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multVar -- extract the sets of multiplicative variables for each generator from an involutive basis

Synopsis

Description

If the argument of multVar is an object of class InvolutiveBasis, then the i-th set in m consists of the multiplicative variables for the i-th generator in J.

If the arguments of multVar are a chain complex and an integer, where C is the result of either janetResolution or resolution called with the optional argument 'Strategy => Involutive', then the i-th set in m consists of the multiplicative variables for the i-th generator in the n-th differential of C.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
i2 : I = ideal(x^3,y^2)

             3   2
o2 = ideal (x , y )

o2 : Ideal of R
i3 : J = janetBasis I;
i4 : multVar J

o4 = {set {y}, set {y}, set {y, x}, set {y}}

o4 : List
i5 : R = QQ[x,y,z]

o5 = R

o5 : PolynomialRing
i6 : I = ideal(x,y,z)

o6 = ideal (x, y, z)

o6 : Ideal of R
i7 : C = res(I, Strategy => Involutive)

      1      3      3      1
o7 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o7 : ChainComplex
i8 : multVar(C, 2)

o8 = {set {z, y, x}, set {z, y, x}, set {z, y}}

o8 : List

See also

Ways to use multVar :