u and f for oneloop massless box

gistfile1.txt

$ 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")

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) 
  lee_pomeransky_g_from_matrix(schwinger_matrix)
 
  schwinger_parameters(ds)
  schwinger_exponents(ds) 
 
  at_zero(ls) 
  c_of_schwinger_matrix(ls,ds) 
  b_of_schwinger_matrix(ls,ds) 
  a_of_schwinger_matrix_(ls,ds)
  a_of_schwinger_matrix(ls,ds) 


  
(%o0) "Schwinger.mac"
(%i1) ls:[l]
(%o1) [l]
(%i2) ds:[l^2,(l+p1)^2,(l+p1+p2)^2,(l+p1+p2+p3)^2]
(%o2) [l^2,(p1+l)^2,(p2+p1+l)^2,(p3+p2+p1+l)^2]
(%i3) sm:schwinger_matrix(ls,ds)
(%o3) matrix([x4+x3+x2+x1,(p3+p2+p1)*x4+(p2+p1)*x3+p1*x2],
             [(p3+p2+p1)*x4+(p2+p1)*x3+p1*x2,
              p3^2*x4+2*p2*p3*x4+2*p1*p3*x4+p2^2*x4+2*p1*p2*x4+p1^2*x4+p2^2*x3
                     +2*p1*p2*x3+p1^2*x3+p1^2*x2])
(%i4) u:symanzik_u(ls,ds)
(%o4) x4+x3+x2+x1
(%i5) f:symanzik_f(ls,ds)
(%o5) p3^2*x3*x4+p3^2*x2*x4+2*p2*p3*x2*x4+p2^2*x2*x4+p3^2*x1*x4+2*p2*p3*x1*x4
                +2*p1*p3*x1*x4+p2^2*x1*x4+2*p1*p2*x1*x4+p1^2*x1*x4+p2^2*x2*x3
                +p2^2*x1*x3+2*p1*p2*x1*x3+p1^2*x1*x3+p1^2*x1*x2
(%i6) g:lee_pomeransky_g(ls,ds)
(%o6) p3^2*x3*x4+p3^2*x2*x4+2*p2*p3*x2*x4+p2^2*x2*x4+p3^2*x1*x4+2*p2*p3*x1*x4
                +2*p1*p3*x1*x4+p2^2*x1*x4+2*p1*p2*x1*x4+p1^2*x1*x4+x4
                +p2^2*x2*x3+p2^2*x1*x3+2*p1*p2*x1*x3+p1^2*x1*x3+x3+p1^2*x1*x2
                +x2+x1
(%i7) u:subst([p1^2 = 0,p2^2 = 0,p3^2 = 0],expand(u))
(%o7) x4+x3+x2+x1
(%i8) f:expand(subst([p1^2 = 0,p2^2 = 0,p3^2 = 0],expand(f)))
(%o8) 2*p2*p3*x2*x4+2*p2*p3*x1*x4+2*p1*p3*x1*x4+2*p1*p2*x1*x4+2*p1*p2*x1*x3
(%i9) f2:coeff(f,p2,2)
(%i10) f1:coeff(f,p2,1)
(%i11) f0:coeff(f,p2,0)
(%i12) ev(f:0+subst([p1 = (-s)/2,p3 = (-t)/2],f1)
             +subst([p1 = (-((-s)-t))/(2*p3)],f0),expand)
(%o12) (-t*x2*x4)-s*x1*x3
(%o14) "/home/rds/Documents/latex/IBP/Schwinger/box.mac"

(%i1) batch("NPT.mac")

read and interpret /home/rds/Documents/latex/IBP/Schwinger/NPT.mac
(%i2) kill(all)
(%o0) done
(%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)
lee_pomeransky_g_from_matrix(schwinger_matrix)

schwinger_parameters(ds)
schwinger_exponents(ds)

at_zero(ls)
c_of_schwinger_matrix(ls,ds)
b_of_schwinger_matrix(ls,ds)
a_of_schwinger_matrix_(ls,ds)
a_of_schwinger_matrix(ls,ds)

(%o0) Schwinger.mac
(%i1) ls:[k1,k2]
(%i2) ds:[k1^2,k2^2-m^2,(p1-k1)^2,(p3-k1+k2)^2-m^2,(k1-k2)^2-m^2,
(p2-k2)^2-m^2,2*(p2+k1)^2-p1^2]
(%i3) u:symanzik_u(ls,ds)
(%o3) 2 x6 x7 + 2 x5 x7 + 2 x4 x7 + 2 x2 x7 + x5 x6 + x4 x6 + x3 x6 + x1 x6
+ x3 x5 + x2 x5 + x1 x5 + x3 x4 + x2 x4 + x1 x4 + x2 x3 + x1 x2
(%i4) f:symanzik_f(ls,ds)
2 2 2 2 2 2 2 2
(%o4) (- 2 p1 x6 x7 ) - 2 p1 x5 x7 - 2 p1 x4 x7 - 2 p1 x2 x7
2 2 2 2 2 2

• 2 m x6 x7 + 8 p2 x5 x6 x7 - p1 x5 x6 x7 - 4 m x5 x6 x7 + 2 p3 x4 x6 x7
  2 2 2

• 8 p2 p3 x4 x6 x7 + 8 p2 x4 x6 x7 - p1 x4 x6 x7 - 4 m x4 x6 x7
  2 2 2
• 2 p2 x3 x6 x7 + 4 p1 p2 x3 x6 x7 + p1 x3 x6 x7 + 2 p2 x2 x6 x7
  2 2 2 2 2 2

• 4 m x2 x6 x7 + 2 p2 x1 x6 x7 - p1 x1 x6 x7 - 2 m x5 x7 + 2 p3 x4 x5 x7
  2 2 2
• 4 m x4 x5 x7 + 2 p2 x3 x5 x7 + 4 p1 p2 x3 x5 x7 + p1 x3 x5 x7
  2 2 2 2

