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Text File  |  2002-05-15  |  1.1 KB  |  30 lines
  1. "File SOLVE.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
  2.  
  3. NEWTON(u,x,x0,n):=ITERATES(x-u/DIF(u,x),x,x0,n)
  4.  
  5. NEWTON_AUX(a,x,x0,n):=ITERATES(xk-ELEMENT(ROW_REDUCE(LIM(a,x,xk))`,DIMENSION(a~
  6. )+1),xk,x0,n)
  7.  
  8. NEWTONS(u,x,x0,n):=NEWTON_AUX(APPEND(GRAD(u,x),[u])`,x,x0,n)
  9.  
  10. FIXED_POINT(g,x,x0,n):=ITERATES(LIM(g,x,xk),xk,x0,n)
  11.  
  12. "Following definitions contributed by Wolfram Koepf:"
  13.  
  14. TAYLOR_SOLVE_AUX2(x,y,x0,y0,n,aux):=y0+SUM(LIM(ELEMENT(aux,k_),[y,x],[y0,x0])/~
  15. k_!*(x-x0)^k_,k_,1,n)
  16.  
  17. TAYLOR_SOLVE_AUX(x,y,x0,y0,n,v):=TAYLOR_SOLVE_AUX2(x,y,x0,y0,n,ITERATES(DIF(g_~
  18. ,y)*v+DIF(g_,x),g_,v,n-1))
  19.  
  20. TAYLOR_SOLVE(u,x,y,x0,y0,n):=TAYLOR_SOLVE_AUX(x,y,x0,y0,n,-DIF(u,x)/DIF(u,y))
  21.  
  22. "Following definitions contributed by Jim FitzSimons:"
  23.  
  24. LAGRANGE_EXPANSION(u,x,y,x0,y0,n):=x0+SUM((y-y0)^k_/k_!*LIM(DIF(((x-x0)/(u-y0)~
  25. )^k_,x,k_-1),x,x0),k_,1,n)
  26.  
  27. TAYLOR_INVERSE(u,x,y,x0,n):=IF(LIM(DIF(u,x),x,x0)=0,"Taylor expansion of inver~
  28. se does not exist",LAGRANGE_EXPANSION(TAYLOR(u,x,x0,n),x,y,x0,LIM(u,x,x0),n),L~
  29. AGRANGE_EXPANSION(TAYLOR(u,x,x0,n),x,y,x0,LIM(u,x,x0),n))
  30.