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getSumDecompositionString -- produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class

Description

Given a Grothendieck-Witt class or unstable Grothendieck-Witt class over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two, this method produces a string representing a simplified diagonal representative of the class.

See getSumDecomposition for more details on the decomposition procedure.

i1 : M = matrix(CC, {{1,2,3},{2,4,5},{3,5,6}});

                3         3
o1 : Matrix CC    <-- CC
              53        53
 
i2 : alpha = makeGWClass M;
 
i3 : getSumDecompositionString alpha

o3 = H + <1>
 
i4 : N = matrix(RR, {{2.091,2.728,6.747},{2.728,7.329,6.257},{6.747,6.257,0.294}});

                3         3
o4 : Matrix RR    <-- RR
              53        53
 
i5 : beta = makeGWClass N;
 
i6 : getSumDecompositionString beta

o6 = H + <1>
 
i7 : P = matrix(QQ, {{1,2,3},{2,4,5},{3,5,6}});

              3       3
o7 : Matrix QQ  <-- QQ
 
i8 : gamma = makeGWClass P;
 
i9 : getSumDecompositionString gamma

o9 = H + <1>
 
i10 : Q = matrix(GF(13), {{9,1,7,4},{1,10,3,2},{7,3,6,7},{4,2,7,5}});

                    4            4
o10 : Matrix (GF 13)  <-- (GF 13)
 
i11 : delta = makeGWClass Q;
 
i12 : getSumDecompositionString delta

o12 = H + <1> + <-5>

See also

Ways to use getSumDecompositionString:

  • getSumDecompositionString(GrothendieckWittClass)
  • getSumDecompositionString(UnstableGrothendieckWittClass)

For the programmer

The object getSumDecompositionString is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2:97:0.