v7中具有GroebnerBasis的怪异行为
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使用
GroebnerBasis
m1
Clear[\"Global`*\"]
g = Module[{x},
x /. Solve[
z - x (1 - b -
b x ( (a (3 - 2 a (1 + x)))/(1 - 3 a x + 2 a^2 x^2))) == 0,
x]][[3]];
m1 = First@GroebnerBasis[\\[Kappa] - g, z]
m2 = First@GroebnerBasis[k - g, z]
GroebnerBasis
x = (-b+Sqrt[b^2-4 a c])/2a;
p = First@GroebnerBasis[k - x,{a,b,c}]; (*get relation or cover for Riemann surface*)
q = First@GroebnerBasis[{D[p,k] == 0, p == 0},{a,b,c},k,
MonomialOrder -> EliminationOrder];
Solve[q==0, b] (*get condition on b for double root or branch point*)
{{b -> -2 Sqrt[a] Sqrt[c]}, {b -> 2 Sqrt[a] Sqrt[c]}}
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2 个回复
茬贺努充尽
懊毁暗
这样的函数中的所有可变阶数有关。这是一个例子：ClearAll[a, b, c] expr = (c^4 b^2)/(c^4 b^2 + a^4 b^2 + c^2 a^2 (1 - 2 b^2)); Simplify[expr] Simplify[expr /. {a -> b, b -> a}]