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virtualOfPair(...,LengthLimit=>...) -- stop when the virtual resolution reaches this length

Description

When the optional argument LengthLimit is specified virtualOfPair will stop computing syzygies after the given length is reached, otherwise computation continues until the resolution terminates.

i1 : X = toricProjectiveSpace(1) ** toricProjectiveSpace(1);
 
i2 : S = ring X; B = ideal X;

o3 : Ideal of S
 
i4 : J = saturate(intersect(
           ideal(x_1 - 1*x_0, x_3 - 4*x_2),
           ideal(x_1 - 2*x_0, x_3 - 5*x_2),
           ideal(x_1 - 3*x_0, x_3 - 6*x_2)),
           B);

o4 : Ideal of S
 
i5 : C = virtualOfPair(J, {{3,1}}, LengthLimit=>2);
 
i6 : isVirtual(B, C)

o6 = true

See also

Functions with optional argument named LengthLimit:

  • bgg(...,LengthLimit=>...) -- see bgg -- make a linear free complex from a module over an exterior algebra or a symmetric algebra
  • connectingExtMap(...,LengthLimit=>...) (missing documentation)
  • connectingTorMap(...,LengthLimit=>...) (missing documentation)
  • epicResolutionMap(...,LengthLimit=>...) (missing documentation)
  • horseshoeResolution(...,LengthLimit=>...) -- see horseshoeResolution(Complex) -- make the horseshoe resolution
  • minimalBetti(...,LengthLimit=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
  • freeResolution(...,LengthLimit=>...) -- see Options for free resolutions -- optional arguments for freeResolution
  • resolutionMap(...,LengthLimit=>...) -- see resolutionMap -- map from a free resolution to the given complex
  • torSymmetry(...,LengthLimit=>...) (missing documentation)
  • virtualOfPair(...,LengthLimit=>...) -- stop when the virtual resolution reaches this length
  • yonedaMap(...,LengthLimit=>...) -- see yonedaMap(Matrix) -- creates a chain complex map representing an extension of modules

Further information

  • Default value: infinity
  • Function: virtualOfPair -- creates a virtual resolution from a free resolution by keeping only summands of specified degrees
  • Option key: LengthLimit -- an optional argument

The source of this document is in VirtualResolutions/doc.m2:523:0.