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multVar -- extract the sets of multiplicative variables for each generator (in several contexts)

Description

If the argument of multVar is an instance of the type 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 complex and an integer, where C is the result of either janetResolution or freeResolution 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.

If the argument of multVar is an instance of the type FactorModuleBasis, then the i-th set in m consists of the multiplicative variables for the i-th monomial cone in F.

i1 : R = QQ[x,y];
 
i2 : I = ideal(x^3,y^2);

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];
 
i6 : I = ideal(x,y,z);

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

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

o7 : Complex
 
i8 : multVar(C, 2)

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

o8 : List
 
i9 : R = QQ[x,y,z];
 
i10 : M = matrix {{x*y,x^3*z}};

              1      2
o10 : Matrix R  <-- R
 
i11 : J = janetBasis M

      +---+---------+
o11 = |x*y|{z, y}   |
      +---+---------+
      | 2 |         |
      |x y|{z, y}   |
      +---+---------+
      | 3 |         |
      |x z|{z, x}   |
      +---+---------+
      | 3 |         |
      |x y|{z, y, x}|
      +---+---------+

o11 : InvolutiveBasis
 
i12 : F = factorModuleBasis J

      +--+------+
o12 = |1 |{z, y}|
      +--+------+
      |x |{z}   |
      +--+------+
      | 2|      |
      |x |{z}   |
      +--+------+
      | 3|      |
      |x |{x}   |
      +--+------+

o12 : FactorModuleBasis
 
i13 : basisElements F

o13 = | 1 x x2 x3 |

              1      4
o13 : Matrix R  <-- R
 
i14 : multVar F

o14 = {set {z, y}, set {z}, set {z}, set {x}}

o14 : List

See also

Ways to use multVar:

  • multVar(Complex,ZZ)
  • multVar(FactorModuleBasis)
  • multVar(InvolutiveBasis)

For the programmer

The object multVar is a method function.

The source of this document is in InvolutiveBases.m2:862:0.