Komputeralgebrai algoritmusok J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak.

restart;

BigIntegerMultiply:=proc(a,b,B) local c,t,i,j,carry; c:=[]; for i from 0 to nops(a)-1 do c:=[op(c),0] od; for j from 0 to nops(b)-1 do carry:=0; for i from 0 to nops(a)-1 do t:=a[i+1]*b[j+1]+c[i+j+1]+carry; carry:=iquo(t,B); c[i+j+1]:=irem(t,B) od; c:=[op(c),carry]; od; c; end;

Zio2JUkiYUc2IkkiYkdGJUkiQkdGJTYnSSJjR0YlSSJ0R0YlSSJpR0YlSSJqR0YlSSZjYXJyeUdGJUYlRiVDJj5GKTciPyhGKyIiISIiIiwmLUklbm9wc0clKnByb3RlY3RlZEc2I0YkRjNGMyEiIkkldHJ1ZUdGNz5GKTckLUkjb3BHRjc2I0YpRjI/KEYsRjJGMywmLUY2NiNGJkYzRjNGOUY6QyU+Ri1GMj8oRitGMkYzRjRGOkMlPkYqLCgqJiZGJDYjLCZGK0YzRjNGM0YzJkYmNiMsJkYsRjNGM0YzRjNGMyZGKTYjLChGK0YzRixGM0YzRjNGM0YtRjM+Ri0tSSVpcXVvR0Y3NiRGKkYnPkZRLUklaXJlbUdGN0ZXPkYpNyRGPUYtRilGJUYlRiU=

a:=floor(evalf(10^10*Pi,20)); b:=floor(evalf(10^10*exp(1))); c:=a*b; a:=convert(a,base,10^4); b:=convert(b,base,10^4); c:=convert(c,base,10^4);

IixObCNmVEo=

IiwhRz1HPUY=

IjYrKWZddCk0QU0oUiYp

NyUiJU5sIiUjZiIiJDkk

NyUiJSFHKSIlIkcpIiRyIw==

NygiJSspKiIlME4iJCgpKiIlQU0iJShSJiIiKQ==

BigIntegerMultiply(a,b,10^4);

NygiJSspKiIlME4iJCgpKiIlQU0iJShSJiIiKQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

with(powseries);

NzdJKGNvbXBvc2VHNiJJKGV2YWxwb3dHRiRJKGludmVyc2VHRiRJKm11bHRjb25zdEdGJEkpbXVsdGlwbHlHRiRJKW5lZ2F0aXZlRyUqcHJvdGVjdGVkR0kncG93YWRkR0YkSSdwb3djb3NHRiRJKnBvd2NyZWF0ZUdGJEkocG93ZGlmZkdGJEkncG93ZXhwR0YkSSdwb3dpbnRHRiRJJ3Bvd2xvZ0dGJEkocG93cG9seUdGJEkncG93c2luR0YkSSlwb3dzb2x2ZUdGJEkocG93c3FydEdGJEkpcXVvdGllbnRHRiRJKnJldmVyc2lvbkdGJEkpc3VidHJhY3RHRiRJKHRwc2Zvcm1HRiQ=

a:=powpoly((1-x)^5,x); tpsform(a,x,8);

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

Ky9JInhHNiIiIiIiIiEhIiZGJSIjNSIiIyEjNSIiJCIiJiIiJSEiIkYs

b:=inverse(a); tpsform(b,x,8);

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

KzVJInhHNiIiIiIiIiEiIiZGJSIjOiIiIyIjTiIiJCIjcSIiJSIkRSJGJyIkNSMiIiciJEkkIiIoLUkiT0clKnByb3RlY3RlZEc2I0YlIiIp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:=powpoly(x,x); b:=powsin(a); tpsform(b,x,8);

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

Ky1JInhHNiIiIiJGJSMhIiIiIiciIiQjRiUiJD8iIiImI0YnIiVTXSIiKC1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiKQ==

c:=reversion(b); tpsform(c,x,8);

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

Ky1JInhHNiIiIiJGJSNGJSIiJyIiJCNGKCIjUyIiJiNGKyIkNyIiIigtSSJPRyUqcHJvdGVjdGVkRzYjRiUiIik=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Karatsuba:=proc(a,b,n,B) local aa,bb,a1,a2,b1,b2,n1,n2,c1,c2,c3,c,t; c:=sign(a)*sign(b); aa:=abs(a); bb:=abs(b); if n=1 then t:=BigIntegerMultiply([aa],[bb],B); return c*(t[2]*B+t[1]) fi; n1:=floor(n/2); n2:=n-n1; a1:=iquo(aa,B^n1); a2:=irem(aa,B^n1); b1:=iquo(bb,B^n1); b2:=irem(bb,B^n2); c1:=Karatsuba(a1,b1,n1,B); c2:=Karatsuba(a1-a2,b2-b1,n2,B); c3:=Karatsuba(a2,b2,n2,B); c*(c1*B^(2*n1)+(c1+c2+c3)*B^n1+c3); end;

