# picture -- displays information about the blocks of a map or maps between direct sum modules

## Synopsis

• Usage:
picture F
picture m
picture M
• Inputs:
• F, ,
• F, ,
• m, , of map between labeled direct sum modules
• M, , a labeled directSum module

## Description

The sources and targets of the differentials in F = burkeResolution(M,n), where M is an R = S/I-module, are direct sums whose summands are labeled, each by a List of ZZ corresponding to a tensor product of components of the S-free resolutions of R and M.

The maps in the AInfinity structures are similarly labeled (each one has a source that has just one summand.)

When applied to such a map, picture prints it as a table, with columns labeled with the symbols associated to the source and rows labeled with the symbols associated to the target. When applied to a complex, the output is a "netList" display of the pictures of each of the maps.

 i1 : R = ZZ/101[a,b,c,d]/ideal"a3,a2b2,b4,c4,d2" o1 = R o1 : QuotientRing i2 : F = burkeResolution(coker vars R, 4) 1 4 11 33 99 o2 = R <-- R <-- R <-- R <-- R 0 1 2 3 4 o2 : Complex i3 : picture F.dd_3 +------+---+------+------+ o3 = | |{3}|{3, 0}|{2, 1}| +------+---+------+------+ | {2} | * | * | * | +------+---+------+------+ |{2, 0}| . | * | * | +------+---+------+------+ i4 : picture F +-------------------------------------------+ |+---+---+ | o4 = || |{1}| | |+---+---+ | ||{0}| * | | |+---+---+ | +-------------------------------------------+ |+---+---+------+ | || |{2}|{2, 0}| | |+---+---+------+ | ||{1}| * | * | | |+---+---+------+ | +-------------------------------------------+ |+------+---+------+------+ | || |{3}|{3, 0}|{2, 1}| | |+------+---+------+------+ | || {2} | * | * | * | | |+------+---+------+------+ | ||{2, 0}| . | * | * | | |+------+---+------+------+ | +-------------------------------------------+ |+------+---+------+------+------+---------+| || |{4}|{4, 0}|{3, 1}|{2, 2}|{2, 2, 0}|| |+------+---+------+------+------+---------+| || {3} | * | * | * | * | * || |+------+---+------+------+------+---------+| ||{3, 0}| . | * | * | . | u || |+------+---+------+------+------+---------+| ||{2, 1}| . | . | * | * | * || |+------+---+------+------+------+---------+| +-------------------------------------------+

The possible symbols in the table produced by picture are:

. if the corresponding matrix is zero * if the corresponding matrix is nonzero u if the entries of the corresponding matrix contain a unit.

• burkeResolution -- compute a resolution from A-infinity structures
• aInfinity -- aInfinity algebra and module structures on free resolutions

## Ways to use picture :

• "picture(ChainComplex)"
• "picture(Complex)"
• "picture(Matrix)"
• "picture(Module)"

## For the programmer

The object picture is .