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tomleslie

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These are answers submitted by tomleslie

Significant(?) observation...

tomleslie 13876
July 18 2018
0 2

I agree with Preben - if Maple's in-built numeric solvers cannot produce a solution, then I think trouble is to be expected if you are writing your own numeric solution method

I probably wouldn't have used fsolve() to 'solve' the equations, but rather LinearAlgebra:-LinearSolve(). Your equations are all linear, and (provided one changes the assignment of sigma__1 from 0.5 to 1/2), the coefficients in all equations are all rational numbers. This has the advantage that (in principle), one can obtain an exact (rational solution) for all unknowns.

However when I try this, LinearSolve() returns the error:

Error, (in LinearAlgebra:-LinearSolve) inconsistent system

If you have an "inconsistent" system of equations it is *possible* that fsolve() *might* return an "answer", depending on big the associated residuals are - but I wouldn't trust it further than I could throw it!

See the attached, in particular the last execution group


 

> 

  restart;
> 

  with(ODETools):
  with(student):
  with(plots):
  with(plottools):
> 

  xmin := 0: xmax := 6: n := 60:
  sigma__1 := 1/2: # changed from 0.5 to 'force' rationals
> 

  ode:=diff(f(eta),eta$3)+f(eta)*diff(f(eta),eta$2)=0:
  bc1:=df(xmin)=2*sigma__1:
  bc2:=d2f(xmin)=0:
  bc3:=d3f(xmax)=2:
> 

#
# Maple's in-built solvers don't work - never a good sign!
#
  dsolve( {ode,  D(f)(0)=1, D[1,1](f)(0), D[1,1,1](f)(6)=2}, numeric, range=0..6);

Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution

  
> 

  dfde:=proc(h)(f[k+1]-f[k-1])/2/h;end proc:
  dfde(h):
  d2fde2:=proc(h)(f[k+1]-2*f[k]+f[k-1])/h^2;end proc:
  d2fde2(h):
  d3fde3:=proc(h)(f[k+1]-3*f[k]+3*f[k-1]-f[k-2])/h^3;end proc:
  d3fde3(h):
  d2fde2f:=proc(h)(f[k+2]-2*f[k+1]+f[k])/h^2;end proc:
  d2fde2f(h):
  d2fde2b:=proc(h)(f[k]-2*f[k-1]+f[k-2])/h^2;end proc:
  d2fde2b(h):
  dfdef:=proc(h)(f[k+1]-f[k])/h;end proc:
  dfdef(h):
> 

#
# OP's solution with fsolve()
#
  h:=xmax/(n-1):
  stencil:=subs(diff(f(eta),eta$3)=d3fde3(h),f(eta)=f[k],diff(f(eta),eta$2)=d2fde2,ode):
  bcEqs:=[subs(k=0,dfdef(h))=rhs(bc1),subs(k=0,d2fde2f(h))=rhs(bc2), subs(k=n-1,d2fde2b(h))=rhs(bc3)]:
  eqs:=Vector(n-2):
  cnt:=0:

  for k from 1 to n-2 do
      cnt:=cnt+1:
      eqs(cnt):=stencil;
  end do:
  eqs:
  eqs := [op(convert(eqs, list)), op(bcEqs)]:
  vars := [seq(f[k], k = 0 .. n-1)]:
 # map(print, eqs):
  sol := fsolve([op(eqs)]);

{f[-1] = 74076407.16, f[0] = 74076407.19, f[1] = 74076407.29, f[2] = 74076407.42, f[3] = 74076407.63, f[4] = 74076407.95, f[5] = 74076408.39, f[6] = 74076408.95, f[7] = 74076409.58, f[8] = 74076410.32, f[9] = 74076411.18, f[10] = 74076412.19, f[11] = 74076413.34, f[12] = 74076414.66, f[13] = 74076416.09, f[14] = 74076417.69, f[15] = 74076419.41, f[16] = 74076421.28, f[17] = 74076423.28, f[18] = 74076425.45, f[19] = 74076427.75, f[20] = 74076430.17, f[21] = 74076432.77, f[22] = 74076435.56, f[23] = 74076438.51, f[24] = 74076441.69, f[25] = 74076445.02, f[26] = 74076448.54, f[27] = 74076452.24, f[28] = 74076456.15, f[29] = 74076460.29, f[30] = 74076464.65, f[31] = 74076469.16, f[32] = 74076473.82, f[33] = 74076478.70, f[34] = 74076483.79, f[35] = 74076489.05, f[36] = 74076494.52, f[37] = 74076500.21, f[38] = 74076506.15, f[39] = 74076512.33, f[40] = 74076518.79, f[41] = 74076525.57, f[42] = 74076532.68, f[43] = 74076540.10, f[44] = 74076547.80, f[45] = 74076555.85, f[46] = 74076564.23, f[47] = 74076572.94, f[48] = 74076581.93, f[49] = 74076591.18, f[50] = 74076600.60, f[51] = 74076610.20, f[52] = 74076620.03, f[53] = 74076630.05, f[54] = 74076640.28, f[55] = 74076650.64, f[56] = 74076661.19, f[57] = 74076671.90, f[58] = 74076682.68, f[59] = 74076693.50}

 (1)
> 

#
# Check number of equations and number of unknowns
# cos if they don't match, that we can all go home
# now
#
  numelems(eqs);
  numelems(indets( eqs ));
#
# Solution using LinearSolve() - claims that
# the system to be solved is inconsistent!!
#
  with(LinearAlgebra):
  A, b := GenerateMatrix(eqs, indets(eqs, name));
  LinearSolve(A, b);

61

  

61

  

