Why is numden function returning values with fractions?

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Lillian 2014-7-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/142315-why-is-numden-function-returning-values-with-fractions

I'm trying to simplify an expression. I wrote:

>> syms r a b c d x y;
A = tanh(a/4)*sqrt((cosh(r)-cosh(a/2))/(cosh(r)+cosh(a/2)));
B = tanh(b/4)*sqrt((cosh(r)-cosh(b/2))/(cosh(r)+cosh(b/2)));
C = tanh(c/4)*sqrt((cosh(r)-cosh(c/2))/(cosh(r)+cosh(c/2)));
D = tanh(d/4)*sqrt((cosh(r)-cosh(d/2))/(cosh(r)+cosh(d/2)));
sigma1 = A + B + C + D;
sigma2 = A*B + A*C + A*D + B*C + B*D + C*D;
sigma3 = A*B*C + A*B*D + A*C*D + B*C*D;
sigma4 = A*B*C*D;
tA4_1 = (sigma1 - sigma3) / (1 + sigma4 - sigma2);
tA4_2 = subs(tA4_1, cosh(r), x/y);
[n1, d1] = numden(expand(tA4_2))

The result that I got was

n1 =
tanh(a/4)*tanh(b/4)*tanh(c/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2) - tanh(b/4)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2) - tanh(c/4)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2) - tanh(d/4)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) - tanh(a/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2) + tanh(a/4)*tanh(b/4)*tanh(d/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) + tanh(a/4)*tanh(c/4)*tanh(d/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) + tanh(b/4)*tanh(c/4)*tanh(d/4)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2)
d1 =
tanh(a/4)*tanh(b/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2) + tanh(a/4)*tanh(c/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2) + tanh(a/4)*tanh(d/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) + tanh(b/4)*tanh(c/4)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2) + tanh(b/4)*tanh(d/4)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) + tanh(c/4)*tanh(d/4)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) - tanh(a/4)*tanh(b/4)*tanh(c/4)*tanh(d/4)*((x - y*cosh(a/2))/(x + y*cosh(a/2)))^(1/2)*((x - y*cosh(b/2))/(x + y*cosh(b/2)))^(1/2)*((x - y*cosh(c/2))/(x + y*cosh(c/2)))^(1/2)*((x - y*cosh(d/2))/(x + y*cosh(d/2)))^(1/2) - 1

This still contains fractions in the numerator and the denominator, but my impression was that numden was supposed to give the numerator and denominator of a simplified fraction. Did I do something wrong, or is the numden commnand not designed to do this?

Thanks.