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Notebooks · lib/cas/check/pion_loop_check
lib/ Shift+Enter in a cell runs it and moves to the next. Running a cell runs every cell above it too, as one program.
[1] ▶ Run lines 1–22
# Written by `viv check --phrases`: each phrase of the program held to the
# closed form lib/cas finds for it (lang/viv/src/cas_check.rs).
from cas.phrases import cas_check_deriv, cas_check_holds, cas_check_summary
MPI = 138.039
Q_REF = [1.0 , 50.0 , 100.0 , 200.0 , 300.0 , 500.0 , 700.0 , 1000.0 ]
L_REF = [1.0000043733362086695 , 1.0107925820719110433 , 1.0415967652983725786 , 1.1464228856495893426 , 1.2792753525586836379 , 1.5487579788258103122 , 1.7848080102098173246 , 2.0735239825621998704 ]
Q_D = [50.0 , 200.0 , 500.0 ]
DL_REF = [0.00042617365415873921187 , 0.0012407510640255769467 , 0.0012762845936279545397 ]
cas_got_0 = differentiate sqrt (4 * MPI^ 2 + x^ 2 )/ x * log ((sqrt (4 * MPI^ 2 + x^ 2 ) + x)/ (2 * MPI)) at 200
cas_check_deriv (0 , 63 , "differentiate sqrt(4*MPI^2 + x^2)/x * log((sqrt(4*MPI^2 + x^2) + x)/(2*MPI)) at 200" , "((sqrt(((4 * ((138.039))^(2)) + (x)^(2))) / x) * log(((sqrt(((4 * ((138.039))^(2)) + (x)^(2))) + x) / (2 * (138.039)))))" , "x" , "200" , cas_got_0, "deriv" )
cas_got_1 = differentiate sqrt (4 * MPI^ 2 + x^ 2 )/ x * log ((sqrt (4 * MPI^ 2 + x^ 2 ) + x)/ (2 * MPI)) at 200 using the symbolic derivative
cas_check_deriv (1 , 64 , "differentiate sqrt(4*MPI^2 + x^2)/x * log((sqrt(4*MPI^2 + x^2) + x)/(2*MPI)) at 200 using the symbolic derivative" , "((sqrt(((4 * ((138.039))^(2)) + (x)^(2))) / x) * log(((sqrt(((4 * ((138.039))^(2)) + (x)^(2))) + x) / (2 * (138.039)))))" , "x" , "200" , cas_got_1, "cas_deriv_at" )
cas_check_summary ()
test "line 63: differentiate sqrt(4*MPI^2 + x^2)/x * log((sqrt(4*MPI^2 + x^2) + x)/(2*MPI)) at 200 agrees with the CAS, or the CAS has no closed form" {
assert_true (cas_check_holds (0 ))
}
test "line 64: differentiate sqrt(4*MPI^2 + x^2)/x * log((sqrt(4*MPI^2 + x^2) + x)/(2*MPI)) at 200 using the symbolic derivative agrees with the CAS, or the CAS has no closed form" {
assert_true (cas_check_holds (1 ))
}