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NumericalGodeaux :: precomputedModelInP3xP5

precomputedModelInP3xP5 -- load the precomputed model

Synopsis

Description

The function loads the equation of the image of a rational map $$F(Q) \cdots \rightarrow \mathbb{P}^3 \times \mathbb{P}^5$$ whose fibers are $G_m$-orbits.

i1 : H = precomputedModelInP3xP5(QQ);

                                1                          1
o1 : Matrix (QQ[w ..w , z ..z ])  <--- (QQ[w ..w , z ..z ])
                 0   3   0   5              0   3   0   5
 
i2 : degrees  ring H

o2 = {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}, {0, 1},
     ------------------------------------------------------------------------
     {0, 1}}

o2 : List
 
i3 : sum degrees ring H == flatten degrees source H

o3 = true
 
i4 : betti H

            0 1
o4 = total: 1 1
         0: 1 .
         1: . .
         2: . .
         3: . .
         4: . .
         5: . .
         6: . .
         7: . .
         8: . .
         9: . 1

o4 : BettiTally
 
i5 : tH=terms H_(0,0);
 
i6 : #tH

o6 = 128
 
i7 : lcmTH=lcm tH

                    3 2 4 2 3 3 3 3 3 3
o7 = 13209037701120w w w w z z z z z z
                    0 1 2 3 0 1 2 3 4 5

o7 : QQ[w ..w , z ..z ]
         0   3   0   5
 
i8 : factor sub((coefficients lcmTH)_1_(0,0),ZZ)

      27 9
o8 = 2  3 5

o8 : Expression of class Product

See also

Ways to use precomputedModelInP3xP5 :

For the programmer

The object precomputedModelInP3xP5 is a method function.