:8:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — part of → list of theorems — Observed provider relationships
    Technical details
    machine_predicate
    P361
    predicate_ref
    wikidata:property:P361
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:9:P361
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • rational root theorem — Relationship label not yet available → n — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:10:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

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