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NeuralIdeals -- neural ideals and their canonical forms

Description

NeuralIdeals allows computation of a neural ideal or its canonical form from a neural code

Caveat

In progress

Authors

Version

This documentation describes version 1.0 of NeuralIdeals, released July 22, 2025.

Citation

If you have used this package in your research, please cite it as follows:

@misc{NeuralIdealsSource,
  title = {{NeuralIdeals: canonical forms of neural ideals. Version~1.0}},
  author = {Hugh Geller and Rebecca R.G.},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

Exports

  • Types
  • Functions and commands
  • Methods
    • NeuralCode == NeuralCode -- see == -- determines whether two NeuralCodes are equal
    • allCodeWords(ZZ) (missing documentation)
    • canonicalForm(Ideal) -- see canonicalForm -- computes the canonical form of a neural ideal
    • canonicalForm(NeuralCode) -- see canonicalForm -- computes the canonical form of a neural ideal
    • canonicalResolution(NeuralCode) -- see canonicalResolution -- canonical resolution of a neural code
    • codeSupport(NeuralCode) -- see codeSupport -- lists which neurons fire together
    • depolarizationMap(Ring,Ring) -- see depolarizationMap -- creates the depolarization map
    • dim(NeuralCode) -- see dim -- dimension of a NeuralCode
    • isCanonical(Ideal) -- see isCanonical -- determines whether a neural ideal is in canonical form
    • isWellDefined(NeuralCode) -- see isWellDefined -- determines whether a NeuralCode is well-defined
    • neuralCode(Ideal) -- see neuralCode -- creates a NeuralCode object
    • neuralCode(List) -- see neuralCode -- creates a NeuralCode object
    • neuralCode(List,Ring) -- see neuralCode -- creates a NeuralCode object
    • neuralCode(List,Ring,Ring) -- see neuralCode -- creates a NeuralCode object
    • neuralCode(List,String,String) -- see neuralCode -- creates a NeuralCode object
    • neuralIdeal(NeuralCode) -- see neuralIdeal -- computes the neural ideal of a neural code.
    • polarizedCanonicalForm(Ideal) -- see polarizedCanonicalForm -- computes the polarized canonical form
    • polarizedCanonicalForm(Ideal,Ring) -- see polarizedCanonicalForm -- computes the polarized canonical form
    • polarizedCanonicalForm(NeuralCode) -- see polarizedCanonicalForm -- computes the polarized canonical form
    • polarizedCanonicalIdeal(Ideal) -- see polarizedCanonicalIdeal -- polarized ideal generated by the canonical form
    • polarizedCanonicalIdeal(Ideal,Ring) -- see polarizedCanonicalIdeal -- polarized ideal generated by the canonical form
    • polarizedCanonicalIdeal(NeuralCode) -- see polarizedCanonicalIdeal -- polarized ideal generated by the canonical form
    • polarizedCanonicalResolution(NeuralCode) -- see polarizedCanonicalResolution -- computes the polarized canonical resolution
    • polarizedRing(NeuralCode) -- see polarizedRing -- returns the polarized ring of a NeuralCode
    • polarizeList(List) -- see polarizeList -- polarizes a list of ring elements
    • polarizeList(List,Ring) -- see polarizeList -- polarizes a list of ring elements
    • polarizePseudomonomial(RingElement) -- see polarizePseudomonomial -- polarizes a pseudomonomial
    • polarizePseudomonomial(RingElement,Ring) -- see polarizePseudomonomial -- polarizes a pseudomonomial
    • receptiveFieldRelation(RingElement) -- see receptiveFieldRelation -- gives the receptive field relation corresponding ot a pseudomonomial
    • ring(NeuralCode) -- see ring -- ring of a NeuralCode
  • Symbols
    • codeWords -- of a neural code
    • Iterative -- the default method for computing the canonical form of a neural code
    • Polar (missing documentation)
    • Polarized -- determine whether a polarized ideal is in canonical form
    • SharedIndex -- the default method for computing the canonical form of a neural ideal

For the programmer

The object NeuralIdeals is a package, defined in NeuralIdeals.m2.

The source of this document is in NeuralIdeals.m2:638:0.