• 2 p2 x2 x5 x7 - p1 x2 x5 x7 - 4 m x2 x5 x7 + 2 p2 x1 x5 x7
  2 2 2 2

• p1 x1 x5 x7 - 2 m x4 x7 + 2 p2 x3 x4 x7 + 4 p1 p2 x3 x4 x7
  2 2 2

• p1 x3 x4 x7 + 2 p3 x2 x4 x7 + 4 p2 p3 x2 x4 x7 + 2 p2 x2 x4 x7
  2 2 2 2

• p1 x2 x4 x7 - 4 m x2 x4 x7 + 2 p2 x1 x4 x7 - p1 x1 x4 x7
  2 2 2 2

• 2 p2 x2 x3 x7 + 4 p1 p2 x2 x3 x7 + p1 x2 x3 x7 - 2 m x2 x7
  2 2 2 2 2 2 2 2
• 2 p2 x1 x2 x7 - p1 x1 x2 x7 - m x5 x6 - m x4 x6 - m x3 x6
  2 2 2 2 2 2 2

• m x1 x6 - m x5 x6 + p3 x4 x5 x6 - 2 m x4 x5 x6 + p2 x3 x5 x6
  2 2 2
• 2 p1 p2 x3 x5 x6 + p1 x3 x5 x6 - 2 m x3 x5 x6 + p2 x2 x5 x6
  2 2 2 2 2 2
• 2 m x2 x5 x6 + p2 x1 x5 x6 - 2 m x1 x5 x6 - m x4 x6 + p3 x3 x4 x6
  2

• 2 p2 p3 x3 x4 x6 - 2 p1 p3 x3 x4 x6 + p2 x3 x4 x6 - 2 p1 p2 x3 x4 x6
  2 2 2 2 2
• p1 x3 x4 x6 - 2 m x3 x4 x6 + p2 x2 x4 x6 - 2 m x2 x4 x6 + p3 x1 x4 x6
  2 2 2
• 2 p2 p3 x1 x4 x6 + p2 x1 x4 x6 - 2 m x1 x4 x6 + p2 x2 x3 x6
  2 2 2 2 2 2

• 2 m x2 x3 x6 + p1 x1 x3 x6 + p2 x1 x2 x6 - 2 m x1 x2 x6 - m x3 x5
  2 2 2 2 2 2 2
• m x2 x5 - m x1 x5 + p3 x3 x4 x5 - 2 m x3 x4 x5 + p3 x2 x4 x5
  2 2 2 2 2
• 2 m x2 x4 x5 + p3 x1 x4 x5 - 2 m x1 x4 x5 + p1 x2 x3 x5 - 2 m x2 x3 x5
  2 2 2 2 2 2 2 2 2 2

• p1 x1 x3 x5 - m x2 x5 - 2 m x1 x2 x5 - m x3 x4 - m x2 x4 - m x1 x4
  2 2 2
• p3 x2 x3 x4 - 2 p1 p3 x2 x3 x4 + p1 x2 x3 x4 - 2 m x2 x3 x4
  2 2 2 2 2 2 2
• p1 x1 x3 x4 - m x2 x4 + p3 x1 x2 x4 - 2 m x1 x2 x4 - m x2 x3
  2 2 2
• p1 x1 x2 x3 - m x1 x2
  (%i5) f:expand(ev(f,p1 = p2+p3))
  (%i6) f:subst([p1^2 = -s,p2^2 = 0,p3^2 = 0],f)
  (%i7) f:ev((-s)coeff(coeff(f,p2,1),p3,1)+coeff(f,p2,0),expand)
  (%i8) display2d:false
  (%i9) u
  (%o9) 2x6x7+2x5x7+2x4x7+2x2x7+x5x6+x4x6+x3x6+x1x6+x3x5+x2x5
  +x1x5+x3x4+x2x4+x1x4+x2x3+x1x2
  (%i10) f
  (%o10) 4sx6x7^2+4sx5x7^2+4sx4x7^2+4sx2x7^2-2m^2x6^2x7
  +2sx5x6x7-4m^2x5x6x7-6sx4x6x7-4m^2x4x6x7
  -6sx3x6x7-4m^2x2x6x7+2sx1x6x7-2m^2x5^2x7
  -4m^2x4x5x7-6sx3x5x7+2sx2x5x7-4m^2x2x5x7
  +2sx1x5x7-2m^2x4^2x7-6sx3x4x7-2sx2x4x7
  -4m^2x2x4x7+2sx1x4x7-6sx2x3x7-2m^2x2^2x7
  +2sx1x2x7-m^2x5x6^2-m^2x4x6^2-m^2x3x6^2
  -m^2x1x6^2-m^2x5^2x6-2m^2x4x5x6-2m^2x3x5x6
  -2m^2x2x5x6-2m^2x1x5x6-m^2x4^2x6-2m^2x3x4x6
  -2m^2x2x4x6-2sx1x4x6-2m^2x1x4x6-2m^2x2x3x6
  -2sx1x3x6-2m^2x1x2x6-m^2x3x5^2-m^2x2x5^2
  -m^2x1x5^2-2m^2x3x4x5-2m^2x2x4x5-2m^2x1x4x5
  -2sx2x3x5-2m^2x2x3x5-2sx1x3x5-m^2x2^2x5
  -2m^2x1x2x5-m^2x3x4^2-m^2x2x4^2-m^2x1x4^2
  -2m^2x2x3x4-2sx1x3x4-m^2x2^2x4-2m^2x1x2x4
  -m^2x2^2x3-2sx1x2x3-m^2x1*x2^2