A, b := Matrix(61, 61, {(1, 1) = -205379/216, (1, 2) = 205379/72, (1, 3) = -205379/72, (1, 4) = 205379/216, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (1, 15) = 0, (1, 16) = 0, (1, 17) = 0, (1, 18) = 0, (1, 19) = 0, (1, 20) = 0, (1, 21) = 0, (1, 22) = 0, (1, 23) = 0, (1, 24) = 0, (1, 25) = 0, (1, 26) = 0, (1, 27) = 0, (1, 28) = 0, (1, 29) = 0, (1, 30) = 0, (1, 31) = 0, (1, 32) = 0, (1, 33) = 0, (1, 34) = 0, (1, 35) = 0, (1, 36) = 0, (1, 37) = 0, (1, 38) = 0, (1, 39) = 0, (1, 40) = 0, (1, 41) = 0, (1, 42) = 0, (1, 43) = 0, (1, 44) = 0, (1, 45) = 0, (1, 46) = 0, (1, 47) = 0, (1, 48) = 0, (1, 49) = 0, (1, 50) = 0, (1, 51) = 0, (1, 52) = 0, (1, 53) = 0, (1, 54) = 0, (1, 55) = 0, (1, 56) = 0, (1, 57) = 0, (1, 58) = 0, (1, 59) = 0, (1, 60) = 0, (1, 61) = 0, (2, 1) = 0, (2, 2) = -205379/216, (2, 3) = 205379/72, (2, 4) = -205379/72, (2, 5) = 205379/216, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (2, 15) = 0, (2, 16) = 0, (2, 17) = 0, (2, 18) = 0, (2, 19) = 0, (2, 20) = 0, (2, 21) = 0, (2, 22) = 0, (2, 23) = 0, (2, 24) = 0, (2, 25) = 0, (2, 26) = 0, (2, 27) = 0, (2, 28) = 0, (2, 29) = 0, (2, 30) = 0, (2, 31) = 0, (2, 32) = 0, (2, 33) = 0, (2, 34) = 0, (2, 35) = 0, (2, 36) = 0, (2, 37) = 0, (2, 38) = 0, (2, 39) = 0, (2, 40) = 0, (2, 41) = 0, (2, 42) = 0, (2, 43) = 0, (2, 44) = 0, (2, 45) = 0, (2, 46) = 0, (2, 47) = 0, (2, 48) = 0, (2, 49) = 0, (2, 50) = 0, (2, 51) = 0, (2, 52) = 0, (2, 53) = 0, (2, 54) = 0, (2, 55) = 0, (2, 56) = 0, (2, 57) = 0, (2, 58) = 0, (2, 59) = 0, (2, 60) = 0, (2, 61) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -205379/216, (3, 4) = 205379/72, (3, 5) = -205379/72, (3, 6) = 205379/216, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (3, 16) = 0, (3, 17) = 0, (3, 18) = 0, (3, 19) = 0, (3, 20) = 0, (3, 21) = 0, (3, 22) = 0, (3, 23) = 0, (3, 24) = 0, (3, 25) = 0, (3, 26) = 0, (3, 27) = 0, (3, 28) = 0, (3, 29) = 0, (3, 30) = 0, (3, 31) = 0, (3, 32) = 0, (3, 33) = 0, (3, 34) = 0, (3, 35) = 0, (3, 36) = 0, (3, 37) = 0, (3, 38) = 0, (3, 39) = 0, (3, 40) = 0, (3, 41) = 0, (3, 42) = 0, (3, 43) = 0, (3, 44) = 0, (3, 45) = 0, (3, 46) = 0, (3, 47) = 0, (3, 48) = 0, (3, 49) = 0, (3, 50) = 0, (3, 51) = 0, (3, 52) = 0, (3, 53) = 0, (3, 54) = 0, (3, 55) = 0, (3, 56) = 0, (3, 57) = 0, (3, 58) = 0, (3, 59) = 0, (3, 60) = 0, (3, 61) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = -205379/216, (4, 5) = 205379/72, (4, 6) = -205379/72, (4, 7) = 205379/216, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (4, 15) = 0, (4, 16) = 0, (4, 17) = 0, (4, 18) = 0, (4, 19) = 0, (4, 20) = 0, (4, 21) = 0, (4, 22) = 0, (4, 23) = 0, (4, 24) = 0, (4, 25) = 0, (4, 26) = 0, (4, 27) = 0, (4, 28) = 0, (4, 29) = 0, (4, 30) = 0, (4, 31) = 0, (4, 32) = 0, (4, 33) = 0, (4, 34) = 0, (4, 35) = 0, (4, 36) = 0, (4, 37) = 0, (4, 38) = 0, (4, 39) = 0, (4, 40) = 0, (4, 41) = 0, (4, 42) = 0, (4, 43) = 0, (4, 44) = 0, (4, 45) = 0, (4, 46) = 0, (4, 47) = 0, (4, 48) = 0, (4, 49) = 0, (4, 50) = 0, (4, 51) = 0, (4, 52) = 0, (4, 53) = 0, (4, 54) = 0, (4, 55) = 0, (4, 56) = 0, (4, 57) = 0, (4, 58) = 0, (4, 59) = 0, (4, 60) = 0, (4, 61) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = -205379/216, (5, 6) = 205379/72, (5, 7) = -205379/72, (5, 8) = 205379/216, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (5, 16) = 0, (5, 17) = 0, (5, 18) = 0, (5, 19) = 0, (5, 20) = 0, (5, 21) = 0, (5, 22) = 0, (5, 23) = 0, (5, 24) = 0, (5, 25) = 0, (5, 26) = 0, (5, 27) = 0, (5, 28) = 0, (5, 29) = 0, (5, 30) = 0, (5, 31) = 0, (5, 32) = 0, (5, 33) = 0, (5, 34) = 0, (5, 35) = 0, (5, 36) = 0, (5, 37) = 0, (5, 38) = 0, (5, 39) = 0, (5, 40) = 0, (5, 41) = 0, (5, 42) = 0, (5, 43) = 0, (5, 44) = 0, (5, 45) = 0, (5, 46) = 0, (5, 47) = 0, (5, 48) = 0, (5, 49) = 0, (5, 50) = 0, (5, 51) = 0, (5, 52) = 0, (5, 53) = 0, (5, 54) = 0, (5, 55) = 0, (5, 56) = 0, (5, 57) = 0, (5, 58) = 0, (5, 59) = 0, (5, 60) = 0, (5, 61) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = -205379/216, (6, 7) = 205379/72, (6, 8) = -205379/72, (6, 9) = 205379/216, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (6, 15) = 0, (6, 16) = 0, (6, 17) = 0, (6, 18) = 0, (6, 19) = 0, (6, 20) = 0, (6, 21) = 0, (6, 22) = 0, (6, 23) = 0, (6, 24) = 0, (6, 25) = 0, (6, 26) = 0, (6, 27) = 0, (6, 28) = 0, (6, 29) = 0, (6, 30) = 0, (6, 31) = 0, (6, 32) = 0, (6, 33) = 0, (6, 34) = 0, (6, 35) = 0, (6, 36) = 0, (6, 37) = 0, (6, 38) = 0, (6, 39) = 0, (6, 40) = 0, (6, 41) = 0, (6, 42) = 0, (6, 43) = 0, (6, 44) = 0, (6, 45) = 0, (6, 46) = 0, (6, 47) = 0, (6, 48) = 0, (6, 49) = 0, (6, 50) = 0, (6, 51) = 0, (6, 52) = 0, (6, 53) = 0, (6, 54) = 0, (6, 55) = 0, (6, 56) = 0, (6, 57) = 0, (6, 58) = 0, (6, 59) = 0, (6, 60) = 0, (6, 61) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -205379/216, (7, 8) = 205379/72, (7, 9) = -205379/72, (7, 10) = 205379/216, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (7, 16) = 0, (7, 17) = 0, (7, 18) = 0, (7, 19) = 0, (7, 20) = 0, (7, 21) = 0, (7, 22) = 0, (7, 23) = 0, (7, 24) = 0, (7, 25) = 0, (7, 26) = 0, (7, 27) = 0, (7, 28) = 0, (7, 29) = 0, (7, 30) = 0, (7, 31) = 0, (7, 32) = 0, (7, 33) = 0, (7, 34) = 0, (7, 35) = 0, (7, 36) = 0, (7, 37) = 0, (7, 38) = 0, (7, 39) = 0, (7, 40) = 0, (7, 41) = 0, (7, 42) = 0, (7, 43) = 0, (7, 44) = 0, (7, 45) = 0, (7, 46) = 0, (7, 47) = 0, (7, 48) = 0, (7, 49) = 0, (7, 50) = 0, (7, 51) = 0, (7, 52) = 0, (7, 53) = 0, (7, 54) = 0, (7, 55) = 0, (7, 56) = 0, (7, 57) = 0, (7, 58) = 0, (7, 59) = 0, (7, 60) = 0, (7, 61) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = -205379/216, (8, 9) = 205379/72, (8, 10) = -205379/72, (8, 11) = 205379/216, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (8, 15) = 0, (8, 16) = 0, (8, 17) = 0, (8, 18) = 0, (8, 19) = 0, (8, 20) = 0, (8, 21) = 0, (8, 22) = 0, (8, 23) = 0, (8, 24) = 0, (8, 25) = 0, (8, 26) = 0, (8, 27) = 0, (8, 28) = 0, (8, 29) = 0, (8, 30) = 0, (8, 31) = 0, (8, 32) = 0, (8, 33) = 0, (8, 34) = 0, (8, 35) = 0, (8, 36) = 0, (8, 37) = 0, (8, 38) = 0, (8, 39) = 0, (8, 40) = 0, (8, 41) = 0, (8, 42) = 0, (8, 43) = 0, (8, 44) = 0, (8, 45) = 0, (8, 46) = 0, (8, 47) = 0, (8, 48) = 0, (8, 49) = 0, (8, 50) = 0, (8, 51) = 0, (8, 52) = 0, (8, 53) = 0, (8, 54) = 0, (8, 55) = 0, (8, 56) = 0, (8, 57) = 0, (8, 58) = 0, (8, 59) = 0, (8, 60) = 0, (8, 61) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -205379/216, (9, 10) = 205379/72, (9, 11) = -205379/72, (9, 12) = 205379/216, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (9, 16) = 0, (9, 17) = 0, (9, 18) = 0, (9, 19) = 0, (9, 20) = 0, (9, 21) = 0, (9, 22) = 0, (9, 23) = 0, (9, 24) = 0, (9, 25) = 0, (9, 26) = 0, (9, 27) = 0, (9, 28) = 0, (9, 29) = 0, (9, 30) = 0, (9, 31) = 0, (9, 32) = 0, (9, 33) = 0, (9, 34) = 0, (9, 35) = 0, (9, 36) = 0, (9, 37) = 0, (9, 38) = 0, (9, 39) = 0, (9, 40) = 0, (9, 41) = 0, (9, 42) = 0, (9, 43) = 0, (9, 44) = 0, (9, 45) = 0, (9, 46) = 0, (9, 47) = 0, (9, 48) = 0, (9, 49) = 0, (9, 50) = 0, (9, 51) = 0, (9, 52) = 0, (9, 53) = 0, (9, 54) = 0, (9, 55) = 0, (9, 56) = 0, (9, 57) = 0, (9, 58) = 0, (9, 59) = 0, (9, 60) = 0, (9, 61) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = -205379/216, (10, 11) = 205379/72, (10, 12) = -205379/72, (10, 13) = 205379/216, (10, 14) = 0, (10, 15) = 0, (10, 16) = 0, (10, 17) = 0, (10, 18) = 0, (10, 19) = 0, (10, 20) = 0, (10, 21) = 0, (10, 22) = 0, (10, 23) = 0, (10, 24) = 0, (10, 25) = 0, (10, 26) = 0, (10, 27) = 0, (10, 28) = 0, (10, 29) = 0, (10, 30) = 0, (10, 31) = 0, (10, 32) = 0, (10, 33) = 0, (10, 34) = 0, (10, 35) = 0, (10, 36) = 0, (10, 37) = 0, (10, 38) = 0, (10, 39) = 0, (10, 40) = 0, (10, 41) = 0, (10, 42) = 0, (10, 43) = 0, (10, 44) = 0, (10, 45) = 0, (10, 46) = 0, (10, 47) = 0, (10, 48) = 0, (10, 49) = 0, (10, 50) = 0, (10, 51) = 0, (10, 52) = 0, (10, 53) = 0, (10, 54) = 0, (10, 55) = 0, (10, 56) = 0, (10, 57) = 0, (10, 58) = 0, (10, 59) = 0, (10, 60) = 0, (10, 61) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = -205379/216, (11, 12) = 205379/72, (11, 13) = -205379/72, (11, 14) = 205379/216, (11, 15) = 0, (11, 16) = 0, (11, 17) = 0, (11, 18) = 0, (11, 19) = 0, (11, 20) = 0, (11, 21) = 0, (11, 22) = 0, (11, 23) = 0, (11, 24) = 0, (11, 25) = 0, (11, 26) = 0, (11, 27) = 0, (11, 28) = 0, (11, 29) = 0, (11, 30) = 0, (11, 31) = 0, (11, 32) = 0, (11, 33) = 0, (11, 34) = 0, (11, 35) = 0, (11, 36) = 0, (11, 37) = 0, (11, 38) = 0, (11, 39) = 0, (11, 40) = 0, (11, 41) = 0, (11, 42) = 0, (11, 43) = 0, (11, 44) = 0, (11, 45) = 0, (11, 46) = 0, (11, 47) = 0, (11, 48) = 0, (11, 49) = 0, (11, 50) = 0, (11, 51) = 0, (11, 52) = 0, (11, 53) = 0, (11, 54) = 0, (11, 55) = 0, (11, 56) = 0, (11, 57) = 0, (11, 58) = 0, (11, 59) = 0, (11, 60) = 0, (11, 61) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = -205379/216, (12, 13) = 205379/72, (12, 14) = -205379/72, (12, 15) = 205379/216, (12, 16) = 0, (12, 17) = 0, (12, 18) = 0, (12, 19) = 0, (12, 20) = 0, (12, 21) = 0, (12, 22) = 0, (12, 23) = 0, (12, 24) = 0, (12, 25) = 0, (12, 26) = 0, (12, 27) = 0, (12, 28) = 0, (12, 29) = 0, (12, 30) = 0, (12, 31) = 0, (12, 32) = 0, (12, 33) = 0, (12, 34) = 0, (12, 35) = 0, (12, 36) = 0, (12, 37) = 0, (12, 38) = 0, (12, 39) = 0, (12, 40) = 0, (12, 41) = 0, (12, 42) = 0, (12, 43) = 0, (12, 44) = 0, (12, 45) = 0, (12, 46) = 0, (12, 47) = 0, (12, 48) = 0, (12, 49) = 0, (12, 50) = 0, (12, 51) = 0, (12, 52) = 0, (12, 53) = 0, (12, 54) = 0, (12, 55) = 0, (12, 56) = 0, (12, 57) = 0, (12, 58) = 0, (12, 59) = 0, (12, 60) = 0, (12, 61) = 0, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = -205379/216, (13, 14) = 205379/72, (13, 15) = -205379/72, (13, 16) = 205379/216, (13, 17) = 0, (13, 18) = 0, (13, 19) = 0, (13, 20) = 0, (13, 21) = 0, (13, 22) = 0, (13, 23) = 0, (13, 24) = 0, (13, 25) = 0, (13, 26) = 0, (13, 27) = 0, (13, 28) = 0, (13, 29) = 0, (13, 30) = 0, (13, 31) = 0, (13, 32) = 0, (13, 33) = 0, (13, 34) = 0, (13, 35) = 0, (13, 36) = 0, (13, 37) = 0, (13, 38) = 0, (13, 39) = 0, (13, 40) = 0, (13, 41) = 0, (13, 42) = 0, (13, 43) = 0, (13, 44) = 0, (13, 45) = 0, (13, 46) = 0, (13, 47) = 0, (13, 48) = 0, (13, 49) = 0, (13, 50) = 0, (13, 51) = 0, (13, 52) = 0, (13, 53) = 0, (13, 54) = 0, (13, 55) = 0, (13, 56) = 0, (13, 57) = 0, (13, 58) = 0, (13, 59) = 0, (13, 60) = 0, (13, 61) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = -205379/216, (14, 15) = 205379/72, (14, 16) = -205379/72, (14, 17) = 205379/216, (14, 18) = 0, (14, 19) = 0, (14, 20) = 0, (14, 21) = 0, (14, 22) = 0, (14, 23) = 0, (14, 24) = 0, (14, 25) = 0, (14, 26) = 0, (14, 27) = 0, (14, 28) = 0, (14, 29) = 0, (14, 30) = 0, (14, 31) = 0, (14, 32) = 0, (14, 33) = 0, (14, 34) = 0, (14, 35) = 0, (14, 36) = 