create an interface for a mathematical search capability for the database

[researcherben]

The page https://derivationmap.net/list_all_expressions current supports "search latex as plain text" and "search latex using regex."

The page https://derivationmap.net/list_all_symbols currently supports "search symbol latex" and "search symbol name".

Here's a bunch of aspects a user might want to search by.

Be able to search all expressions and symbols and derivations:

1. provide a list of symbols, either by latex or by numeric ID
2. which expressions feature variables from step 1?
3. which derivations do expressions from step 2 show up in?

Also, be able to search by notation:

• search by contravariant/covariant (which is distinct from "raise __ to the power"
• search by Dirac notation
• search by vector
• search by matrix
• search by operator (quantum)

Search for expressions that are inputs/outputs to a given inference rule -- https://derivationmap.net/list_all_inference_rules

Be able to search by operator:

• search by dot product
• search by cross product
• search by addition, multiplication
• search by power

dimensions and units:

• Search by which expressions have these dimensions?
• Search by which variables have these dimensions?
• Search by which expressions have these units?
• Search by which variables have these units?

Search by constant versus variable

by name:

• Search by derivation name
• Search by expression name
• Search by variable name

The impact of an ability to search derivations and expressions by latex or by numeric id include

• helps users identify relevant content
• people entering derivations need to be able to quickly identify intersections with existing content

[researcherben]

Suppose a user is looking for a variable. What could they provide as input?

• constant versus variable
• field (real values, integer values, complex values) or vector space
• range (negative, positive, non-negative)
• dimensions (length, width, time) and power per dimension (e.g., 0, 1, 2). If powers for each dimension are zero, then the variable is dimensionless
• units (m, kg, s)
• domain (quantum, electromagnetics, thermodynamics)
• notation (vector, matrix, operator, bra, ket)
• latex for symbol
• numeric ID
• symbol plain text
• symbol regex
• name

some combination of the above fields using and/or/not

[researcherben]

Suppose a user is looking for an expression. What could they provide as input?

• equality versus inequality
• dimensions (length, width, time) and power per dimension
• units (m, kg, s)
• domain (quantum, electromagnetics, thermodynamics)
• notation (vector, matrix, operator, bra, ket)
• operators (+, *, ^)
• latex for symbols and operators involved
• numeric ID of symbols in the expression
• numeric ID of expression
• regex for symbols and operators involved
• name of expression

some combination of the above fields using and/or/not.

The aspects that distinguish the above list from the symbol search are

• operators
• equality versus inequality
• numeric ID of symbols in the expression

[researcherben]

Suppose a user is looking for an operator. What could they provide as input?

• latex for operator
• regex for operator
• notation (vector, matrix, quantum operator, Dirac notation)
• applies to scalar fields or vector spaces
• unitary versus binary
• name ("add", "multiply", "cross product")
• domain (quantum, electromagnetics, thermodynamics)

[bhpayne]

A custom (regex) search would be in constrast to

• the current "site:derivationmap.net" method
• A programmable Google Search interface; see https://support.google.com/programmable-search/answer/4513751?hl=en and https://developers.google.com/custom-search/docs/overview and https://programmablesearchengine.google.com/controlpanel/all

[bhpayne]

The functionality of user search is similar to the semantic equation matching described in https://github.com/allofphysicsgraph/proofofconcept/issues/283