WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

SymbolicDeltaProductArray
✖
SymbolicDeltaProductArray

New in 14.1[Experimental]

✖
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

open allclose all

Basic Examples  (2)Summary of the most common use cases

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

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-vp0kt
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-vxjxp
Out[2]=2

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

In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-guotj
Out[3]=3

Create a SymbolicDeltaProductArray with explicit numeric dimensions:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-cfqmya
Out[1]=1

Convert a to an explicit array:

In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-d2sqr7
Out[2]=2

Convert a to a SparseArray:

In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-wr1qc
Out[3]=3

Scope  (2)Survey of the scope of standard use cases

Array with explicit numeric dimensions:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-byl14x
Out[1]=1

Convert to a SparseArray:

In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-euxhim
Out[2]=2

Convert to an explicit array:

In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-dnutgt
Out[3]=3

Array with symbolic dimensions:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-drm7id
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-e1t8f2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-zejpl
Out[3]=3

Properties & Relations  (7)Properties of the function, and connections to other functions

SymbolicDeltaProductArray gives a symbolic representation of the array:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-z7pn2i
Out[1]=1

Use Normal to convert a to an explicit array:

In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-4mh225
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-b651zf
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-p2dtqe
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-kcbwdh
Out[3]=3

SymbolicIdentityArray is a special case of SymbolicDeltaProductArray:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-60ex52
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-el9d6c
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-cakgwq
Out[3]=3

SymbolicOnesArray is a special case of SymbolicDeltaProductArray:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-xp6ykb
Out[1]=1

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

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-qhjmc2
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-ophey7
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-bmx98s
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-rc3jcn
Out[4]=4

The derivative of Tr[a] is a SymbolicDeltaProductArray:

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-bnnk0y
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-nu4aok
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-g3tbey
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-jhbxhy
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-bzpxvn
Out[3]=3

Compare with the results computed in the symbolic array format:

In[4]:=4
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-fb8bcv
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-fh4axf
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0cf0wp5wiuuqsc6-dhbl4x
Out[6]=6
Wolfram Research (2024), SymbolicDeltaProductArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html.
✖
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.

✖
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.

✖
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

✖
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 ]}

✖
@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 ]}

✖
@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 ]}