0, (14, 37) = 0, (14, 38) = 0, (14, 39) = 0, (14, 40) = 0, (14, 41) = 0, (14, 42) = 0, (14, 43) = 0, (14, 44) = 0, (14, 45) = 0, (14, 46) = 0, (14, 47) = 0, (14, 48) = 0, (14, 49) = 0, (14, 50) = 0, (14, 51) = 0, (14, 52) = 0, (14, 53) = 0, (14, 54) = 0, (14, 55) = 0, (14, 56) = 0, (14, 57) = 0, (14, 58) = 0, (14, 59) = 0, (14, 60) = 0, (14, 61) = 0, (15, 1) = 0, (15, 2) = 0, (15, 3) = 0, (15, 4) = 0, (15, 5) = 0, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = -205379/216, (15, 16) = 205379/72, (15, 17) = -205379/72, (15, 18) = 205379/216, (15, 19) = 0, (15, 20) = 0, (15, 21) = 0, (15, 22) = 0, (15, 23) = 0, (15, 24) = 0, (15, 25) = 0, (15, 26) = 0, (15, 27) = 0, (15, 28) = 0, (15, 29) = 0, (15, 30) = 0, (15, 31) = 0, (15, 32) = 0, (15, 33) = 0, (15, 34) = 0, (15, 35) = 0, (15, 36) = 0, (15, 37) = 0, (15, 38) = 0, (15, 39) = 0, (15, 40) = 0, (15, 41) = 0, (15, 42) = 0, (15, 43) = 0, (15, 44) = 0, (15, 45) = 0, (15, 46) = 0, (15, 47) = 0, (15, 48) = 0, (15, 49) = 0, (15, 50) = 0, (15, 51) = 0, (15, 52) = 0, (15, 53) = 0, (15, 54) = 0, (15, 55) = 0, (15, 56) = 0, (15, 57) = 0, (15, 58) = 0, (15, 59) = 0, (15, 60) = 0, (15, 61) = 0, (16, 1) = 0, (16, 2) = 0, (16, 3) = 0, (16, 4) = 0, (16, 5) = 0, (16, 6) = 0, (16, 7) = 0, (16, 8) = 0, (16, 9) = 0, (16, 10) = 0, (16, 11) = 0, (16, 12) = 0, (16, 13) = 0, (16, 14) = 0, (16, 15) = 0, (16, 16) = -205379/216, (16, 17) = 205379/72, (16, 18) = -205379/72, (16, 19) = 205379/216, (16, 20) = 0, (16, 21) = 0, (16, 22) = 0, (16, 23) = 0, (16, 24) = 0, (16, 25) = 0, (16, 26) = 0, (16, 27) = 0, (16, 28) = 0, (16, 29) = 0, (16, 30) = 0, (16, 31) = 0, (16, 32) = 0, (16, 33) = 0, (16, 34) = 0, (16, 35) = 0, (16, 36) = 0, (16, 37) = 0, (16, 38) = 0, (16, 39) = 0, (16, 40) = 0, (16, 41) = 0, (16, 42) = 0, (16, 43) = 0, (16, 44) = 0, (16, 45) = 0, (16, 46) = 0, (16, 47) = 0, (16, 48) = 0, (16, 49) = 0, (16, 50) = 0, (16, 51) = 0, (16, 52) = 0, (16, 53) = 0, (16, 54) = 0, (16, 55) = 0, (16, 56) = 0, (16, 57) = 0, (16, 58) = 0, (16, 59) = 0, (16, 60) = 0, (16, 61) = 0, (17, 1) = 0, (17, 2) = 0, (17, 3) = 0, (17, 4) = 0, (17, 5) = 0, (17, 6) = 0, (17, 7) = 0, (17, 8) = 0, (17, 9) = 0, (17, 10) = 0, (17, 11) = 0, (17, 12) = 0, (17, 13) = 0, (17, 14) = 0, (17, 15) = 0, (17, 16) = 0, (17, 17) = -205379/216, (17, 18) = 205379/72, (17, 19) = -205379/72, (17, 20) = 205379/216, (17, 21) = 0, (17, 22) = 0, (17, 23) = 0, (17, 24) = 0, (17, 25) = 0, (17, 26) = 0, (17, 27) = 0, (17, 28) = 0, (17, 29) = 0, (17, 30) = 0, (17, 31) = 0, (17, 32) = 0, (17, 33) = 0, (17, 34) = 0, (17, 35) = 0, (17, 36) = 0, (17, 37) = 0, (17, 38) = 0, (17, 39) = 0, (17, 40) = 0, (17, 41) = 0, (17, 42) = 0, (17, 43) = 0, (17, 44) = 0, (17, 45) = 0, (17, 46) = 0, (17, 47) = 0, (17, 48) = 0, (17, 49) = 0, (17, 50) = 0, (17, 51) = 0, (17, 52) = 0, (17, 53) = 0, (17, 54) = 0, (17, 55) = 0, (17, 56) = 0, (17, 57) = 0, (17, 58) = 0, (17, 59) = 0, (17, 60) = 0, (17, 61) = 0, (18, 1) = 0, (18, 2) = 0, (18, 3) = 0, (18, 4) = 0, (18, 5) = 0, (18, 6) = 0, (18, 7) = 0, (18, 8) = 0, (18, 9) = 0, (18, 10) = 0, (18, 11) = 0, (18, 12) = 0, (18, 13) = 0, (18, 14) = 0, (18, 15) = 0, (18, 16) = 0, (18, 17) = 0, (18, 18) = -205379/216, (18, 19) = 205379/72, (18, 20) = -205379/72, (18, 21) = 205379/216, (18, 22) = 0, (18, 23) = 0, (18, 24) = 0, (18, 25) = 0, (18, 26) = 0, (18, 27) = 0, (18, 28) = 0, (18, 29) = 0, (18, 30) = 0, (18, 31) = 0, (18, 32) = 0, (18, 33) = 0, (18, 34) = 0, (18, 35) = 0, (18, 36) = 0, (18, 37) = 0, (18, 38) = 0, (18, 39) = 0, (18, 40) = 0, (18, 41) = 0, (18, 42) = 0, (18, 43) = 0, (18, 44) = 0, (18, 45) = 0, (18, 46) = 0, (18, 47) = 0, (18, 48) = 0, (18, 49) = 0, (18, 50) = 0, (18, 51) = 0, (18, 52) = 0, (18, 53) = 0, (18, 54) = 0, (18, 55) = 0, (18, 56) = 0, (18, 57) = 0, (18, 58) = 0, (18, 59) = 0, (18, 60) = 0, (18, 61) = 0, (19, 1) = 0, (19, 2) = 0, (19, 3) = 0, (19, 4) = 0, (19, 5) = 0, (19, 6) = 0, (19, 7) = 0, (19, 8) = 0, (19, 9) = 0, (19, 10) = 0, (19, 11) = 0, (19, 12) = 0, (19, 13) = 0, (19, 14) = 0, (19, 15) = 0, (19, 16) = 0, (19, 17) = 0, (19, 18) = 0, (19, 19) = -205379/216, (19, 20) = 205379/72, (19, 21) = -205379/72, (19, 22) = 205379/216, (19, 23) = 0, (19, 24) = 0, (19, 25) = 0, (19, 26) = 0, (19, 27) = 0, (19, 28) = 0, (19, 29) = 0, (19, 30) = 0, (19, 31) = 0, (19, 32) = 0, (19, 33) = 0, (19, 34) = 0, (19, 35) = 0, (19, 36) = 0, (19, 37) = 0, (19, 38) = 0, (19, 39) = 0, (19, 40) = 0, (19, 41) = 0, (19, 42) = 0, (19, 43) = 0, (19, 44) = 0, (19, 45) = 0, (19, 46) = 0, (19, 47) = 0, (19, 48) = 0, (19, 49) = 0, (19, 50) = 0, (19, 51) = 0, (19, 52) = 0, (19, 53) = 0, (19, 54) = 0, (19, 55) = 0, (19, 56) = 0, (19, 57) = 0, (19, 58) = 0, (19, 59) = 0, (19, 60) = 0, (19, 61) = 0, (20, 1) = 0, (20, 2) = 0, (20, 3) = 0, (20, 4) = 0, (20, 5) = 0, (20, 6) = 0, (20, 7) = 0, (20, 8) = 0, (20, 9) = 0, (20, 10) = 0, (20, 11) = 0, (20, 12) = 0, (20, 13) = 0, (20, 14) = 0, (20, 15) = 0, (20, 16) = 0, (20, 17) = 0, (20, 18) = 0, (20, 19) = 0, (20, 20) = -205379/216, (20, 21) = 205379/72, (20, 22) = -205379/72, (20, 23) = 205379/216, (20, 24) = 0, (20, 25) = 0, (20, 26) = 0, (20, 27) = 0, (20, 28) = 0, (20, 29) = 0, (20, 30) = 0, (20, 31) = 0, (20, 32) = 0, (20, 33) = 0, (20, 34) = 0, (20, 35) = 0, (20, 36) = 0, (20, 37) = 0, (20, 38) = 0, (20, 39) = 0, (20, 40) = 0, (20, 41) = 0, (20, 42) = 0, (20, 43) = 0, (20, 44) = 0, (20, 45) = 0, (20, 46) = 0, (20, 47) = 0, (20, 48) = 0, (20, 49) = 0, (20, 50) = 0, (20, 51) = 0, (20, 52) = 0, (20, 53) = 0, (20, 54) = 0, (20, 55) = 0, (20, 56) = 0, (20, 57) = 0, (20, 58) = 0, (20, 59) = 0, (20, 60) = 0, (20, 61) = 0, (21, 1) = 0, (21, 2) = 0, (21, 3) = 0, (21, 4) = 0, (21, 5) = 0, (21, 6) = 0, (21, 7) = 0, (21, 8) = 0, (21, 9) = 0, (21, 10) = 0, (21, 11) = 0, (21, 12) = 0, (21, 13) = 0, (21, 14) = 0, (21, 15) = 0, (21, 16) = 0, (21, 17) = 0, (21, 18) = 0, (21, 19) = 0, (21, 20) = 0, (21, 21) = -205379/216, (21, 22) = 205379/72, (21, 23) = -205379/72, (21, 24) = 205379/216, (21, 25) = 0, (21, 26) = 0, (21, 27) = 0, (21, 28) = 0, (21, 29) = 0, (21, 30) = 0, (21, 31) = 0, (21, 32) = 0, (21, 33) = 0, (21, 34) = 0, (21, 35) = 0, (21, 36) = 0, (21, 37) = 0, (21, 38) = 0, (21, 39) = 0, (21, 40) = 0, (21, 41) = 0, (21, 42) = 0, (21, 43) = 0, (21, 44) = 0, (21, 45) = 0, (21, 46) = 0, (21, 47) = 0, (21, 48) = 0, (21, 49) = 0, (21, 50) = 0, (21, 51) = 0, (21, 52) = 0, (21, 53) = 0, (21, 54) = 0, (21, 55) = 0, (21, 56) = 0, (21, 57) = 0, (21, 58) = 0, (21, 59) = 0, (21, 60) = 0, (21, 61) = 0, (22, 1) = 0, (22, 2) = 0, (22, 3) = 0, (22, 4) = 0, (22, 5) = 0, (22, 6) = 0, (22, 7) = 0, (22, 8) = 0, (22, 9) = 0, (22, 10) = 0, (22, 11) = 0, (22, 12) = 0, (22, 13) = 0, (22, 14) = 0, (22, 15) = 0, (22, 16) = 0, (22, 17) = 0, (22, 18) = 0, (22, 19) = 0, (22, 20) = 0, (22, 21) = 0, (22, 22) = -205379/216, (22, 23) = 205379/72, (22, 24) = -205379/72, (22, 25) = 205379/216, (22, 26) = 0, (22, 27) = 0, (22, 28) = 0, (22, 29) = 0, (22, 30) = 0, (22, 31) = 0, (22, 32) = 0, (22, 33) = 0, (22, 34) = 0, (22, 35) = 0, (22, 36) = 0, (22, 37) = 0, (22, 38) = 0, (22, 39) = 0, (22, 40) = 0, (22, 41) = 0, (22, 42) = 0, (22, 43) = 0, (22, 44) = 0, (22, 45) = 0, (22, 46) = 0, (22, 47) = 0, (22, 48) = 0, (22, 49) = 0, (22, 50) = 0, (22, 51) = 0, (22, 52) = 0, (22, 53) = 0, (22, 54) = 0, (22, 55) = 0, (22, 56) = 0, (22, 57) = 0, (22, 58) = 0, (22, 59) = 0, (22, 60) = 0, (22, 61) = 0, (23, 1) = 0, (23, 2) = 0, (23, 3) = 0, (23, 4) = 0, (23, 5) = 0, (23, 6) = 0, (23, 7) = 0, (23, 8) = 0, (23, 9) = 0, (23, 10) = 0, (23, 11) = 0, (23, 12) = 0, (23, 13) = 0, (23, 14) = 0, (23, 15) = 0, (23, 16) = 0, (23, 17) = 0, (23, 18) = 0, (23, 19) = 0, (23, 20) = 0, (23, 21) = 0, (23, 22) = 0, (23, 23) = -205379/216, (23, 24) = 205379/72, (23, 25) = -205379/72, (23, 26) = 205379/216, (23, 27) = 0, (23, 28) = 0, (23, 29) = 0, (23, 30) = 0, (23, 31) = 0, (23, 32) = 0, (23, 33) = 0, (23, 34) = 0, (23, 35) = 0, (23, 36) = 0, (23, 37) = 0, (23, 38) = 0, (23, 39) = 0, (23, 40) = 0, (23, 41) = 0, (23, 42) = 0, (23, 43) = 0, (23, 44) = 0, (23, 45) = 0, (23, 46) = 0, (23, 47) = 0, (23, 48) = 0, (23, 49) = 0, (23, 50) = 0, (23, 51) = 0, (23, 52) = 0, (23, 53) = 0, (23, 54) = 0, (23, 55) = 0, (23, 56) = 0, (23, 57) = 0, (23, 58) = 0, (23, 59) = 0, (23, 60) = 0, (23, 61) = 0, (24, 1) = 0, (24, 2) = 0, (24, 3) = 0, (24, 4) = 0, (24, 5) = 0, (24, 6) = 0, (24, 7) = 0, (24, 8) = 0, (24, 9) = 0, (24, 10) = 0, (24, 11) = 0, (24, 12) = 0, (24, 13) = 0, (24, 14) = 0, (24, 15) = 0, (24, 16) = 0, (24, 17) = 0, (24, 18) = 0, (24, 19) = 0, (24, 20) = 0, (24, 21) = 0, (24, 22) = 0, (24, 23) = 0, (24, 24) = -205379/216, (24, 25) = 205379/72, (24, 26) = -205379/72, (24, 27) = 205379/216, (24, 28) = 0, (24, 29) = 0, (24, 30) = 0, (24, 31) = 0, (24, 32) = 0, (24, 33) = 0, (24, 34) = 0, (24, 35) = 0, (24, 36) = 0, (24, 37) = 0, (24, 38) = 0, (24, 39) = 0, (24, 40) = 0, (24, 41) = 0, (24, 42) = 0, (24, 43) = 0, (24, 44) = 0, (24, 45) = 0, (24, 46) = 0, (24, 47) = 0, (24, 48) = 0, (24, 49) = 0, (24, 50) = 0, (24, 51) = 0, (24, 52) = 0, (24, 53) = 0, (24, 54) = 0, (24, 55) = 0, (24, 56) = 0, (24, 57) = 0, (24, 58) = 0, (24, 59) = 0, (24, 60) = 0, (24, 61) = 0, (25, 1) = 0, (25, 2) = 0, (25, 3) = 0, (25, 4) = 0, (25, 5) = 0, (25, 6) = 0, (25, 7) = 0, (25, 8) = 0, (25, 9) = 0, (25, 10) = 0, (25, 11) = 0, (25, 12) = 0, (25, 13) = 0, (25, 14) = 0, (25, 15) = 0, (25, 16) = 0, (25, 17) = 0, (25, 18) = 0, (25, 19) = 0, (25, 20) = 0, (25, 21) = 0, (25, 22) = 0, (25, 23) = 0, (25, 24) = 0, (25, 25) = -205379/216, (25, 26) = 205379/72, (25, 27) = -205379/72, (25, 28) = 205379/216, (25, 29) = 0, (25, 30) = 0, (25, 31) = 0, (25, 32) = 0, (25, 33) = 0, (25, 34) = 0, (25, 35) = 0, (25, 36) = 0, (25, 37) = 0, (25, 38) = 0, (25, 39) = 0, (25, 40) = 0, (25, 41) = 0, (25, 42) = 0, (25, 43) = 0, (25, 44) = 0, (25, 45) = 0, (25, 46) = 0, (25, 47) = 0, (25, 48) = 0, (25, 49) = 0, (25, 50) = 0, (25, 51) = 0, (25, 52) = 0, (25, 53) = 0, (25, 54) = 0, (25, 55) = 0, (25, 56) = 0, (25, 57) = 0, (25, 58) = 0, (25, 59) = 0, (25, 60) = 0, (25, 61) = 0, (26, 1) = 0, (26, 2) = 0, (26, 3) = 0, (26, 4) = 0, (26, 5) = 0, (26, 6) = 0, (26, 7) = 0, (26, 8) = 0, (26, 9) = 0, (26, 10) = 0, (26, 11) = 0, (26, 12) = 0, (26, 13) = 0, (26, 14) = 0, (26, 15) = 0, (26, 16) = 0, (26, 17) = 0, (26, 18) = 0, (26, 19) = 0, (26, 20) = 0, (26, 21) = 0, (26, 22) = 0, (26, 23) = 0, (26, 24) = 0, (26, 25) = 0, (26, 26) = -205379/216, (26, 27) = 205379/72, (26, 28) = -205379/72, (26, 29) = 205379/216, (26, 30) = 0, (26, 31) = 0, (26, 32) = 0, (26, 33) = 0, (26, 34) = 0, (26, 35) = 0, (26, 36) = 0, (26, 37) = 