SymbolicDeltaProductArray

SymbolicDeltaProductArray[{n1,n2,…},{{j1,1,j1,2,…},{j2,1,j2,2,…},…}]

represents an n1×n2×… array with elements ai1,i2,… equal to 1 if all ijp,1ijp,2…, and 0 otherwise.

Details

Examples

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Basic Examples  (2)

The derivative of Total[a] with respect to a is a SymbolicDeltaProductArray:

The derivative of Tr[a] is a SymbolicDeltaProductArray as well:

Create a SymbolicDeltaProductArray with explicit numeric dimensions:

Convert a to an explicit array:

Convert a to a SparseArray:

Scope  (2)

Array with explicit numeric dimensions:

Convert to a SparseArray:

Convert to an explicit array:

Array with symbolic dimensions:

Properties & Relations  (7)

SymbolicDeltaProductArray gives a symbolic representation of the array:

Use Normal to convert a to an explicit array:

IdentityMatrix[n] gives an explicit version of SymbolicDeltaProductArray[{n,n},{{1,2}}]:

SymbolicIdentityArray is a special case of SymbolicDeltaProductArray:

SymbolicOnesArray is a special case of SymbolicDeltaProductArray:

The derivative of Total[a] with respect to a is a SymbolicDeltaProductArray:

The derivative of Tr[a] is a SymbolicDeltaProductArray:

The derivative of Total[a] with respect to a can be computed in the indexed format:

Compare with the results computed in the symbolic array format:

Wolfram Research (2024), SymbolicDeltaProductArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html.

Text

Wolfram Research (2024), SymbolicDeltaProductArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html.

CMS

Wolfram Language. 2024. "SymbolicDeltaProductArray." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html.

APA

Wolfram Language. (2024). SymbolicDeltaProductArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html

BibTeX

@misc{reference.wolfram_2025_symbolicdeltaproductarray, author="Wolfram Research", title="{SymbolicDeltaProductArray}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html}", note=[Accessed: 03-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_symbolicdeltaproductarray, organization={Wolfram Research}, title={SymbolicDeltaProductArray}, year={2024}, url={https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html}, note=[Accessed: 03-April-2025 ]}