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

a:=floor(evalf(10^10*Pi,20)); b:=floor(evalf(10^10*exp(1))); c:=a*b; debug(Karatsuba); Karatsuba(a,b,3,10^4);

IixObCNmVEo=

IiwhRz1HPUY=

IjYrKWZddCk0QU0oUiYp

SSpLYXJhdHN1YmFHNiI=

{--> enter Karatsuba, args = 31415926535, 27182818280, 3, 10000

IiIi

IixObCNmVEo=

IiwhRz1HPUY=

IiIi

IiIj

IigjZlRK

IiVObA==

IigiRz1G

IikhRz1HKQ==

{--> enter Karatsuba, args = 3141592, 2718281, 1, 10000

IiIi

IigjZlRK

IigiRz1G

NyQiJV9MIiolKUgoUiYp

<-- exit Karatsuba (now in Karatsuba) = 8539729843352}

Ii5fTCUpSChSJik=

{--> enter Karatsuba, args = 3135057, 80099999, 2, 10000

IiIi

IihkXTgk

IikqKioqNCEp

IiIi

IiIi

IiQ4JA==

IiVkXQ==

IiU0ISk=

IiUqKioq

{--> enter Karatsuba, args = 313, 8009, 1, 10000

IiIi

IiQ4JA==

IiU0ISk=

NyQiJTxvIiRdIw==

<-- exit Karatsuba (now in Karatsuba) = 2506817}

Iig8b10j

{--> enter Karatsuba, args = 4744, 1990, 1, 10000

ISIi

IiVXWg==

IiUhKj4=

NyQiJGcmIiRXKg==

<-- exit Karatsuba (now in Karatsuba) = 9440560}

IShnMFcq

{--> enter Karatsuba, args = 5057, 9999, 1, 10000

IiIi

IiVkXQ==

IiUqKioq

NyQiJVZcIiVjXQ==

<-- exit Karatsuba (now in Karatsuba) = 50564943}

IilWXGNd

IjBWXGNpIT02RA==

<-- exit Karatsuba (now in Karatsuba) = 251118062564943}

IjBWXGNpIT02RA==

{--> enter Karatsuba, args = 6535, 82818280, 2, 10000

IiIi

IiVObA==

IikhRz1HKQ==

IiIi

IiIi

IiIh

IiVObA==

IiUiRyk=

IiUhRyk=

{--> enter Karatsuba, args = 0, 8281, 1, 10000

IiIi

IiIh

IiUiRyk=

NyQiIiFGIw==

<-- exit Karatsuba (now in Karatsuba) = 0}

IiIh

{--> enter Karatsuba, args = 6535, 1, 1, 10000

IiIi

IiVObA==

IiIi

NyQiJU5sIiIh

<-- exit Karatsuba (now in Karatsuba) = 6535}

IiVObA==

{--> enter Karatsuba, args = 6535, 8280, 1, 10000

IiIi

IiVObA==

IiUhRyk=

NyQiJSspKiIlNWE=

<-- exit Karatsuba (now in Karatsuba) = 54109800}

IikrKTRUJg==

Ii0rKWZ1QFQm

<-- exit Karatsuba (now in Karatsuba) = 541217459800}

Ii0rKWZ1QFQm

IjYrKTQlKTR2XChcZGMp

<-- exit Karatsuba (now at top level) = 856574974975098409800}

IjYrKTQlKTR2XChcZGMp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

with(CurveFitting);

NypJKEJTcGxpbmVHNiJJLUJTcGxpbmVDdXJ2ZUdGJEksSW50ZXJhY3RpdmVHRiRJLUxlYXN0U3F1YXJlc0dGJEk4UG9seW5vbWlhbEludGVycG9sYXRpb25HRiRJNlJhdGlvbmFsSW50ZXJwb2xhdGlvbkdGJEknU3BsaW5lR0YkSTRUaGllbGVJbnRlcnBvbGF0aW9uR0Yk

TrialDivision:=proc(a,b,x,L) local i,c,y,La,Lb; La:=map(y->subs(x=y,a),L); Lb:=map(y->subs(x=y,b),L); for i to nops(L) do if Lb[i]=0 then if La[i]<>0 then return FAIL else La[i]=0 fi; else La[i]:=La[i]/Lb[i] fi; od; c:=PolynomialInterpolation(L,La,x); if degree(c,x)=degree(a,x)-degree(b,x) then c else FAIL fi; end;