0, (26, 38) = 0, (26, 39) = 0, (26, 40) = 0, (26, 41) = 0, (26, 42) = 0, (26, 43) = 0, (26, 44) = 0, (26, 45) = 0, (26, 46) = 0, (26, 47) = 0, (26, 48) = 0, (26, 49) = 0, (26, 50) = 0, (26, 51) = 0, (26, 52) = 0, (26, 53) = 0, (26, 54) = 0, (26, 55) = 0, (26, 56) = 0, (26, 57) = 0, (26, 58) = 0, (26, 59) = 0, (26, 60) = 0, (26, 61) = 0, (27, 1) = 0, (27, 2) = 0, (27, 3) = 0, (27, 4) = 0, (27, 5) = 0, (27, 6) = 0, (27, 7) = 0, (27, 8) = 0, (27, 9) = 0, (27, 10) = 0, (27, 11) = 0, (27, 12) = 0, (27, 13) = 0, (27, 14) = 0, (27, 15) = 0, (27, 16) = 0, (27, 17) = 0, (27, 18) = 0, (27, 19) = 0, (27, 20) = 0, (27, 21) = 0, (27, 22) = 0, (27, 23) = 0, (27, 24) = 0, (27, 25) = 0, (27, 26) = 0, (27, 27) = -205379/216, (27, 28) = 205379/72, (27, 29) = -205379/72, (27, 30) = 205379/216, (27, 31) = 0, (27, 32) = 0, (27, 33) = 0, (27, 34) = 0, (27, 35) = 0, (27, 36) = 0, (27, 37) = 0, (27, 38) = 0, (27, 39) = 0, (27, 40) = 0, (27, 41) = 0, (27, 42) = 0, (27, 43) = 0, (27, 44) = 0, (27, 45) = 0, (27, 46) = 0, (27, 47) = 0, (27, 48) = 0, (27, 49) = 0, (27, 50) = 0, (27, 51) = 0, (27, 52) = 0, (27, 53) = 0, (27, 54) = 0, (27, 55) = 0, (27, 56) = 0, (27, 57) = 0, (27, 58) = 0, (27, 59) = 0, (27, 60) = 0, (27, 61) = 0, (28, 1) = 0, (28, 2) = 0, (28, 3) = 0, (28, 4) = 0, (28, 5) = 0, (28, 6) = 0, (28, 7) = 0, (28, 8) = 0, (28, 9) = 0, (28, 10) = 0, (28, 11) = 0, (28, 12) = 0, (28, 13) = 0, (28, 14) = 0, (28, 15) = 0, (28, 16) = 0, (28, 17) = 0, (28, 18) = 0, (28, 19) = 0, (28, 20) = 0, (28, 21) = 0, (28, 22) = 0, (28, 23) = 0, (28, 24) = 0, (28, 25) = 0, (28, 26) = 0, (28, 27) = 0, (28, 28) = -205379/216, (28, 29) = 205379/72, (28, 30) = -205379/72, (28, 31) = 205379/216, (28, 32) = 0, (28, 33) = 0, (28, 34) = 0, (28, 35) = 0, (28, 36) = 0, (28, 37) = 0, (28, 38) = 0, (28, 39) = 0, (28, 40) = 0, (28, 41) = 0, (28, 42) = 0, (28, 43) = 0, (28, 44) = 0, (28, 45) = 0, (28, 46) = 0, (28, 47) = 0, (28, 48) = 0, (28, 49) = 0, (28, 50) = 0, (28, 51) = 0, (28, 52) = 0, (28, 53) = 0, (28, 54) = 0, (28, 55) = 0, (28, 56) = 0, (28, 57) = 0, (28, 58) = 0, (28, 59) = 0, (28, 60) = 0, (28, 61) = 0, (29, 1) = 0, (29, 2) = 0, (29, 3) = 0, (29, 4) = 0, (29, 5) = 0, (29, 6) = 0, (29, 7) = 0, (29, 8) = 0, (29, 9) = 0, (29, 10) = 0, (29, 11) = 0, (29, 12) = 0, (29, 13) = 0, (29, 14) = 0, (29, 15) = 0, (29, 16) = 0, (29, 17) = 0, (29, 18) = 0, (29, 19) = 0, (29, 20) = 0, (29, 21) = 0, (29, 22) = 0, (29, 23) = 0, (29, 24) = 0, (29, 25) = 0, (29, 26) = 0, (29, 27) = 0, (29, 28) = 0, (29, 29) = -205379/216, (29, 30) = 205379/72, (29, 31) = -205379/72, (29, 32) = 205379/216, (29, 33) = 0, (29, 34) = 0, (29, 35) = 0, (29, 36) = 0, (29, 37) = 0, (29, 38) = 0, (29, 39) = 0, (29, 40) = 0, (29, 41) = 0, (29, 42) = 0, (29, 43) = 0, (29, 44) = 0, (29, 45) = 0, (29, 46) = 0, (29, 47) = 0, (29, 48) = 0, (29, 49) = 0, (29, 50) = 0, (29, 51) = 0, (29, 52) = 0, (29, 53) = 0, (29, 54) = 0, (29, 55) = 0, (29, 56) = 0, (29, 57) = 0, (29, 58) = 0, (29, 59) = 0, (29, 60) = 0, (29, 61) = 0, (30, 1) = 0, (30, 2) = 0, (30, 3) = 0, (30, 4) = 0, (30, 5) = 0, (30, 6) = 0, (30, 7) = 0, (30, 8) = 0, (30, 9) = 0, (30, 10) = 0, (30, 11) = 0, (30, 12) = 0, (30, 13) = 0, (30, 14) = 0, (30, 15) = 0, (30, 16) = 0, (30, 17) = 0, (30, 18) = 0, (30, 19) = 0, (30, 20) = 0, (30, 21) = 0, (30, 22) = 0, (30, 23) = 0, (30, 24) = 0, (30, 25) = 0, (30, 26) = 0, (30, 27) = 0, (30, 28) = 0, (30, 29) = 0, (30, 30) = -205379/216, (30, 31) = 205379/72, (30, 32) = -205379/72, (30, 33) = 205379/216, (30, 34) = 0, (30, 35) = 0, (30, 36) = 0, (30, 37) = 0, (30, 38) = 0, (30, 39) = 0, (30, 40) = 0, (30, 41) = 0, (30, 42) = 0, (30, 43) = 0, (30, 44) = 0, (30, 45) = 0, (30, 46) = 0, (30, 47) = 0, (30, 48) = 0, (30, 49) = 0, (30, 50) = 0, (30, 51) = 0, (30, 52) = 0, (30, 53) = 0, (30, 54) = 0, (30, 55) = 0, (30, 56) = 0, (30, 57) = 0, (30, 58) = 0, (30, 59) = 0, (30, 60) = 0, (30, 61) = 0, (31, 1) = 0, (31, 2) = 0, (31, 3) = 0, (31, 4) = 0, (31, 5) = 0, (31, 6) = 0, (31, 7) = 0, (31, 8) = 0, (31, 9) = 0, (31, 10) = 0, (31, 11) = 0, (31, 12) = 0, (31, 13) = 0, (31, 14) = 0, (31, 15) = 0, (31, 16) = 0, (31, 17) = 0, (31, 18) = 0, (31, 19) = 0, (31, 20) = 0, (31, 21) = 0, (31, 22) = 0, (31, 23) = 0, (31, 24) = 0, (31, 25) = 0, (31, 26) = 0, (31, 27) = 0, (31, 28) = 0, (31, 29) = 0, (31, 30) = 0, (31, 31) = -205379/216, (31, 32) = 205379/72, (31, 33) = -205379/72, (31, 34) = 205379/216, (31, 35) = 0, (31, 36) = 0, (31, 37) = 0, (31, 38) = 0, (31, 39) = 0, (31, 40) = 0, (31, 41) = 0, (31, 42) = 0, (31, 43) = 0, (31, 44) = 0, (31, 45) = 0, (31, 46) = 0, (31, 47) = 0, (31, 48) = 0, (31, 49) = 0, (31, 50) = 0, (31, 51) = 0, (31, 52) = 0, (31, 53) = 0, (31, 54) = 0, (31, 55) = 0, (31, 56) = 0, (31, 57) = 0, (31, 58) = 0, (31, 59) = 0, (31, 60) = 0, (31, 61) = 0, (32, 1) = 0, (32, 2) = 0, (32, 3) = 0, (32, 4) = 0, (32, 5) = 0, (32, 6) = 0, (32, 7) = 0, (32, 8) = 0, (32, 9) = 0, (32, 10) = 0, (32, 11) = 0, (32, 12) = 0, (32, 13) = 0, (32, 14) = 0, (32, 15) = 0, (32, 16) = 0, (32, 17) = 0, (32, 18) = 0, (32, 19) = 0, (32, 20) = 0, (32, 21) = 0, (32, 22) = 0, (32, 23) = 0, (32, 24) = 0, (32, 25) = 0, (32, 26) = 0, (32, 27) = 0, (32, 28) = 0, (32, 29) = 0, (32, 30) = 0, (32, 31) = 0, (32, 32) = -205379/216, (32, 33) = 205379/72, (32, 34) = -205379/72, (32, 35) = 205379/216, (32, 36) = 0, (32, 37) = 0, (32, 38) = 0, (32, 39) = 0, (32, 40) = 0, (32, 41) = 0, (32, 42) = 0, (32, 43) = 0, (32, 44) = 0, (32, 45) = 0, (32, 46) = 0, (32, 47) = 0, (32, 48) = 0, (32, 49) = 0, (32, 50) = 0, (32, 51) = 0, (32, 52) = 0, (32, 53) = 0, (32, 54) = 0, (32, 55) = 0, (32, 56) = 0, (32, 57) = 0, (32, 58) = 0, (32, 59) = 0, (32, 60) = 0, (32, 61) = 0, (33, 1) = 0, (33, 2) = 0, (33, 3) = 0, (33, 4) = 0, (33, 5) = 0, (33, 6) = 0, (33, 7) = 0, (33, 8) = 0, (33, 9) = 0, (33, 10) = 0, (33, 11) = 0, (33, 12) = 0, (33, 13) = 0, (33, 14) = 0, (33, 15) = 0, (33, 16) = 0, (33, 17) = 0, (33, 18) = 0, (33, 19) = 0, (33, 20) = 0, (33, 21) = 0, (33, 22) = 0, (33, 23) = 0, (33, 24) = 0, (33, 25) = 0, (33, 26) = 0, (33, 27) = 0, (33, 28) = 0, (33, 29) = 0, (33, 30) = 0, (33, 31) = 0, (33, 32) = 0, (33, 33) = -205379/216, (33, 34) = 205379/72, (33, 35) = -205379/72, (33, 36) = 205379/216, (33, 37) = 0, (33, 38) = 0, (33, 39) = 0, (33, 40) = 0, (33, 41) = 0, (33, 42) = 0, (33, 43) = 0, (33, 44) = 0, (33, 45) = 0, (33, 46) = 0, (33, 47) = 0, (33, 48) = 0, (33, 49) = 0, (33, 50) = 0, (33, 51) = 0, (33, 52) = 0, (33, 53) = 0, (33, 54) = 0, (33, 55) = 0, (33, 56) = 0, (33, 57) = 0, (33, 58) = 0, (33, 59) = 0, (33, 60) = 0, (33, 61) = 0, (34, 1) = 0, (34, 2) = 0, (34, 3) = 0, (34, 4) = 0, (34, 5) = 0, (34, 6) = 0, (34, 7) = 0, (34, 8) = 0, (34, 9) = 0, (34, 10) = 0, (34, 11) = 0, (34, 12) = 0, (34, 13) = 0, (34, 14) = 0, (34, 15) = 0, (34, 16) = 0, (34, 17) = 0, (34, 18) = 0, (34, 19) = 0, (34, 20) = 0, (34, 21) = 0, (34, 22) = 0, (34, 23) = 0, (34, 24) = 0, (34, 25) = 0, (34, 26) = 0, (34, 27) = 0, (34, 28) = 0, (34, 29) = 0, (34, 30) = 0, (34, 31) = 0, (34, 32) = 0, (34, 33) = 0, (34, 34) = -205379/216, (34, 35) = 205379/72, (34, 36) = -205379/72, (34, 37) = 205379/216, (34, 38) = 0, (34, 39) = 0, (34, 40) = 0, (34, 41) = 0, (34, 42) = 0, (34, 43) = 0, (34, 44) = 0, (34, 45) = 0, (34, 46) = 0, (34, 47) = 0, (34, 48) = 0, (34, 49) = 0, (34, 50) = 0, (34, 51) = 0, (34, 52) = 0, (34, 53) = 0, (34, 54) = 0, (34, 55) = 0, (34, 56) = 0, (34, 57) = 0, (34, 58) = 0, (34, 59) = 0, (34, 60) = 0, (34, 61) = 0, (35, 1) = 0, (35, 2) = 0, (35, 3) = 0, (35, 4) = 0, (35, 5) = 0, (35, 6) = 0, (35, 7) = 0, (35, 8) = 0, (35, 9) = 0, (35, 10) = 0, (35, 11) = 0, (35, 12) = 0, (35, 13) = 0, (35, 14) = 0, (35, 15) = 0, (35, 16) = 0, (35, 17) = 0, (35, 18) = 0, (35, 19) = 0, (35, 20) = 0, (35, 21) = 0, (35, 22) = 0, (35, 23) = 0, (35, 24) = 0, (35, 25) = 0, (35, 26) = 0, (35, 27) = 0, (35, 28) = 0, (35, 29) = 0, (35, 30) = 0, (35, 31) = 0, (35, 32) = 0, (35, 33) = 0, (35, 34) = 0, (35, 35) = -205379/216, (35, 36) = 205379/72, (35, 37) = -205379/72, (35, 38) = 205379/216, (35, 39) = 0, (35, 40) = 0, (35, 41) = 0, (35, 42) = 0, (35, 43) = 0, (35, 44) = 0, (35, 45) = 0, (35, 46) = 0, (35, 47) = 0, (35, 48) = 0, (35, 49) = 0, (35, 50) = 0, (35, 51) = 0, (35, 52) = 0, (35, 53) = 0, (35, 54) = 0, (35, 55) = 0, (35, 56) = 0, (35, 57) = 0, (35, 58) = 0, (35, 59) = 0, (35, 60) = 0, (35, 61) = 0, (36, 1) = 0, (36, 2) = 0, (36, 3) = 0, (36, 4) = 0, (36, 5) = 0, (36, 6) = 0, (36, 7) = 0, (36, 8) = 0, (36, 9) = 0, (36, 10) = 0, (36, 11) = 0, (36, 12) = 0, (36, 13) = 0, (36, 14) = 0, (36, 15) = 0, (36, 16) = 0, (36, 17) = 0, (36, 18) = 0, (36, 19) = 0, (36, 20) = 0, (36, 21) = 0, (36, 22) = 0, (36, 23) = 0, (36, 24) = 0, (36, 25) = 0, (36, 26) = 0, (36, 27) = 0, (36, 28) = 0, (36, 29) = 0, (36, 30) = 0, (36, 31) = 0, (36, 32) = 0, (36, 33) = 0, (36, 34) = 0, (36, 35) = 0, (36, 36) = -205379/216, (36, 37) = 205379/72, (36, 38) = -205379/72, (36, 39) = 205379/216, (36, 40) = 0, (36, 41) = 0, (36, 42) = 0, (36, 43) = 0, (36, 44) = 0, (36, 45) = 0, (36, 46) = 0, (36, 47) = 0, (36, 48) = 0, (36, 49) = 0, (36, 50) = 0, (36, 51) = 0, (36, 52) = 0, (36, 53) = 0, (36, 54) = 0, (36, 55) = 0, (36, 56) = 0, (36, 57) = 0, (36, 58) = 0, (36, 59) = 0, (36, 60) = 0, (36, 61) = 0, (37, 1) = 0, (37, 2) = 0, (37, 3) = 0, (37, 4) = 0, (37, 5) = 0, (37, 6) = 0, (37, 7) = 0, (37, 8) = 0, (37, 9) = 0, (37, 10) = 0, (37, 11) = 0, (37, 12) = 0, (37, 13) = 0, (37, 14) = 0, (37, 15) = 0, (37, 16) = 0, (37, 17) = 0, (37, 18) = 0, (37, 19) = 0, (37, 20) = 0, (37, 21) = 0, (37, 22) = 0, (37, 23) = 0, (37, 24) = 0, (37, 25) = 0, (37, 26) = 0, (37, 27) = 0, (37, 28) = 0, (37, 29) = 0, (37, 30) = 0, (37, 31) = 0, (37, 32) = 0, (37, 33) = 0, (37, 34) = 0, (37, 35) = 0, (37, 36) = 0, (37, 37) = -205379/216, (37, 38) = 205379/72, (37, 39) = -205379/72, (37, 40) = 205379/216, (37, 41) = 0, (37, 42) = 0, (37, 43) = 0, (37, 44) = 0, (37, 45) = 0, (37, 46) = 0, (37, 47) = 0, (37, 48) = 0, (37, 49) = 0, (37, 50) = 0, (37, 51) = 0, (37, 52) = 0, (37, 53) = 0, (37, 54) = 0, (37, 55) = 0, (37, 56) = 0, (37, 57) = 0, (37, 58) = 0, (37, 59) = 0, (37, 60) = 0, (37, 61) = 0, (38, 1) = 0, (38, 2) = 0, (38, 3) = 0, (38, 4) = 0, (38, 5) = 0, (38, 6) = 0, (38, 7) = 0, (38, 8) = 0, (38, 9) = 0, (38, 10) = 0, (38, 11) = 0, (38, 12) = 0, (38, 13) = 0, (38, 14) = 0, (38, 15) = 0, (38, 16) = 0, (38, 17) = 0, (38, 18) = 0, (38, 19) = 0, (38, 20) = 0, (38, 21) = 0, (38, 22) = 0, (38, 23) = 0, (38, 24) = 0, (38, 25) = 0, (38, 26) = 0, (38, 27) = 0, (38, 28) = 0, (38, 29) = 0, (38, 30) = 0, (38, 31) = 0, (38, 32) = 0, (38, 33) = 0, (38, 34) = 0, (38, 35) = 