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NormalToricVarieties :: variety(ToricDivisor)

variety(ToricDivisor) -- get the underlying normal toric variety

Synopsis

Description

This function allows one to easily access the normal toric variety over which the torus-invariant Weil divisor is defined.

i1 : PP2 = toricProjectiveSpace 2;
i2 : D1 = 2*PP2_0 - 7*PP2_1 + 3*PP2_2

o2 = 2*PP2  - 7*PP2  + 3*PP2
          0        1        2

o2 : ToricDivisor on normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} )))))
i3 : variety D1

o3 = normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} )))))

o3 : NormalToricVariety
i4 : normalToricVariety D1

o4 = normalToricVariety((({{-1, -1}, {1, 0}, {0, 1}}(,({{0, 1}, {0, 2}, {1, 2}} )))))

o4 : NormalToricVariety
i5 : assert(variety D1 === PP2 and normalToricVariety D1 === PP2)
i6 : X = normalToricVariety(id_(ZZ^3) | - id_(ZZ^3));
i7 : D2 = X_0 - 5 * X_3

o7 = X  - 5*X
      0      3

o7 : ToricDivisor on normalToricVariety((({{1, 1, 1}, {-1, 1, 1}, {1, -1, 1}, {-1, -1, 1}, {1, 1, -1}, {-1, 1, -1}, {1, -1, -1}, {-1, -1, -1}}(,({{0, 1, 2, 3}, {0, 1, 4, 5}, {0, 2, 4, 6}, {1, 3, 5, 7}, {2, 3, 6, 7}, {4, 5, 6, 7}} )))))
i8 : variety D2

o8 = normalToricVariety((({{1, 1, 1}, {-1, 1, 1}, {1, -1, 1}, {-1, -1, 1}, {1, 1, -1}, {-1, 1, -1}, {1, -1, -1}, {-1, -1, -1}}(,({{0, 1, 2, 3}, {0, 1, 4, 5}, {0, 2, 4, 6}, {1, 3, 5, 7}, {2, 3, 6, 7}, {4, 5, 6, 7}} )))))

o8 : NormalToricVariety
i9 : assert(X === variety D2 and X === normalToricVariety D2)

See also