raydsameshima
/ gist:82af4eddf169528faec2434419a48ad3
Created
November 16, 2022 20:22
For Pole-Pushing lemma
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| sage: j = var('j') | |
| sage: k = var('k') | |
| sage: f(j,k) = factorial(j+k)/( factorial(j-1) * factorial(k) ) * 1/2^k | |
| sage: F(j) = sum( f(j,k),k,0,oo) | |
| sage: F(j) | |
| 2^(j + 1)*factorial(j)/factorial(j - 1) | |
| sage: Fj = F(j) | |
| sage: Fj.simplify_factorial() | |
| 2^(j + 1)*j |
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| sage: t = var('t') | |
| sage: r = 10*1000 - 400*t | |
| sage: z = 300 + 110*t -10/2*t^2 | |
| sage: sol = solve( z, t) | |
| sage: s = sol[1] | |
| sage: z.subs(sol[1]) | |
| -5*(sqrt(181) + 11)^2 + 110*sqrt(181) + 1510 | |
| sage: expand(_) | |
| 0 | |
| sage: r.subs(sol[1]) |
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| sage: g = 9.8*units.length.meter/(units.time.second^2); | |
| ....: h = 10*units.length.meter; | |
| ....: cw = 4.1868*units.energy.joule/(units.temperature.celsius*units.mass.gram);t = g*h/cw | |
| sage: t | |
| 23.4068978694946*celsius*gram*meter^2/(joule*second^2) | |
| sage: tt = t/(units.temperature.celsius) | |
| sage: tt.convert() | |
| 0.0234068978694946 |
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| print("Problem 3, 12, 18, 23, 44, 46, 66") | |
| print("Problem 3:") | |
| print("(a) distance traveled:", abs(10-2) + abs(8-10) + abs(11-8), " [m]") | |
| print("(b) magnitude of the displacement:", abs(11-2), " [m]") | |
| # (2.1) | |
| print("(c) displacement:", 11-2, " [m].") |
raydsameshima
/ sqrt
Created
October 21, 2020 02:46
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| A.F.Beardon Complex Analysis page 13: | |
| ```maxima | |
| (%i1) z: sqrt( 1/2*( sqrt(u^2+v^2) + u) ) + %i*(v/sqrt( 2*( sqrt(u^2+v^2) + u) ) ); | |
| 2 2 | |
| sqrt(sqrt(v + u ) + u) %i v | |
| (%o1) ----------------------- + ------------------------------- | |
| sqrt(2) 2 2 | |
| sqrt(2) sqrt(sqrt(v + u ) + u) | |
| (%i2) z^2; |
raydsameshima
/ complex gaussian
Created
October 21, 2020 02:01
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| (%i73) assume(l>0); | |
| (%o73) [l > 0] | |
| (%i74) integrate( exp(-%i*l*t^2),t,-inf,inf); | |
| 1 %i | |
| sqrt(%pi) (------- - -------) | |
| sqrt(2) sqrt(2) | |
| (%o74) ----------------------------- | |
| sqrt(l) | |
| (%i75) polarform (%); | |
| %i %pi |
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| (%i13) limit(integrate( ev( (-%i*x)^(n-1)*exp(%i*x*(D+%i*e))/gamma(n), n:3), x,0,inf), e,0); | |
| %i | |
| (%o13) -- | |
| 3 | |
| D | |
| (%i14) limit(integrate( ev( (-%i*x)^(n-1)*exp(%i*x*(D+%i*e))/gamma(n), n:4), x,0,inf), e,0); | |
| %i | |
| (%o14) -- | |
| 4 | |
| D |
raydsameshima
/ gist:97c2097a3fdeec41c46af0d828ea1efa
Created
August 15, 2020 01:00
2 by 2 example of Moon's formula
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| (%i12) a: (-s11+r11+r12)*(-s22+r21+r22)-s12*s21; | |
| (%o12) ((- s11) + r12 + r11) ((- s22) + r22 + r21) - s12 s21 | |
| (%i13) b: (r12*r21-s12*s21) + (r21*(r11-s11)+ r12*(r22-s22)) + (r11-s11)*(r22-s22); | |
| (%o13) (r11 - s11) (r22 - s22) + r12 (r22 - s22) - s12 s21 + r21 (r11 - s11) | |
| + r12 r21 | |
| (%i14) is(a=b); | |
| (%o14) false | |
| (%i15) a-b, expand; | |
| (%o15) 0 | |
| (%i16) is(ev(a=b, expand)); |
raydsameshima
/ kite lp and some swap symmetry
Last active
November 30, 2023 17:05
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| (%i1) load("Schwinger.mac"); | |
| The list of functions: | |
| schwinger_matrix(list_of_loop_momenta, list_of_denominators) | |
| symanzik_u(ls,ds) | |
| symanzik_f(ls,ds) | |
| lee_pomeransky_g(ls,ds) | |
| homogeneous_lee_pomeransky_g(ls,ds) | |
| As helper functions, the following functions are used: | |
| det_but_outer_egdes(matrix) |
raydsameshima
/ gist:8ad7b3f7b2feee8ea169da34b5f0ec4d
Created
February 13, 2020 18:32
u and f for oneloop massless box
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| $ maxima -qb box.mac | |
| maxima_userdir is /home/rds/.maxima | |
| (%i1) batch("box.mac") | |
| read and interpret /home/rds/Documents/latex/IBP/Schwinger/box.mac | |
| (%i2) kill(all) | |
| (%o0) done | |
| (%i1) display2d:false | |
| (%o1) false | |
| (%i2) load("Schwinger.mac") |
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