0, (38, 36) = 0, (38, 37) = 0, (38, 38) = -205379/216, (38, 39) = 205379/72, (38, 40) = -205379/72, (38, 41) = 205379/216, (38, 42) = 0, (38, 43) = 0, (38, 44) = 0, (38, 45) = 0, (38, 46) = 0, (38, 47) = 0, (38, 48) = 0, (38, 49) = 0, (38, 50) = 0, (38, 51) = 0, (38, 52) = 0, (38, 53) = 0, (38, 54) = 0, (38, 55) = 0, (38, 56) = 0, (38, 57) = 0, (38, 58) = 0, (38, 59) = 0, (38, 60) = 0, (38, 61) = 0, (39, 1) = 0, (39, 2) = 0, (39, 3) = 0, (39, 4) = 0, (39, 5) = 0, (39, 6) = 0, (39, 7) = 0, (39, 8) = 0, (39, 9) = 0, (39, 10) = 0, (39, 11) = 0, (39, 12) = 0, (39, 13) = 0, (39, 14) = 0, (39, 15) = 0, (39, 16) = 0, (39, 17) = 0, (39, 18) = 0, (39, 19) = 0, (39, 20) = 0, (39, 21) = 0, (39, 22) = 0, (39, 23) = 0, (39, 24) = 0, (39, 25) = 0, (39, 26) = 0, (39, 27) = 0, (39, 28) = 0, (39, 29) = 0, (39, 30) = 0, (39, 31) = 0, (39, 32) = 0, (39, 33) = 0, (39, 34) = 0, (39, 35) = 0, (39, 36) = 0, (39, 37) = 0, (39, 38) = 0, (39, 39) = -205379/216, (39, 40) = 205379/72, (39, 41) = -205379/72, (39, 42) = 205379/216, (39, 43) = 0, (39, 44) = 0, (39, 45) = 0, (39, 46) = 0, (39, 47) = 0, (39, 48) = 0, (39, 49) = 0, (39, 50) = 0, (39, 51) = 0, (39, 52) = 0, (39, 53) = 0, (39, 54) = 0, (39, 55) = 0, (39, 56) = 0, (39, 57) = 0, (39, 58) = 0, (39, 59) = 0, (39, 60) = 0, (39, 61) = 0, (40, 1) = 0, (40, 2) = 0, (40, 3) = 0, (40, 4) = 0, (40, 5) = 0, (40, 6) = 0, (40, 7) = 0, (40, 8) = 0, (40, 9) = 0, (40, 10) = 0, (40, 11) = 0, (40, 12) = 0, (40, 13) = 0, (40, 14) = 0, (40, 15) = 0, (40, 16) = 0, (40, 17) = 0, (40, 18) = 0, (40, 19) = 0, (40, 20) = 0, (40, 21) = 0, (40, 22) = 0, (40, 23) = 0, (40, 24) = 0, (40, 25) = 0, (40, 26) = 0, (40, 27) = 0, (40, 28) = 0, (40, 29) = 0, (40, 30) = 0, (40, 31) = 0, (40, 32) = 0, (40, 33) = 0, (40, 34) = 0, (40, 35) = 0, (40, 36) = 0, (40, 37) = 0, (40, 38) = 0, (40, 39) = 0, (40, 40) = -205379/216, (40, 41) = 205379/72, (40, 42) = -205379/72, (40, 43) = 205379/216, (40, 44) = 0, (40, 45) = 0, (40, 46) = 0, (40, 47) = 0, (40, 48) = 0, (40, 49) = 0, (40, 50) = 0, (40, 51) = 0, (40, 52) = 0, (40, 53) = 0, (40, 54) = 0, (40, 55) = 0, (40, 56) = 0, (40, 57) = 0, (40, 58) = 0, (40, 59) = 0, (40, 60) = 0, (40, 61) = 0, (41, 1) = 0, (41, 2) = 0, (41, 3) = 0, (41, 4) = 0, (41, 5) = 0, (41, 6) = 0, (41, 7) = 0, (41, 8) = 0, (41, 9) = 0, (41, 10) = 0, (41, 11) = 0, (41, 12) = 0, (41, 13) = 0, (41, 14) = 0, (41, 15) = 0, (41, 16) = 0, (41, 17) = 0, (41, 18) = 0, (41, 19) = 0, (41, 20) = 0, (41, 21) = 0, (41, 22) = 0, (41, 23) = 0, (41, 24) = 0, (41, 25) = 0, (41, 26) = 0, (41, 27) = 0, (41, 28) = 0, (41, 29) = 0, (41, 30) = 0, (41, 31) = 0, (41, 32) = 0, (41, 33) = 0, (41, 34) = 0, (41, 35) = 0, (41, 36) = 0, (41, 37) = 0, (41, 38) = 0, (41, 39) = 0, (41, 40) = 0, (41, 41) = -205379/216, (41, 42) = 205379/72, (41, 43) = -205379/72, (41, 44) = 205379/216, (41, 45) = 0, (41, 46) = 0, (41, 47) = 0, (41, 48) = 0, (41, 49) = 0, (41, 50) = 0, (41, 51) = 0, (41, 52) = 0, (41, 53) = 0, (41, 54) = 0, (41, 55) = 0, (41, 56) = 0, (41, 57) = 0, (41, 58) = 0, (41, 59) = 0, (41, 60) = 0, (41, 61) = 0, (42, 1) = 0, (42, 2) = 0, (42, 3) = 0, (42, 4) = 0, (42, 5) = 0, (42, 6) = 0, (42, 7) = 0, (42, 8) = 0, (42, 9) = 0, (42, 10) = 0, (42, 11) = 0, (42, 12) = 0, (42, 13) = 0, (42, 14) = 0, (42, 15) = 0, (42, 16) = 0, (42, 17) = 0, (42, 18) = 0, (42, 19) = 0, (42, 20) = 0, (42, 21) = 0, (42, 22) = 0, (42, 23) = 0, (42, 24) = 0, (42, 25) = 0, (42, 26) = 0, (42, 27) = 0, (42, 28) = 0, (42, 29) = 0, (42, 30) = 0, (42, 31) = 0, (42, 32) = 0, (42, 33) = 0, (42, 34) = 0, (42, 35) = 0, (42, 36) = 0, (42, 37) = 0, (42, 38) = 0, (42, 39) = 0, (42, 40) = 0, (42, 41) = 0, (42, 42) = -205379/216, (42, 43) = 205379/72, (42, 44) = -205379/72, (42, 45) = 205379/216, (42, 46) = 0, (42, 47) = 0, (42, 48) = 0, (42, 49) = 0, (42, 50) = 0, (42, 51) = 0, (42, 52) = 0, (42, 53) = 0, (42, 54) = 0, (42, 55) = 0, (42, 56) = 0, (42, 57) = 0, (42, 58) = 0, (42, 59) = 0, (42, 60) = 0, (42, 61) = 0, (43, 1) = 0, (43, 2) = 0, (43, 3) = 0, (43, 4) = 0, (43, 5) = 0, (43, 6) = 0, (43, 7) = 0, (43, 8) = 0, (43, 9) = 0, (43, 10) = 0, (43, 11) = 0, (43, 12) = 0, (43, 13) = 0, (43, 14) = 0, (43, 15) = 0, (43, 16) = 0, (43, 17) = 0, (43, 18) = 0, (43, 19) = 0, (43, 20) = 0, (43, 21) = 0, (43, 22) = 0, (43, 23) = 0, (43, 24) = 0, (43, 25) = 0, (43, 26) = 0, (43, 27) = 0, (43, 28) = 0, (43, 29) = 0, (43, 30) = 0, (43, 31) = 0, (43, 32) = 0, (43, 33) = 0, (43, 34) = 0, (43, 35) = 0, (43, 36) = 0, (43, 37) = 0, (43, 38) = 0, (43, 39) = 0, (43, 40) = 0, (43, 41) = 0, (43, 42) = 0, (43, 43) = -205379/216, (43, 44) = 205379/72, (43, 45) = -205379/72, (43, 46) = 205379/216, (43, 47) = 0, (43, 48) = 0, (43, 49) = 0, (43, 50) = 0, (43, 51) = 0, (43, 52) = 0, (43, 53) = 0, (43, 54) = 0, (43, 55) = 0, (43, 56) = 0, (43, 57) = 0, (43, 58) = 0, (43, 59) = 0, (43, 60) = 0, (43, 61) = 0, (44, 1) = 0, (44, 2) = 0, (44, 3) = 0, (44, 4) = 0, (44, 5) = 0, (44, 6) = 0, (44, 7) = 0, (44, 8) = 0, (44, 9) = 0, (44, 10) = 0, (44, 11) = 0, (44, 12) = 0, (44, 13) = 0, (44, 14) = 0, (44, 15) = 0, (44, 16) = 0, (44, 17) = 0, (44, 18) = 0, (44, 19) = 0, (44, 20) = 0, (44, 21) = 0, (44, 22) = 0, (44, 23) = 0, (44, 24) = 0, (44, 25) = 0, (44, 26) = 0, (44, 27) = 0, (44, 28) = 0, (44, 29) = 0, (44, 30) = 0, (44, 31) = 0, (44, 32) = 0, (44, 33) = 0, (44, 34) = 0, (44, 35) = 0, (44, 36) = 0, (44, 37) = 0, (44, 38) = 0, (44, 39) = 0, (44, 40) = 0, (44, 41) = 0, (44, 42) = 0, (44, 43) = 0, (44, 44) = -205379/216, (44, 45) = 205379/72, (44, 46) = -205379/72, (44, 47) = 205379/216, (44, 48) = 0, (44, 49) = 0, (44, 50) = 0, (44, 51) = 0, (44, 52) = 0, (44, 53) = 0, (44, 54) = 0, (44, 55) = 0, (44, 56) = 0, (44, 57) = 0, (44, 58) = 0, (44, 59) = 0, (44, 60) = 0, (44, 61) = 0, (45, 1) = 0, (45, 2) = 0, (45, 3) = 0, (45, 4) = 0, (45, 5) = 0, (45, 6) = 0, (45, 7) = 0, (45, 8) = 0, (45, 9) = 0, (45, 10) = 0, (45, 11) = 0, (45, 12) = 0, (45, 13) = 0, (45, 14) = 0, (45, 15) = 0, (45, 16) = 0, (45, 17) = 0, (45, 18) = 0, (45, 19) = 0, (45, 20) = 0, (45, 21) = 0, (45, 22) = 0, (45, 23) = 0, (45, 24) = 0, (45, 25) = 0, (45, 26) = 0, (45, 27) = 0, (45, 28) = 0, (45, 29) = 0, (45, 30) = 0, (45, 31) = 0, (45, 32) = 0, (45, 33) = 0, (45, 34) = 0, (45, 35) = 0, (45, 36) = 0, (45, 37) = 0, (45, 38) = 0, (45, 39) = 0, (45, 40) = 0, (45, 41) = 0, (45, 42) = 0, (45, 43) = 0, (45, 44) = 0, (45, 45) = -205379/216, (45, 46) = 205379/72, (45, 47) = -205379/72, (45, 48) = 205379/216, (45, 49) = 0, (45, 50) = 0, (45, 51) = 0, (45, 52) = 0, (45, 53) = 0, (45, 54) = 0, (45, 55) = 0, (45, 56) = 0, (45, 57) = 0, (45, 58) = 0, (45, 59) = 0, (45, 60) = 0, (45, 61) = 0, (46, 1) = 0, (46, 2) = 0, (46, 3) = 0, (46, 4) = 0, (46, 5) = 0, (46, 6) = 0, (46, 7) = 0, (46, 8) = 0, (46, 9) = 0, (46, 10) = 0, (46, 11) = 0, (46, 12) = 0, (46, 13) = 0, (46, 14) = 0, (46, 15) = 0, (46, 16) = 0, (46, 17) = 0, (46, 18) = 0, (46, 19) = 0, (46, 20) = 0, (46, 21) = 0, (46, 22) = 0, (46, 23) = 0, (46, 24) = 0, (46, 25) = 0, (46, 26) = 0, (46, 27) = 0, (46, 28) = 0, (46, 29) = 0, (46, 30) = 0, (46, 31) = 0, (46, 32) = 0, (46, 33) = 0, (46, 34) = 0, (46, 35) = 0, (46, 36) = 0, (46, 37) = 0, (46, 38) = 0, (46, 39) = 0, (46, 40) = 0, (46, 41) = 0, (46, 42) = 0, (46, 43) = 0, (46, 44) = 0, (46, 45) = 0, (46, 46) = -205379/216, (46, 47) = 205379/72, (46, 48) = -205379/72, (46, 49) = 205379/216, (46, 50) = 0, (46, 51) = 0, (46, 52) = 0, (46, 53) = 0, (46, 54) = 0, (46, 55) = 0, (46, 56) = 0, (46, 57) = 0, (46, 58) = 0, (46, 59) = 0, (46, 60) = 0, (46, 61) = 0, (47, 1) = 0, (47, 2) = 0, (47, 3) = 0, (47, 4) = 0, (47, 5) = 0, (47, 6) = 0, (47, 7) = 0, (47, 8) = 0, (47, 9) = 0, (47, 10) = 0, (47, 11) = 0, (47, 12) = 0, (47, 13) = 0, (47, 14) = 0, (47, 15) = 0, (47, 16) = 0, (47, 17) = 0, (47, 18) = 0, (47, 19) = 0, (47, 20) = 0, (47, 21) = 0, (47, 22) = 0, (47, 23) = 0, (47, 24) = 0, (47, 25) = 0, (47, 26) = 0, (47, 27) = 0, (47, 28) = 0, (47, 29) = 0, (47, 30) = 0, (47, 31) = 0, (47, 32) = 0, (47, 33) = 0, (47, 34) = 0, (47, 35) = 0, (47, 36) = 0, (47, 37) = 0, (47, 38) = 0, (47, 39) = 0, (47, 40) = 0, (47, 41) = 0, (47, 42) = 0, (47, 43) = 0, (47, 44) = 0, (47, 45) = 0, (47, 46) = 0, (47, 47) = -205379/216, (47, 48) = 205379/72, (47, 49) = -205379/72, (47, 50) = 205379/216, (47, 51) = 0, (47, 52) = 0, (47, 53) = 0, (47, 54) = 0, (47, 55) = 0, (47, 56) = 0, (47, 57) = 0, (47, 58) = 0, (47, 59) = 0, (47, 60) = 0, (47, 61) = 0, (48, 1) = 0, (48, 2) = 0, (48, 3) = 0, (48, 4) = 0, (48, 5) = 0, (48, 6) = 0, (48, 7) = 0, (48, 8) = 0, (48, 9) = 0, (48, 10) = 0, (48, 11) = 0, (48, 12) = 0, (48, 13) = 0, (48, 14) = 0, (48, 15) = 0, (48, 16) = 0, (48, 17) = 0, (48, 18) = 0, (48, 19) = 0, (48, 20) = 0, (48, 21) = 0, (48, 22) = 0, (48, 23) = 0, (48, 24) = 0, (48, 25) = 0, (48, 26) = 0, (48, 27) = 0, (48, 28) = 0, (48, 29) = 0, (48, 30) = 0, (48, 31) = 0, (48, 32) = 0, (48, 33) = 0, (48, 34) = 0, (48, 35) = 0, (48, 36) = 0, (48, 37) = 0, (48, 38) = 0, (48, 39) = 0, (48, 40) = 0, (48, 41) = 0, (48, 42) = 0, (48, 43) = 0, (48, 44) = 0, (48, 45) = 0, (48, 46) = 0, (48, 47) = 0, (48, 48) = -205379/216, (48, 49) = 205379/72, (48, 50) = -205379/72, (48, 51) = 205379/216, (48, 52) = 0, (48, 53) = 0, (48, 54) = 0, (48, 55) = 0, (48, 56) = 0, (48, 57) = 0, (48, 58) = 0, (48, 59) = 0, (48, 60) = 0, (48, 61) = 0, (49, 1) = 0, (49, 2) = 0, (49, 3) = 0, (49, 4) = 0, (49, 5) = 0, (49, 6) = 0, (49, 7) = 0, (49, 8) = 0, (49, 9) = 0, (49, 10) = 0, (49, 11) = 0, (49, 12) = 0, (49, 13) = 0, (49, 14) = 0, (49, 15) = 0, (49, 16) = 0, (49, 17) = 0, (49, 18) = 0, (49, 19) = 0, (49, 20) = 0, (49, 21) = 0, (49, 22) = 0, (49, 23) = 0, (49, 24) = 0, (49, 25) = 0, (49, 26) = 0, (49, 27) = 0, (49, 28) = 0, (49, 29) = 0, (49, 30) = 0, (49, 31) = 0, (49, 32) = 0, (49, 33) = 0, (49, 34) = 0, (49, 35) = 0, (49, 36) = 0, (49, 37) = 0, (49, 38) = 0, (49, 39) = 0, (49, 40) = 0, (49, 41) = 0, (49, 42) = 0, (49, 43) = 0, (49, 44) = 0, (49, 45) = 0, (49, 46) = 0, (49, 47) = 0, (49, 48) = 0, (49, 49) = -205379/216, (49, 50) = 205379/72, (49, 51) = -205379/72, (49, 52) = 205379/216, (49, 53) = 0, (49, 54) = 0, (49, 55) = 0, (49, 56) = 0, (49, 57) = 0, (49, 58) = 0, (49, 59) = 0, (49, 60) = 0, (49, 61) = 0, (50, 1) = 0, (50, 2) = 0, (50, 3) = 0, (50, 4) = 0, (50, 5) = 0, (50, 6) = 0, (50, 7) = 0, (50, 8) = 0, (50, 9) = 0, (50, 10) = 0, (50, 11) = 0, (50, 12) = 0, (50, 13) = 0, (50, 14) = 0, (50, 15) = 0, (50, 16) = 0, (50, 17) = 0, (50, 18) = 0, (50, 19) = 0, (50, 20) = 0, (50, 21) = 0, (50, 22) = 0, (50, 23) = 0, (50, 24) = 0, (50, 25) = 0, (50, 26) = 0, (50, 27) = 0, (50, 28) = 0, (50, 29) = 0, (50, 30) = 