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Member "pari-2.13.1/src/test/in/ser" (14 Jan 2021, 2511 Bytes) of package /linux/misc/pari-2.13.1.tar.gz:


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    1 default(realprecision,38);
    2 s=x+x^2+O(x^5)
    3 f=[atan,asin,acos,cosh,sinh,tanh,cotanh,acosh,asinh,atanh];
    4 {
    5 for (i=1,#f,
    6   print(f[i](s));
    7   print(f[i](O(x^5)));
    8   print(f[i]([Pol(1)]));
    9 )
   10 }
   11 O(x^-2)
   12 O(1/x^2)
   13 trace(I*x+1+O(x^2))
   14 norm(I*x+1+O(x^2))
   15 a=Ser(vector(200,i,i));
   16 a^2 == a*(a+1) - a \\ test RgX_mullow, RgX_sqrlow
   17 3+O(1)
   18 serreverse(x/2+O(x^2))
   19 serreverse(tan(x)/2)
   20 
   21 iferr(sqrt(x+1/y),E,E)
   22 
   23 \\ #2063
   24 ((y^-3+O(y))*x+1)/x
   25 
   26 s = 1/x + x + 2*x^2 + O(x^3);
   27 serchop(s)
   28 serchop(s, 2)
   29 serchop(s, 100)
   30 s = Mod(0,3) + x + O(x^2)
   31 serchop(s)
   32 serchop(Mod(0,3)+O(x^2))
   33 serchop(Mod(0,3)*x+O(x^2))
   34 
   35 Ser(Qfb(1,2,3))
   36 Ser(Qfb(1,2,3),, 5.5)
   37 Ser(Qfb(1,2,-5))
   38 Ser(Qfb(1,2,-5),y,2)
   39 Ser([1,2,3], y, 5)
   40 Ser([1,2,3]~, y, 5)
   41 Ser([],,3)
   42 Ser(Vecsmall([1,2,3]), y, 5)
   43 Ser(x+O(x^2),,3)
   44 Ser(O(x^2),,3)
   45 Ser(x+x^2+x^3+O(x^4),,2)
   46 Ser(x^2+x^3,x,0)
   47 Ser(1+x,x,0)
   48 Ser(1/(x+1),x,0)
   49 Ser(1/x,x,0)
   50 Ser(1/y,x,0)
   51 
   52 Ser(x+y+O(x^2),x)
   53 Ser(x+y+O(x^2),y)
   54 s = Ser(Mod(0,7))
   55 Ser(Mod(1,7)*(x^4+x^2), x,3)
   56 s+O(x^16)
   57 s+Mod(1,7)
   58 s+Mod(1,7)*x
   59 s/x
   60 s'
   61 deriv(s,y)
   62 trace(s)
   63 round(s)
   64 round(s,&e)
   65 lift(s)
   66 lift(s,x)
   67 liftint(s)
   68 O(x^2)*0
   69 deriv(Mod(2,4)*x^2+O(x^3))
   70 x^3*(1+O(y^2))
   71 Mod(1,3)*x^3*(1+O(y^2))
   72 O(x)/2
   73 s = O(3^2)+O(x);
   74 s/3
   75 s/2
   76 s*3
   77 (1+O(x))^2
   78 1/(x+0.)+O(x^2)
   79 [1==O(x), 1==O(x^0), 1==O(x^-1)]
   80 [-1==O(x), -1==O(x^0), -1==O(x^-1)]
   81 [2==O(x), 2==O(x^0), 2==O(x^-1)]
   82 
   83 a=Mod(3,9) + O(x^2); b=Mod(3,9) + O(x^2); a*b
   84 
   85 a=1./x+O(1);a-a
   86 a=1/x+O(1);a-a
   87 a=Mod(1,2)/x+O(1);a-a
   88 
   89 Mod(0,5) * O(x^1)
   90 Mod(1,5) * O(x^0)
   91 O(x^0) / Mod(1,5)
   92 
   93 subst(1+O(x),x,y)
   94 subst(1+x+O(x^2),x,y^2)
   95 O(1)==O(x)
   96 O(1)==x
   97 O(x)==1
   98 
   99 \\ #2188
  100 S = x+O(x^2);T = O(y) + x + O(x^2); T==S
  101 S = x+O(x^2);T = O(y) + x + x^2 + O(x^3); T==S
  102 S = x+O(x^2);T = O(y) + O(x); T==S
  103 S = x+x^2+ O(x^3);T = O(y) + x + O(x^2); T==S
  104 
  105 exp(x+O(x^200))*exp(-x+O(x^200))
  106 exp(x+O(x^200))^2==exp(2*x+O(x^200))
  107 
  108 subst(1+x^3+O(x^6),x,x+O(x^4))
  109 subst(1+x^2+O(x^6),x,x+O(x^3))
  110 subst(1+x^3+x^4+O(x^6),x,x+x^2+O(x^3))
  111 
  112 subst(x^2+O(x^3),x,0*x)
  113 subst(x^2+O(x^3),x,Mod(0,3)*x)
  114 subst(x^2+O(x^3),x,O(3)*x)
  115 subst(1+x+O(x^2),x,0*x)
  116 subst(1+x+O(x^2),x,Mod(0,3)*x)
  117 subst(1+x+O(x^2),x,O(3)*x)
  118 subst(1+x^2+O(x^3),x,z)
  119 subst(1+x^2+y^2+O(x^3),x,z)
  120 
  121 laurentseries(x->sin(x)/x^2, 3)
  122 laurentseries(x->sin(x)/x^2, 3, t)
  123 laurentseries(x->(cos(x)-1)/x)
  124 
  125 \\ Errors. Keep at end of file
  126 subst(x^-1+O(x),x,Mod(0,3))
  127 subst(O(x^-1),x,Mod(0,3))
  128 subst(x^-1+O(x),x,0*x)
  129 subst(O(x^-1),x,0*x)
  130 Ser(1/x,y)
  131 Ser(x,y)
  132 Ser([x],y)
  133 Ser(x,, -5)
  134 Ser("")
  135 O(13^-5)/Mat(Mod(2,26)*y*x+(Mod(1,2)*y^-1+O(y^3)))
  136 laurentseries(1)
  137 laurentseries((x,y)->1)
  138 O(x) / Mod(0,5)
  139 O(x) / O(y)
  140 O(y) / O(x)