# UPB

 Other toolboxes required UPB Generates an unextendible product basis none

UPB is a function that generates an unextendible product basis (UPB). The user may either request a specific UPB from the literature such as 'Tiles' or 'Pyramid'[1], or they may request a UPB of specified dimensions.

## Syntax

• U = UPB(NAME)
• [U,V,W,...] = UPB(NAME)
• U = UPB(DIM)
• [U,V,W,...] = UPB(DIM)

## Argument descriptions

### Input arguments

• NAME: The name of a UPB that is found in the literature. Accepted values are:
• 'Min4x4': A UPB in $\mathbb{C}^4 \otimes \mathbb{C}^4$ constructed in [2].
• 'Pyramid': A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in [1].
• 'Tiles': A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in [1].
• 'Shifts': A UPB in $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ constructed in [3] (though a slightly different version appeared in [1]).