0, (50, 31) = 0, (50, 32) = 0, (50, 33) = 0, (50, 34) = 0, (50, 35) = 0, (50, 36) = 0, (50, 37) = 0, (50, 38) = 0, (50, 39) = 0, (50, 40) = 0, (50, 41) = 0, (50, 42) = 0, (50, 43) = 0, (50, 44) = 0, (50, 45) = 0, (50, 46) = 0, (50, 47) = 0, (50, 48) = 0, (50, 49) = 0, (50, 50) = -205379/216, (50, 51) = 205379/72, (50, 52) = -205379/72, (50, 53) = 205379/216, (50, 54) = 0, (50, 55) = 0, (50, 56) = 0, (50, 57) = 0, (50, 58) = 0, (50, 59) = 0, (50, 60) = 0, (50, 61) = 0, (51, 1) = 0, (51, 2) = 0, (51, 3) = 0, (51, 4) = 0, (51, 5) = 0, (51, 6) = 0, (51, 7) = 0, (51, 8) = 0, (51, 9) = 0, (51, 10) = 0, (51, 11) = 0, (51, 12) = 0, (51, 13) = 0, (51, 14) = 0, (51, 15) = 0, (51, 16) = 0, (51, 17) = 0, (51, 18) = 0, (51, 19) = 0, (51, 20) = 0, (51, 21) = 0, (51, 22) = 0, (51, 23) = 0, (51, 24) = 0, (51, 25) = 0, (51, 26) = 0, (51, 27) = 0, (51, 28) = 0, (51, 29) = 0, (51, 30) = 0, (51, 31) = 0, (51, 32) = 0, (51, 33) = 0, (51, 34) = 0, (51, 35) = 0, (51, 36) = 0, (51, 37) = 0, (51, 38) = 0, (51, 39) = 0, (51, 40) = 0, (51, 41) = 0, (51, 42) = 0, (51, 43) = 0, (51, 44) = 0, (51, 45) = 0, (51, 46) = 0, (51, 47) = 0, (51, 48) = 0, (51, 49) = 0, (51, 50) = 0, (51, 51) = -205379/216, (51, 52) = 205379/72, (51, 53) = -205379/72, (51, 54) = 205379/216, (51, 55) = 0, (51, 56) = 0, (51, 57) = 0, (51, 58) = 0, (51, 59) = 0, (51, 60) = 0, (51, 61) = 0, (52, 1) = 0, (52, 2) = 0, (52, 3) = 0, (52, 4) = 0, (52, 5) = 0, (52, 6) = 0, (52, 7) = 0, (52, 8) = 0, (52, 9) = 0, (52, 10) = 0, (52, 11) = 0, (52, 12) = 0, (52, 13) = 0, (52, 14) = 0, (52, 15) = 0, (52, 16) = 0, (52, 17) = 0, (52, 18) = 0, (52, 19) = 0, (52, 20) = 0, (52, 21) = 0, (52, 22) = 0, (52, 23) = 0, (52, 24) = 0, (52, 25) = 0, (52, 26) = 0, (52, 27) = 0, (52, 28) = 0, (52, 29) = 0, (52, 30) = 0, (52, 31) = 0, (52, 32) = 0, (52, 33) = 0, (52, 34) = 0, (52, 35) = 0, (52, 36) = 0, (52, 37) = 0, (52, 38) = 0, (52, 39) = 0, (52, 40) = 0, (52, 41) = 0, (52, 42) = 0, (52, 43) = 0, (52, 44) = 0, (52, 45) = 0, (52, 46) = 0, (52, 47) = 0, (52, 48) = 0, (52, 49) = 0, (52, 50) = 0, (52, 51) = 0, (52, 52) = -205379/216, (52, 53) = 205379/72, (52, 54) = -205379/72, (52, 55) = 205379/216, (52, 56) = 0, (52, 57) = 0, (52, 58) = 0, (52, 59) = 0, (52, 60) = 0, (52, 61) = 0, (53, 1) = 0, (53, 2) = 0, (53, 3) = 0, (53, 4) = 0, (53, 5) = 0, (53, 6) = 0, (53, 7) = 0, (53, 8) = 0, (53, 9) = 0, (53, 10) = 0, (53, 11) = 0, (53, 12) = 0, (53, 13) = 0, (53, 14) = 0, (53, 15) = 0, (53, 16) = 0, (53, 17) = 0, (53, 18) = 0, (53, 19) = 0, (53, 20) = 0, (53, 21) = 0, (53, 22) = 0, (53, 23) = 0, (53, 24) = 0, (53, 25) = 0, (53, 26) = 0, (53, 27) = 0, (53, 28) = 0, (53, 29) = 0, (53, 30) = 0, (53, 31) = 0, (53, 32) = 0, (53, 33) = 0, (53, 34) = 0, (53, 35) = 0, (53, 36) = 0, (53, 37) = 0, (53, 38) = 0, (53, 39) = 0, (53, 40) = 0, (53, 41) = 0, (53, 42) = 0, (53, 43) = 0, (53, 44) = 0, (53, 45) = 0, (53, 46) = 0, (53, 47) = 0, (53, 48) = 0, (53, 49) = 0, (53, 50) = 0, (53, 51) = 0, (53, 52) = 0, (53, 53) = -205379/216, (53, 54) = 205379/72, (53, 55) = -205379/72, (53, 56) = 205379/216, (53, 57) = 0, (53, 58) = 0, (53, 59) = 0, (53, 60) = 0, (53, 61) = 0, (54, 1) = 0, (54, 2) = 0, (54, 3) = 0, (54, 4) = 0, (54, 5) = 0, (54, 6) = 0, (54, 7) = 0, (54, 8) = 0, (54, 9) = 0, (54, 10) = 0, (54, 11) = 0, (54, 12) = 0, (54, 13) = 0, (54, 14) = 0, (54, 15) = 0, (54, 16) = 0, (54, 17) = 0, (54, 18) = 0, (54, 19) = 0, (54, 20) = 0, (54, 21) = 0, (54, 22) = 0, (54, 23) = 0, (54, 24) = 0, (54, 25) = 0, (54, 26) = 0, (54, 27) = 0, (54, 28) = 0, (54, 29) = 0, (54, 30) = 0, (54, 31) = 0, (54, 32) = 0, (54, 33) = 0, (54, 34) = 0, (54, 35) = 0, (54, 36) = 0, (54, 37) = 0, (54, 38) = 0, (54, 39) = 0, (54, 40) = 0, (54, 41) = 0, (54, 42) = 0, (54, 43) = 0, (54, 44) = 0, (54, 45) = 0, (54, 46) = 0, (54, 47) = 0, (54, 48) = 0, (54, 49) = 0, (54, 50) = 0, (54, 51) = 0, (54, 52) = 0, (54, 53) = 0, (54, 54) = -205379/216, (54, 55) = 205379/72, (54, 56) = -205379/72, (54, 57) = 205379/216, (54, 58) = 0, (54, 59) = 0, (54, 60) = 0, (54, 61) = 0, (55, 1) = 0, (55, 2) = 0, (55, 3) = 0, (55, 4) = 0, (55, 5) = 0, (55, 6) = 0, (55, 7) = 0, (55, 8) = 0, (55, 9) = 0, (55, 10) = 0, (55, 11) = 0, (55, 12) = 0, (55, 13) = 0, (55, 14) = 0, (55, 15) = 0, (55, 16) = 0, (55, 17) = 0, (55, 18) = 0, (55, 19) = 0, (55, 20) = 0, (55, 21) = 0, (55, 22) = 0, (55, 23) = 0, (55, 24) = 0, (55, 25) = 0, (55, 26) = 0, (55, 27) = 0, (55, 28) = 0, (55, 29) = 0, (55, 30) = 0, (55, 31) = 0, (55, 32) = 0, (55, 33) = 0, (55, 34) = 0, (55, 35) = 0, (55, 36) = 0, (55, 37) = 0, (55, 38) = 0, (55, 39) = 0, (55, 40) = 0, (55, 41) = 0, (55, 42) = 0, (55, 43) = 0, (55, 44) = 0, (55, 45) = 0, (55, 46) = 0, (55, 47) = 0, (55, 48) = 0, (55, 49) = 0, (55, 50) = 0, (55, 51) = 0, (55, 52) = 0, (55, 53) = 0, (55, 54) = 0, (55, 55) = -205379/216, (55, 56) = 205379/72, (55, 57) = -205379/72, (55, 58) = 205379/216, (55, 59) = 0, (55, 60) = 0, (55, 61) = 0, (56, 1) = 0, (56, 2) = 0, (56, 3) = 0, (56, 4) = 0, (56, 5) = 0, (56, 6) = 0, (56, 7) = 0, (56, 8) = 0, (56, 9) = 0, (56, 10) = 0, (56, 11) = 0, (56, 12) = 0, (56, 13) = 0, (56, 14) = 0, (56, 15) = 0, (56, 16) = 0, (56, 17) = 0, (56, 18) = 0, (56, 19) = 0, (56, 20) = 0, (56, 21) = 0, (56, 22) = 0, (56, 23) = 0, (56, 24) = 0, (56, 25) = 0, (56, 26) = 0, (56, 27) = 0, (56, 28) = 0, (56, 29) = 0, (56, 30) = 0, (56, 31) = 0, (56, 32) = 0, (56, 33) = 0, (56, 34) = 0, (56, 35) = 0, (56, 36) = 0, (56, 37) = 0, (56, 38) = 0, (56, 39) = 0, (56, 40) = 0, (56, 41) = 0, (56, 42) = 0, (56, 43) = 0, (56, 44) = 0, (56, 45) = 0, (56, 46) = 0, (56, 47) = 0, (56, 48) = 0, (56, 49) = 0, (56, 50) = 0, (56, 51) = 0, (56, 52) = 0, (56, 53) = 0, (56, 54) = 0, (56, 55) = 0, (56, 56) = -205379/216, (56, 57) = 205379/72, (56, 58) = -205379/72, (56, 59) = 205379/216, (56, 60) = 0, (56, 61) = 0, (57, 1) = 0, (57, 2) = 0, (57, 3) = 0, (57, 4) = 0, (57, 5) = 0, (57, 6) = 0, (57, 7) = 0, (57, 8) = 0, (57, 9) = 0, (57, 10) = 0, (57, 11) = 0, (57, 12) = 0, (57, 13) = 0, (57, 14) = 0, (57, 15) = 0, (57, 16) = 0, (57, 17) = 0, (57, 18) = 0, (57, 19) = 0, (57, 20) = 0, (57, 21) = 0, (57, 22) = 0, (57, 23) = 0, (57, 24) = 0, (57, 25) = 0, (57, 26) = 0, (57, 27) = 0, (57, 28) = 0, (57, 29) = 0, (57, 30) = 0, (57, 31) = 0, (57, 32) = 0, (57, 33) = 0, (57, 34) = 0, (57, 35) = 0, (57, 36) = 0, (57, 37) = 0, (57, 38) = 0, (57, 39) = 0, (57, 40) = 0, (57, 41) = 0, (57, 42) = 0, (57, 43) = 0, (57, 44) = 0, (57, 45) = 0, (57, 46) = 0, (57, 47) = 0, (57, 48) = 0, (57, 49) = 0, (57, 50) = 0, (57, 51) = 0, (57, 52) = 0, (57, 53) = 0, (57, 54) = 0, (57, 55) = 0, (57, 56) = 0, (57, 57) = -205379/216, (57, 58) = 205379/72, (57, 59) = -205379/72, (57, 60) = 205379/216, (57, 61) = 0, (58, 1) = 0, (58, 2) = 0, (58, 3) = 0, (58, 4) = 0, (58, 5) = 0, (58, 6) = 0, (58, 7) = 0, (58, 8) = 0, (58, 9) = 0, (58, 10) = 0, (58, 11) = 0, (58, 12) = 0, (58, 13) = 0, (58, 14) = 0, (58, 15) = 0, (58, 16) = 0, (58, 17) = 0, (58, 18) = 0, (58, 19) = 0, (58, 20) = 0, (58, 21) = 0, (58, 22) = 0, (58, 23) = 0, (58, 24) = 0, (58, 25) = 0, (58, 26) = 0, (58, 27) = 0, (58, 28) = 0, (58, 29) = 0, (58, 30) = 0, (58, 31) = 0, (58, 32) = 0, (58, 33) = 0, (58, 34) = 0, (58, 35) = 0, (58, 36) = 0, (58, 37) = 0, (58, 38) = 0, (58, 39) = 0, (58, 40) = 0, (58, 41) = 0, (58, 42) = 0, (58, 43) = 0, (58, 44) = 0, (58, 45) = 0, (58, 46) = 0, (58, 47) = 0, (58, 48) = 0, (58, 49) = 0, (58, 50) = 0, (58, 51) = 0, (58, 52) = 0, (58, 53) = 0, (58, 54) = 0, (58, 55) = 0, (58, 56) = 0, (58, 57) = 0, (58, 58) = -205379/216, (58, 59) = 205379/72, (58, 60) = -205379/72, (58, 61) = 205379/216, (59, 1) = 0, (59, 2) = -59/6, (59, 3) = 59/6, (59, 4) = 0, (59, 5) = 0, (59, 6) = 0, (59, 7) = 0, (59, 8) = 0, (59, 9) = 0, (59, 10) = 0, (59, 11) = 0, (59, 12) = 0, (59, 13) = 0, (59, 14) = 0, (59, 15) = 0, (59, 16) = 0, (59, 17) = 0, (59, 18) = 0, (59, 19) = 0, (59, 20) = 0, (59, 21) = 0, (59, 22) = 0, (59, 23) = 0, (59, 24) = 0, (59, 25) = 0, (59, 26) = 0, (59, 27) = 0, (59, 28) = 0, (59, 29) = 0, (59, 30) = 0, (59, 31) = 0, (59, 32) = 0, (59, 33) = 0, (59, 34) = 0, (59, 35) = 0, (59, 36) = 0, (59, 37) = 0, (59, 38) = 0, (59, 39) = 0, (59, 40) = 0, (59, 41) = 0, (59, 42) = 0, (59, 43) = 0, (59, 44) = 0, (59, 45) = 0, (59, 46) = 0, (59, 47) = 0, (59, 48) = 0, (59, 49) = 0, (59, 50) = 0, (59, 51) = 0, (59, 52) = 0, (59, 53) = 0, (59, 54) = 0, (59, 55) = 0, (59, 56) = 0, (59, 57) = 0, (59, 58) = 0, (59, 59) = 0, (59, 60) = 0, (59, 61) = 0, (60, 1) = 0, (60, 2) = 3481/36, (60, 3) = -3481/18, (60, 4) = 3481/36, (60, 5) = 0, (60, 6) = 0, (60, 7) = 0, (60, 8) = 0, (60, 9) = 0, (60, 10) = 0, (60, 11) = 0, (60, 12) = 0, (60, 13) = 0, (60, 14) = 0, (60, 15) = 0, (60, 16) = 0, (60, 17) = 0, (60, 18) = 0, (60, 19) = 0, (60, 20) = 0, (60, 21) = 0, (60, 22) = 0, (60, 23) = 0, (60, 24) = 0, (60, 25) = 0, (60, 26) = 0, (60, 27) = 0, (60, 28) = 0, (60, 29) = 0, (60, 30) = 0, (60, 31) = 0, (60, 32) = 0, (60, 33) = 0, (60, 34) = 0, (60, 35) = 0, (60, 36) = 0, (60, 37) = 0, (60, 38) = 0, (60, 39) = 0, (60, 40) = 0, (60, 41) = 0, (60, 42) = 0, (60, 43) = 0, (60, 44) = 0, (60, 45) = 0, (60, 46) = 0, (60, 47) = 0, (60, 48) = 0, (60, 49) = 0, (60, 50) = 0, (60, 51) = 0, (60, 52) = 0, (60, 53) = 0, (60, 54) = 0, (60, 55) = 0, (60, 56) = 0, (60, 57) = 0, (60, 58) = 0, (60, 59) = 0, (60, 60) = 0, (60, 61) = 0, (61, 1) = 0, (61, 2) = 0, (61, 3) = 0, (61, 4) = 0, (61, 5) = 0, (61, 6) = 0, (61, 7) = 0, (61, 8) = 0, (61, 9) = 0, (61, 10) = 0, (61, 11) = 0, (61, 12) = 0, (61, 13) = 0, (61, 14) = 0, (61, 15) = 0, (61, 16) = 0, (61, 17) = 0, (61, 18) = 0, (61, 19) = 0, (61, 20) = 0, (61, 21) = 0, (61, 22) = 0, (61, 23) = 0, (61, 24) = 0, (61, 25) = 0, (61, 26) = 0, (61, 27) = 0, (61, 28) = 0, (61, 29) = 0, (61, 30) = 0, (61, 31) = 0, (61, 32) = 0, (61, 33) = 0, (61, 34) = 0, (61, 35) = 0, (61, 36) = 0, (61, 37) = 0, (61, 38) = 0, (61, 39) = 0, (61, 40) = 0, (61, 41) = 0, (61, 42) = 0, (61, 43) = 0, (61, 44) = 0, (61, 45) = 0, (61, 46) = 0, (61, 47) = 0, (61, 48) = 0, (61, 49) = 0, (61, 50) = 0, (61, 51) = 0, (61, 52) = 0, (61, 53) = 0, (61, 54) = 0, (61, 55) = 0, (61, 56) = 0, (61, 57) = 0, (61, 58) = 0, (61, 59) = 3481/36, (61, 60) = -3481/18, (61, 61) = 3481/36}), Vector(61, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 0, (20) = 0, (21) = 0, (22) = 0, (23) = 0, (24) = 0, (25) = 0, (26) = 0, (27) = 0, (28) = 0, (29) = 0, (30) = 0, (31) = 0, (32) = 0, (33) = 0, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 0, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 0, (51) = 0, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 1, (60) = 0, (61) = 2})

