# The-erinaceous-one

Joined 22 July 2020
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 $\,\,e^{i\pi }$ This user is a member ofWikiProject Mathematics This user is a member ofWikiProject Ontology This user is a member ofWikiProject Properties.
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My name is Paul Wintz, AKA The Erinaceous One 🦔. I am a PhD student at the University of California, Santa Cruz (Q1047293), where I study control theory (Q6501221) in the Department of Applied Mathematics.

Where to find me accross the internet:

## To-do List

The following are tasks that I am planning to work on.

1. Add explanation of third-order class (Q24017465) (and similar items) on its talk page. (Maybe track down the "true" documentation for ontology and link it there).
2. Add a more complete example to defining formula page with demonstrates how to use "calculated from" and "in defining formula"
3. Add more "generalization of" statements to mathematical items
4. Create "mathematically equivalent to" property?
5. Create "has conclusion" property for proof items?
6. Integrate Wikidata:List of properties/mathematics into the mathematics project page.
7. Clarify the difference between numerical method has quality A-stability and Euler backward method has quality A-stability.
8. Why is musical trio (Q281643) instance of musical term? Isn't that language dependent?
9. What the relationship between signed curvature and curvature?
10. Clean up the instances of mathematical object. In particular, shape (Q207961) has many subclasses that should not be mathematical objects.
11. Develop Template:Instance Criteria

## Properties and Templates I Find Useful

Qualifiers:

### Templates

To talk about templates, use the template {{Tl}}

How do we represent that instances of dimension of a vector space (Q929302) will be integer values?

## Important Math Items

The following are classes of mathematical objects that I patrol occasionally to make sure the ontology of their instances and subclasses are correct.

I also have some expertise in the following categories, so I try to develop and maintian them:

### Frequently misused

There are several mathematics terms that are easily confused with everyday terms, so I periodically check them for misuse.

## Property Proposals

### Properties I'm considering proposing:

#### Other

• "Belmann equation" "necessary condition for" "solution to dynamic program"
• "solution to dynamic program" "has necessary condition" "Bellman equation"
• " " "suffcicient condition for" " "
• " " "is suffcicient condition" " "
• "control signal" produced by controller
• "is porportional to"
• negation truth table <truth table>
• R^2 cartesian product of "items listed as qualifiers" / of R / of R
• R^2 direct product of "items listed as qualifiers" / of $\{(x,y)\mid x=0\}$  / of $\{(x,y)\mid y=0\}$

#### qualities for this type

• Human "qualities for this type" male, female (alternatively, maybe Human "qualities for this type" gender / "possible values" male, female, etc. would be a better model)
• iterative numerical method "qualities for this type" L-stable, A-stable, zero-stable,

#### Instances all have quality

• Runge-Kutta method "All instances have quality" Butcher tableau
• linear functional "All instances have quality" "Listed as qualifiers" / codomain field of scalars

#### Units

ISQ dimension (P4020)
${\mathsf {M}}{\mathsf {T}}^{-2}$
 SI mass unit power 1
 SI time unit power -2
0 references

#### Conditions for inclusion of items in class

Throughout Wikidata, we have a heirarchy of classes, but there is not a clear modeling of what the criteria for a item to by an instance or a subclass of another. There are two solutions I see for this:

The first is to create a template for talk pages that would allow users to describe the criteria (such as necessary and sufficient conditions) for inclusion in the class. When giving a definition, it is generally a good idea to conscribe the scope of the definition by stating non-examples. Thus, we could have several categories:

• Intensional definition: State the necessary and sufficient conditions for an item to be included in the class
• Ostensive definition: Provide a list of examples that exemplify the characteristics of the class. Edge cases are also helpful to show the extent of the definition.
• Non-examples: Several items that might be included in the class, but are not, along with a explanation for each about what characteristic(s) violates the definition.

The second option is to try and model this information in Wikidata statement. The value of such statement seems obvious to me, but would be a substatial addition to the project.

### Failed Proposals Worth Revisting

Wikidata:Property proposal/Implies (necessary condition) (Also includes logical/axiomatic system)

## SPARQL Queries

### Runge-Kutta methods

Show all the Runge-Kutta methods sorted by the number of stages.

select distinct
?method
?methodLabel
?formula
?Butcher
?stages
?orderOfConvergence
where {
?method wdt:P31*/wdt:P279* wd:Q725944.
optional{?method wdt:P2534 ?formula .}
optional{?method wdt:P8558 ?Butcher.}
optional{?method p:P1552 [ps:P1552 wd:Q97672364; pq:P1114 ?stages].}
optional{?method p:P1552 [ps:P1552 wd:Q97940482; pq:P1181 ?orderOfConvergence].}
SERVICE wikibase:label { bd:serviceParam wikibase:language "[AUTO_LANGUAGE],en". }
} ORDER BY (!bound(?stages)) ASC(?stages) (!bound(?orderOfConvergence)) ASC(?orderOfConvergence)

Try it!

### Linear Multistep Methods

Show all linear multistep methods sorted by the number of steps.

select distinct
?method
?methodLabel
?formula
?steps
?orderOfConvergence
where {
?method wdt:P31*/wdt:P279* wd:Q1462003.
optional{?method wdt:P2534 ?formula .}
optional{?method p:P1552 [ps:P1552 wd:Q98293869; pq:P1114 ?steps].}
optional{?method p:P1552 [ps:P1552 wd:Q97940482; pq:P1181 ?orderOfConvergence].}
SERVICE wikibase:label { bd:serviceParam wikibase:language "[AUTO_LANGUAGE],en". }
} ORDER BY (!bound(?steps)) ASC(?steps) ASC(?orderOfConvergence)

Try it!

### Defining Formulas

select
?quantity
(sample(?label) as ?label)
(sample(?desc) as ?desc)
(sample(?symbol) as ?symbol)
(sample(?formula) as ?formula)
(
strdt(
concat(
"<", "math><mtable columnalign=left>",
group_concat(?symbolAndLabel),
"</mtable>[/itex]"
),
<http://www.w3.org/1998/Math/MathML>
) as ?otherSymbols
)
where {
?quantity wdt:P279+ wd:Q71550118 .
optional { ?quantity rdfs:label ?label . filter (lang(?label) = "en") }
optional { ?quantity schema:description ?desc . filter (lang(?desc) = "en") }
?quantity wdt:P2534 ?formula .
?quantity wdt:P7235 ?symbol .
{
select distinct * where {
?quantity p:P4934 [ pq:P7235 ?otherSymbol ; ps:P4934 / rdfs:label ?otherLabel ] .
filter (lang(?otherLabel) = "en")
bind (
concat(
"<mrow>",
str(?otherSymbol), "<mtext>", ": ", ?otherLabel, "</mtext>",
"</mrow>"
) as ?symbolAndLabel
)
}
}
} group by ?quantity ?formula

Try it!

### Number classification

The following might be useful information on the mathematics project page.

Important Number Items
Natural Numbers Integers Rationals Real Numbers
number (Q11563) natural number (Q21199) integer (Q12503) rational number (Q1244890) real number (Q12916)
set of numbers (Q3054943) set of natural numbers (Q28777634) set of integers (Q47007735) set of rational numbers (Q47005650) set of real numbers (Q26851380)
type of number (Q47460393) type of natural numbers (Q77359186) type of integer (Q77358734) ?? ??