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# negativeWeightedLaplacian -- Computes the negative of the weighted Laplacian matrix of a Reaction Network.

## Synopsis

• Usage:
L = negativeWeightedLaplacian N
• Inputs:
• Outputs:
• L, , the negative of the weighted Laplacian matrix of N.

## Description

Computes the negative of the weighted Laplacian matrix of a Reaction Network.

 i1 : N = reactionNetwork "A <--> B" o1 = A-->B B-->A o1 : ReactionNetwork i2 : L = negativeWeightedLaplacian N o2 = | -kk_{0, 1} kk_{0, 1} | | kk_{1, 0} -kk_{1, 0} | 2 2 o2 : Matrix (QQ[xx , xx , cc , cc , kk , kk ]) <-- (QQ[xx , xx , cc , cc , kk , kk ]) A B A B {0, 1} {1, 0} A B A B {0, 1} {1, 0}

A bigger example:

 i3 : N = oneSiteModificationA() o3 = S_0+E-->X X-->S_0+E X-->E+S_1 S_1+F-->Y Y-->S_1+F Y-->S_0+F o3 : ReactionNetwork i4 : L = negativeWeightedLaplacian N o4 = | -kk_{0, 1} kk_{0, 1} 0 0 0 | kk_{1, 0} -kk_{1, 0}-kk_{1, 2} kk_{1, 2} 0 0 | 0 0 0 0 0 | 0 0 0 -kk_{3, 4} kk_{3, 4} | 0 0 0 kk_{4, 3} -kk_{4, 3}-kk_{4, | 0 0 0 0 0 ------------------------------------------------------------------------ 0 | 0 | 0 | 0 | 5} kk_{4, 5} | 0 | 6 6 o4 : Matrix (QQ[xx , xx , xx , xx , xx , xx , cc , cc , cc , cc , cc , cc , kk , kk , kk , kk , kk , kk ]) <-- (QQ[xx , xx , xx , xx , xx , xx , cc , cc , cc , cc , cc , cc , kk , kk , kk , kk , kk , kk ]) S_0 E X S_1 F Y S_0 E X S_1 F Y {0, 1} {1, 0} {1, 2} {3, 4} {4, 3} {4, 5} S_0 E X S_1 F Y S_0 E X S_1 F Y {0, 1} {1, 0} {1, 2} {3, 4} {4, 3} {4, 5}