  

Error, (in LinearAlgebra:-LinearSolve) inconsistent system

  
> 

 


 

Download FDM1Prob.mw

I agree with Carl...

tomleslie 13876
July 15 2018
1 1

but if you are doing this as an educational exercise, then the attached code now excutes without error after I fixed numerous minor typos.

Note that I did not check the logic/algorithm/output - I just fixed typos which prevented executioon

RKF.mw

 

Should probably be a question...

tomleslie 13876
July 15 2018
1 0

rather than a 'Post'

I have just opened the ?CUDA help page as a worksheet, using

View -> Open Page As Worksheet

and run the complete page using !!!. Everything seems to work - see the attached. Rather obviously the upload function (big green up-arrow in toolbar) also seeem to be working correctly. In order to get any sensible help  you are going to have to be a bit more specific about your problem.

Just a thought: in the CUDA help page, it says (my emphasis)

The CUDA package allows Maple to use the graphics processing unit (GPU) of your NVIDIA(R) Compute Unified Device Architecture (CUDA)-enabled hardware to accelerate certain LinearAlgebra routines.

I do have an NVIDIA gpu, and as far as I know it is "CUDA-enabled"

Do you have an appropriate GPU?

CUDA Package

use CUDA(R) technology to accelerate certain LinearAlgebra routines

 

 

Calling Sequence

Introduction

List of CUDA Package Commands

Examples

 

 

 

Calling Sequence

 

CUDA[command]( arguments )

command( arguments )

Introduction

 
• 

The CUDA package allows Maple to use the graphics processing unit (GPU) of your NVIDIA(R) Compute Unified Device Architecture (CUDA)-enabled hardware to accelerate certain LinearAlgebra  routines.

• 

For more information about NVIDIA and CUDA technology, visit http://www.nvidia.com and http://www.nvidia.com/object/cuda_home.html.

• 

To use this package, you need NVIDIA CUDA-enabled hardware  and the most recent drivers for that hardware installed on your computer. For more information about supported hardware and a complete list of requirements, see the Supported Hardware for CUDA Acceleration  help page.

• 

For more information about the routines that are accelerated when CUDA technology is turned on, see the Routines Accelerated by the CUDA Package  help page.

List of CUDA Package Commands

 

 

ComputeLevel

Enable

HasDoubleSupport

IsEnabled

Properties

 

 

 

 

 

• 

The Enable  function turns CUDA acceleration on and off.

• 

The IsEnabled  function returns a value of true if CUDA acceleration is turned on and false otherwise.

• 

The ComputeLevel  function indicates the compute level of the CUDA-enabled devices available on your computer.

• 

The HasDoubleSupport  function checks whether the CUDA-enabled devices available on your computer support double precision computations.

• 

The Properties  function displays information about the CUDA-enabled devices available on your computer.

Examples

 
> 

n := 4000:

> 

M1 := LinearAlgebra:-RandomMatrix(n, n, datatype = float[4]):

> 

M2 := LinearAlgebra:-RandomMatrix(n, n, datatype = float[4]):

> 

CUDA:-IsEnabled();

false

(1)
> 

tNoCUDA := time[real](M1.M2);

1.984

(2)
> 

CUDA:-Enable( true );

false

(3)
> 

CUDA:-IsEnabled();

true

(4)
> 

tCUDA := time[real](M1.M2);

1.927

(5)
> 

evalf( tNoCUDA/tCUDA );

1.029579657

(6)
> 

CUDA:-Enable( false );

true

(7)
> 

CUDA:-IsEnabled();

false

(8)
> 

 

 

See Also

LinearAlgebra

 

 
 

 

 

Download CUDATest.mw

 

With a few amendments...

tomleslie 13876
July 14 2018
0 0

some, syntax and some to assist the dsolve(..,numeric) command, the attached now produces all the plots

ODE.mw

No solution for fsolve()...

tomleslie 13876
July 13 2018
1 2

The command

Q[h+1] := fsolve(eval(f[3], {R = R[h], S = S[h]}) = 0, Q = 2 .. infinity)

fails because there is no numerical solution for f[3] in the specified range. Since this command returns no solution, most subsequent commands then fail. For most of the cases I have tried, f[3] does have a solution around Q=1.5, so changing the above command to

Q[h+1] := fsolve(eval(f[3], {R = R[h], S = S[h]}) = 0, Q = 1 .. infinity)

means that your code will actually run - although I didnt' have the patience to wait for the potential 40k evaluations to see if subsequent stuff produced anything meaningful

An alternative...

tomleslie 13876
July 12 2018
0 2

even if I am not on the list of "approved" responders.

The attached performs two slight variations because I'm not exactly sure the precise output form which you want

> 

restart;
H1 := 3*y^4*a[1]^5*b[1]+6*y^4*a[1]^3*b[1]^3+3*y^4*a[1]*b[1]^5+6*x*y^3*a[1]^5+6*x*y^3*a[1]^4*b[1]+12*x*y^3*a[1]^3*b[1]^2+12*x*y^3*a[1]^2*b[1]^3+6*x*y^3*a[1]*b[1]^4+6*x*y^3*b[1]^5+6*y^3*a[1]^5*b[2]+6*y^3*a[1]^4*a[2]*b[1]+12*y^3*a[1]^3*b[1]^2*b[2]+12*y^3*a[1]^2*a[2]*b[1]^3+6*y^3*a[1]*b[1]^4*b[2]+6*y^3*a[2]*b[1]^5+18*x^2*y^2*a[1]^4+36*x^2*y^2*a[1]^2*b[1]^2+18*x^2*y^2*b[1]^4+18*x*y^2*a[1]^4*a[2]+18*x*y^2*a[1]^4*b[2]+36*x*y^2*a[1]^2*a[2]*b[1]^2+36*x*y^2*a[1]^2*b[1]^2*b[2]+18*x*y^2*a[2]*b[1]^4+18*x*y^2*b[1]^4*b[2]+18*y^2*a[1]^4*a[2]*b[2]+36*y^2*a[1]^2*a[2]*b[1]^2*b[2]+18*y^2*a[2]*b[1]^4*b[2]-5*delta*y^2*a[1]^4-8*delta*y^2*a[1]^3*b[1]-10*delta*y^2*a[1]^2*b[1]^2-8*delta*y^2*a[1]*b[1]^3-5*delta*y^2*b[1]^4+12*x^3*y*a[1]^3+12*x^3*y*a[1]^2*b[1]+12*x^3*y*a[1]*b[1]^2+12*x^3*y*b[1]^3+36*x^2*y*a[1]^3*a[2]+36*x^2*y*a[1]^2*b[1]*b[2]+36*x^2*y*a[1]*a[2]*b[1]^2+36*x^2*y*b[1]^3*b[2]+18*x*y*a[1]^3*a[2]^2+36*x*y*a[1]^3*a[2]*b[2]-18*x*y*a[1]^3*b[2]^2-18*x*y*a[1]^2*a[2]^2*b[1]+36*x*y*a[1]^2*a[2]*b[1]*b[2]+18*x*y*a[1]^2*b[1]*b[2]^2+18*x*y*a[1]*a[2]^2*b[1]^2+36*x*y*a[1]*a[2]*b[1]^2*b[2]-18*x*y*a[1]*b[1]^2*b[2]^2-18*x*y*a[2]^2*b[1]^3+36*x*y*a[2]*b[1]^3*b[2]+18*x*y*b[1]^3*b[2]^2+18*y*a[1]^3*a[2]^2*b[2]-6*y*a[1]^3*b[2]^3-6*y*a[1]^2*a[2]^3*b[1]+18*y*a[1]^2*a[2]*b[1]*b[2]^2+18*y*a[1]*a[2]^2*b[1]^2*b[2]-6*y*a[1]*b[1]^2*b[2]^3-6*y*a[2]^3*b[1]^3+18*y*a[2]*b[1]^3*b[2]^2-16*delta*x*y*a[1]^3-20*delta*x*y*a[1]^2*b[1]-20*delta*x*y*a[1]*b[1]^2-16*delta*x*y*b[1]^3-10*delta*y*a[1]^3*a[2]-6*delta*y*a[1]^3*b[2]-10*delta*y*a[1]^2*a[2]*b[1]-10*delta*y*a[1]^2*b[1]*b[2]-10*delta*y*a[1]*a[2]*b[1]^2-10*delta*y*a[1]*b[1]^2*b[2]-6*delta*y*a[2]*b[1]^3-10*delta*y*b[1]^3*b[2]+12*x^4*a[1]*b[1]+12*x^3*a[1]^2*a[2]-12*x^3*a[1]^2*b[2]+24*x^3*a[1]*a[2]*b[1]+24*x^3*a[1]*b[1]*b[2]-12*x^3*a[2]*b[1]^2+12*x^3*b[1]^2*b[2]+18*x^2*a[1]^2*a[2]^2-18*x^2*a[1]^2*b[2]^2+72*x^2*a[1]*a[2]*b[1]*b[2]-18*x^2*a[2]^2*b[1]^2+18*x^2*b[1]^2*b[2]^2+6*x*a[1]^2*a[2]^3+18*x*a[1]^2*a[2]^2*b[2]-18*x*a[1]^2*a[2]*b[2]^2-6*x*a[1]^2*b[2]^3-12*x*a[1]*a[2]^3*b[1]+36*x*a[1]*a[2]^2*b[1]*b[2]+36*x*a[1]*a[2]*b[1]*b[2]^2-12*x*a[1]*b[1]*b[2]^3-6*x*a[2]^3*b[1]^2-18*x*a[2]^2*b[1]^2*b[2]+18*x*a[2]*b[1]^2*b[2]^2+6*x*b[1]^2*b[2]^3+6*a[1]^2*a[2]^3*b[2]-6*a[1]^2*a[2]*b[2]^3-3*a[1]*a[2]^4*b[1]+18*a[1]*a[2]^2*b[1]*b[2]^2-3*a[1]*b[1]*b[2]^4-6*a[2]^3*b[1]^2*b[2]+6*a[2]*b[1]^2*b[2]^3-10*delta*x^2*a[1]^2-16*delta*x^2*a[1]*b[1]-10*delta*x^2*b[1]^2-16*delta*x*a[1]^2*a[2]-4*delta*x*a[1]^2*b[2]-16*delta*x*a[1]*a[2]*b[1]-16*delta*x*a[1]*b[1]*b[2]-4*delta*x*a[2]*b[1]^2-16*delta*x*b[1]^2*b[2]-5*delta*a[1]^2*a[2]^2-6*delta*a[1]^2*a[2]*b[2]+delta*a[1]^2*b[2]^2-2*delta*a[1]*a[2]^2*b[1]-12*delta*a[1]*a[2]*b[1]*b[2]-2*delta*a[1]*b[1]*b[2]^2+delta*a[2]^2*b[1]^2-6*delta*a[2]*b[1]^2*b[2]-5*delta*b[1]^2*b[2]^2+delta^2*a[1]^2+delta^2*a[1]*b[1]+delta^2*b[1]^2+16*y^2*a[1]^2+48*y^2*a[1]*b[1]+16*y^2*b[1]^2+80*x*y*a[1]+80*x*y*b[1]+32*y*a[1]*a[2]+48*y*a[1]*b[2]+48*y*a[2]*b[1]+32*y*b[1]*b[2]+80*x^2+80*x*a[2]+80*x*b[2]+16*a[2]^2+48*a[2]*b[2]+16*b[2]^2-8*delta:

