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Evaluate Inverse Laplace transform of a rational function

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proy
proy 2024-1-2
评论： Dyuman Joshi 2024-1-2
Hello.
I have the following rational function:
((4277106574556691*u^4)/1152921504606846976 - (1257694548906265*u^3)/281474976710656 + (5698702517425679*u^2)/4398046511104 + (1997475952800115*u)/137438953472 - 531873529530479/8589934592)/(u^4 + (4199658565989735*u^3)/70368744177664 + (2823782334942045*u^2)/1099511627776 + (5310607259221623*u)/549755813888 - 8541529549052223/137438953472)
When I try to find Inverse Laplace Transform, I got the following answer:
(4277106574556691*dirac(t))/1152921504606846976 + (9189017890449910061927721134279467*symsum((exp(root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)*t)*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k))/(361444138872581760*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k) + 12598975697969205*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^2 + 281474976710656*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^3 + 679757729180367744), k, 1, 4))/9007199254740992 - (9774801846638324177398136662629971*symsum(exp(t*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k))/(12598975697969205*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^2 + 281474976710656*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^3 + 361444138872581760*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k) + 679757729180367744), k, 1, 4))/2251799813685248 + (1630461552184412442890819099501081*symsum((exp(t*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k))*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^2)/(12598975697969205*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^2 + 281474976710656*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^3 + 361444138872581760*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k) + 679757729180367744), k, 1, 4))/18014398509481984 - (380468160178698203651280037243045*symsum((exp(t*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k))*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^3)/(12598975697969205*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^2 + 281474976710656*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k)^3 + 361444138872581760*root(z^4 + (4199658565989735*z^3)/70368744177664 + (2823782334942045*z^2)/1099511627776 + (5310607259221623*z)/549755813888 - 8541529549052223/137438953472, z, k) + 679757729180367744), k, 1, 4))/1152921504606846976
How do I evaluate this function at some points? Like t=1? There are other variables and I can't evaluate the expression.

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采纳的回答

Dyuman Joshi
Dyuman Joshi 2024-1-2
Ran in:
Use subs to substitute in place of a symbolic variable (or function, expression, array) -
syms u
%Expression
fun = ((4277106574556691*u^4)/1152921504606846976 - (1257694548906265*u^3)/281474976710656 + (5698702517425679*u^2)/4398046511104 + (1997475952800115*u)/137438953472 - 531873529530479/8589934592)/(u^4 + (4199658565989735*u^3)/70368744177664 + (2823782334942045*u^2)/1099511627776 + (5310607259221623*u)/549755813888 - 8541529549052223/137438953472);
%Inverse laplace of the expression, w.r.t the specified variable
%t is the default symbolic variable for inv laplace
FUN = ilaplace(fun, u);
out = subs(FUN, u, 1)
out = 
Now, you can use vpa() or double() to obtain the numerical value -
val1 = vpa(out)
val1 = 
0.023921292634752566165032684725215
val2 = double(out)
val2 = 0.0239

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