#
# Define a function which will select the complete term
# containing x^n*y^m from H1
#
  f:=(n,m)->select( j->patmatch(j, a::anything*x^n*y^m), H1):
#
# Define a function which will select the coefficient
# of the term x^n*y^m from H1
#
  g:= (n,m)-> coeff
              ( collect
                ( algsubs
                  ( x^n*y^m=z,
                    select
                    ( j->patmatch(j, a::anything*x^n*y^m),
                      H1
                    )
                  ),
                  z
                ),
                z
              ):
#
# Example: get the complete term involving x^1*y^1,
# or its coefficient
#
  f(1,1);
  g(1,1);
#
# Example: get the complete term involving x^1*y^3,
# or its coefficient
#
  f(1,3);
  g(1,3);
#
# Example get the complete term involving x^3*y^1,
# or its coefficient
#
  f(3,1);
  g(3,1);

18*x*y*a[1]^3*a[2]^2+36*x*y*a[1]^3*a[2]*b[2]-18*x*y*a[1]^3*b[2]^2-18*x*y*a[1]^2*a[2]^2*b[1]+36*x*y*a[1]^2*a[2]*b[1]*b[2]+18*x*y*a[1]^2*b[1]*b[2]^2+18*x*y*a[1]*a[2]^2*b[1]^2+36*x*y*a[1]*a[2]*b[1]^2*b[2]-18*x*y*a[1]*b[1]^2*b[2]^2-18*x*y*a[2]^2*b[1]^3+36*x*y*a[2]*b[1]^3*b[2]+18*x*y*b[1]^3*b[2]^2-16*delta*x*y*a[1]^3-20*delta*x*y*a[1]^2*b[1]-20*delta*x*y*a[1]*b[1]^2-16*delta*x*y*b[1]^3+80*x*y*a[1]+80*x*y*b[1]

  

18*a[1]^3*a[2]^2+36*a[1]^3*a[2]*b[2]-18*a[1]^3*b[2]^2-18*a[1]^2*a[2]^2*b[1]+36*a[1]^2*a[2]*b[1]*b[2]+18*a[1]^2*b[1]*b[2]^2+18*a[1]*a[2]^2*b[1]^2+36*a[1]*a[2]*b[1]^2*b[2]-18*a[1]*b[1]^2*b[2]^2-18*a[2]^2*b[1]^3+36*a[2]*b[1]^3*b[2]+18*b[1]^3*b[2]^2-16*delta*a[1]^3-20*delta*a[1]^2*b[1]-20*delta*a[1]*b[1]^2-16*delta*b[1]^3+80*a[1]+80*b[1]

  

6*x*y^3*a[1]^5+6*x*y^3*a[1]^4*b[1]+12*x*y^3*a[1]^3*b[1]^2+12*x*y^3*a[1]^2*b[1]^3+6*x*y^3*a[1]*b[1]^4+6*x*y^3*b[1]^5

  

6*a[1]^5+6*a[1]^4*b[1]+12*a[1]^3*b[1]^2+12*a[1]^2*b[1]^3+6*a[1]*b[1]^4+6*b[1]^5

  

12*x^3*y*a[1]^3+12*x^3*y*a[1]^2*b[1]+12*x^3*y*a[1]*b[1]^2+12*x^3*y*b[1]^3

  

12*a[1]^3+12*a[1]^2*b[1]+12*a[1]*b[1]^2+12*b[1]^3

 (1)
> 

 

Download coeffs.mw

Obviously you can stick f() or g() in a double loop to get all possibilities

Something like...

tomleslie 13876
July 12 2018
0 1

the attached, perhaps - although I'm not sure what teh purpose of this calculation is!!!

> 

with(StringTools):
word := "ARITHMETIC,ALGORITHM,ASYMPTOTE,AVERAGE,CARTESIAN,CALCULUS,COEFFICIENT,COORDINATE,NUMERATOR,
DENOMINATOR,DIFFERENTIATE,DERIVATIVE,DIAMETER,DYNAMICS,EXTRAPOLATION,FACTORIALS,GEOMETRIC,
HYPOTENUSE,INTEGRATION,IRRATIONAL,INVERSE,ITERATION,POLYNOMIAL,COMBINATIONS,PERMUTATIONS,POLYGON"

"ARITHMETIC,ALGORITHM,ASYMPTOTE,AVERAGE,CARTESIAN,CALCULUS,COEFFICIENT,COORDINATE,NUMERATOR, DENOMINATOR,DIFFERENTIATE,DERIVATIVE,DIAMETER,DYNAMICS,EXTRAPOLATION,FACTORIALS,GEOMETRIC, HYPOTENUSE,INTEGRATION,IRRATIONAL,INVERSE,ITERATION,POLYNOMIAL,COMBINATIONS,PERMUTATIONS,POLYGON"

 (1)
> 

#
# Get the number of occurences of "A"-"Z", as
# a list of sublists, where each sublist is
# [char, numberOfOccurrences]
#
  ans:= [ seq( [ j,
                 CountCharacterOccurrences( word, j )
               ],
               j in seq( Char(j),
                         j=65..90
                       )
             )
       ];

[["A", 26], ["B", 1], ["C", 11], ["D", 6], ["E", 27], ["F", 5], ["G", 5], ["H", 3], ["I", 28], ["J", 0], ["K", 0], ["L", 9], ["M", 11], ["N", 20], ["O", 23], ["P", 6], ["Q", 0], ["R", 20], ["S", 9], ["T", 27], ["U", 5], ["V", 4], ["W", 0], ["X", 1], ["Y", 5], ["Z", 0]]

 (2)
> 

#
# Compute the product of the factorials of the
# numberOfOccurrences in the above list. Divide
# this into the factorial of the length of the
# original word - I subtracted out the number
# of comma (ie ',') characters in the original
# word
#
  (Length(word)-CountCharacterOccurrences( word, "," ))!/mul( j[2]!, j in ans);;

1813659818308267130892482754085174318878156620794774911148024019808948009686481649990274344113858540573562217501547767535138849277306186526788556137157269147519958749841609345698169625634616465601684616612991156086292884361281129792415137716965243581998943024878718205244211200000000000000

 (3)
> 

 

Download stringCounts.mw

Depending precisely...

tomleslie 13876
July 12 2018
2 7

@ianmccr 

on what you are trying to achieve, one of the two options in the attached ought to be applicable.

I can anticipate an issue when you want to store procedures which accept arguments in MetricTab; This wouldn't be difficult to handle, but I haven't attempted to address it

> 

restart;
> 

Glyph2 := module()
    export    AddSpace, GetSpace, RemoveSpace,DoSpace;
    local     MetricTab;

    MetricTab := table():

    AddSpace := proc( theName::symbol, implementation )
        local    old_imp;
        old_imp := NULL;
        if assigned( MetricTab[ theName ] ) then
            WARNING( "replacing existing extension `%1'", theName );
            old_imp := eval( MetricTab[ theName ] )
        end if;
        MetricTab[ theName ] := eval( implementation, 1 );
        eval( old_imp, 1 )
    end proc;

    RemoveSpace := proc( theName::symbol )
        if assigned( MetricTab[ theName ] ) then
            MetricTab[ theName ] := evaln( MetricTab[ theName ] )
        end if;
        NULL
    end proc;

    GetSpace := proc( theName::symbol )
        if assigned( MetricTab[ theName ] ) then
            eval( MetricTab[ theName ], 1 )
        else
            NULL
        end if
    end proc;
    AddSpace('default','proc() print("Metric is default")end proc');
    GetSpace( 'default');   
end module:
> 

#
# Return the procedure
#
  Glyph2:-GetSpace('default');
#
# Return the procedure and evaluate it
# Note the addition of () at the end
#
  Glyph2:-GetSpace('default')();

proc () print("Metric is default") end proc

  

"Metric is default"

 (1)
> 

  restart;
#
# Remove a few unnecessary eval() commands
# and some uneval quotes from the module
# Also remove the Addspace() and GetSpace()
# commands from within the module - not sure
# if they are there for test purposes, or not
#
  Glyph2 := module()
            export    AddSpace, GetSpace, RemoveSpace,DoSpace;
            local     MetricTab;

            MetricTab := table():

            AddSpace := proc( theName::symbol, implementation )
                              local    old_imp;
                              old_imp := NULL;
                              if   assigned( MetricTab[ theName ] )
                              then WARNING( "replacing existing extension %1", theName );
                                   old_imp := eval( MetricTab[ theName ] )
                              end if;
                              MetricTab[ theName ] := implementation;
                              old_imp()
                        end proc;

            GetSpace := proc( theName::symbol )
                              if   assigned( MetricTab[ theName ] )
                              then MetricTab[ theName ]()
                              else NULL
                              end if
                        end proc;  
  end module:
> 

#
# Add a procedure to MetricTab - produces
# no output
#
  Glyph2:-AddSpace( default , proc() print("Metric is default") end proc);
#
# Return the results of executing the above
# procedure
#
  Glyph2:-GetSpace( default );
#
# Add another procedure with the same name -
# should overwrite the previous one, but the
# Addspace() command should now execute the
# procedure being overwritten (as well as
# printing the warning message)
#
  Glyph2:-AddSpace( default , proc() print("foo bar") end proc);
#
# And GetSpace() now returns the results of
# executing the new procedure
#
  Glyph2:-GetSpace( default );

"Metric is default"

  

Warning, replacing existing extension default

  

"Metric is default"

  

"foo bar"

 (2)
> 

 

Download modProb.mw

Not exactly sure...

tomleslie 13876
July 11 2018
1 0

how you are entering the data in the table, or subsequently calling it, but the following

restart;
T1:=table([(p1)=proc() print("Metric is default") end proc, (p2)=3]):
T1[p1]();

produces

"Metric is default"

which is what I would expect

Like the following...

tomleslie 13876
July 11 2018
1 0

First generate the solution in an appropriate form, the select the imaginary parts, as in

restart;
y := x^2+x+7;
A := solve(y, x);
Im~([A])
 

You are plotting numerical noise...

tomleslie 13876
July 11 2018
0 1

When you perform an explicit plot of the expression

(1/2)*(exp(x)+exp(-x))*(1/2)*(exp(I*y)+exp(-I*y)),

then for given ranges of x- and y-values, you are plotting the points at which the expression is zero. The second term, ie (1/2)*(exp(I*y)+exp(-I*y)) evaluates to cos(y), which will be zero when y=Pi/2, which is why the y-axis on your graphs is 1.57079.....more or less. Any deviation from Pi/2 is numerical noise.

If you really want to increase/decrease the amount of numerical noise which you are plotting, then try

plots:-implicitplot( (1/2)*(exp(x)+exp(-x))*(1/2)*(exp(I*y)+exp(-I*y)), x=0..1000, y=1.5..1.6, numpoints=100000);

and vary the value of numpoints - say 1000, 10000, 100000.

If you want a different set of numerical noise, then you can also 'force' the answer y=3*Pi/2, using

plots:-implicitplot( (1/2)*(exp(x)+exp(-x))*(1/2)*(exp(I*y)+exp(-I*y)), x=0..1000, y=4.7..4.8, numpoints=100000);

(and again vary the amount of numerical noise you want by varying numpoints)

Did you mean...

tomleslie 13876
July 08 2018
0 3

the attached - where I fixed several mior syntax issues

plotProb.mw

I would have displayed the contents of ths worksheet here, rather than just post the link, but someone seems to have broken the maplenet/convert utiility (again!)

Use copy(..., deep)...

tomleslie 13876
July 07 2018
2 2

As its help page states (my emphasis)

The purpose of the copy function is to create a duplicate table, rtable, or record which can be altered without changing the original table, rtable, or record.

so

restart;
c:=Record('a','b'):
c:-a:=0:
c:-b:=-1:
#
# Perform deep copy
#
c1:=copy(c, deep);
#
# Change value of 'a' in c1
#
  c1:-a:=23;
#
# Check value of 'a' in 'c' and 'c1'
#
  c:-a;
  c1:-a;

will work

 

May be a version issue...

tomleslie 13876
July 06 2018
0 0

I'm running 64-bit Maple 2018.1, interfaced to Microsoft Office Professional 2010/Excel version 14.0.7208.5000 (64-bit), and your example *works* for me with no errors. See the screen grab below

The actual Excel File which I used is located here testMaple.xlsx

I suggest that you try it.

Since my Maple version works OK with my Excel version, and we share the same Maple verison, I can only conclude that any discrepancy is cause by the difference in our Excel versions.

Regrettably, whilst I can try all Maple versions for  the last 10 years, I only run one Excel version

Wouldn't like to bet...

tomleslie 13876
July 06 2018
1 2

that this will work all of the time, but consider something like

expr1:=sqrt(x^2+y^2)/x;
sqrt(collect(expr1^2,x));

 

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