Zio2JkkiYUc2IkkiYkdGJUkieEdGJUkiTEdGJTYnSSJpR0YlSSJjR0YlSSJ5R0YlSSNMYUdGJUkjTGJHRiVGJUYlQyc+Ri0tSSRtYXBHJSpwcm90ZWN0ZWRHNiRmKjYjRixGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJXN1YnNHRjM2JC9GJ0YsRiRGJUYlNiZGJzkmRiQ5JEYoPkYuLUYyNiRmKkY2RiVGN0YlLUY7NiRGPUYmRiVGJTYmRidGP0YmOSVGKD8oRioiIiJGSi1JJW5vcHNHRjM2I0YoSSV0cnVlR0YzQCUvJkYuNiNGKiIiIUAlMCZGLUZSRlNPSSVGQUlMR0YzL0ZWRlM+RlYqJkZWRkpGUSEiIj5GKy1fSS1DdXJ2ZUZpdHRpbmdHNiRGM0koX3N5c2xpYkdGJUk4UG9seW5vbWlhbEludGVycG9sYXRpb25HRiU2JUYoRi1GJ0AlLy1JJ2RlZ3JlZUdGMzYkRitGJywmLUZibzYkRiRGJ0ZKLUZibzYkRiZGJ0ZmbkYrRlhGJUYlRiU=

b:=3*x^3-4*x^2+x-3; c:=6*x^2+2*x-7; a:=expand(b*c); L:=[i$i=0..5];

LCoqJiIiJCIiIilJInhHNiJGJEYlRiUqJiIiJUYlKUYnIiIjRiUhIiJGJ0YlRiRGLQ==

LCgqJiIiJyIiIilJInhHNiIiIiNGJUYlKiZGKUYlRidGJUYlIiIoISIi

LC4qJiIjPSIiIilJInhHNiIiIiZGJUYlKiZGJEYlKUYnIiIlRiUhIiIqJiIjQkYlKUYnIiIkRiVGLSomIiM3RiUpRiciIiNGJUYlKiYiIzhGJUYnRiVGLSIjQEYl

NygiIiEiIiIiIiMiIiQiIiUiIiY=

debug(TrialDivision); TrialDivision(a,b,x,L);

SS5UcmlhbERpdmlzaW9uRzYi

{--> enter TrialDivision, args = 18*x^5-18*x^4-23*x^3+12*x^2-13*x+21, 3*x^3-4*x^2+x-3, x, [0, 1, 2, 3, 4, 5]

NygiI0AhIiQiJFoiIiUmUSMiJjhEIiImIlFV

NyghIiRGIyIiKCIjWCIkSCIiJHgj

ISIo

IiIi

IiNA

IiNg

IiMoKg==

IiRgIg==

LCgqJiIiJyIiIilJInhHNiIiIiNGJUYlKiZGKUYlRidGJUYlIiIoISIi

LCgqJiIiJyIiIilJInhHNiIiIiNGJUYlKiZGKUYlRidGJUYlIiIoISIi

<-- exit TrialDivision (now at top level) = 6*x^2+2*x-7}

LCgqJiIiJyIiIilJInhHNiIiIiNGJUYlKiZGKUYlRidGJUYlIiIoISIi

a:=a-1; TrialDivision(a,b,x,L);

LC4qJiIjPSIiIilJInhHNiIiIiZGJUYlKiZGJEYlKUYnIiIlRiUhIiIqJiIjQkYlKUYnIiIkRiVGLSomIiM3RiUpRiciIiNGJUYlKiYiIzhGJUYnRiVGLUYkRiU=

{--> enter TrialDivision, args = 18*x^5-18*x^4-23*x^3+12*x^2-13*x+18, 3*x^3-4*x^2+x-3, x, [0, 1, 2, 3, 4, 5]

NygiIz0hIiciJFciIiUjUSMiJjVEIiImeUIl

NyghIiRGIyIiKCIjWCIkSCIiJHgj

ISIn

IiIj

IyIkVyIiIig=

IyIkJXoiIzo=

IyIlcVQiI1Y=

IyImeUIlIiR4Iw==

LC4qJiMiJzw6QyIobD52JCIiIilJInhHNiIiIiZGJ0YnKiYjIicsNE8iJyYpb1RGJylGKSIiJUYnISIiKiYjIikpb2phIkYmRicpRikiIiRGJ0YnKiYjIidccyMpRi9GJylGKSIiI0YnRjIqJiMiKHQyKyYiJyRSXShGJ0YpRidGJyIiJ0Yy

SSVGQUlMRyUqcHJvdGVjdGVkRw==

<-- exit TrialDivision (now at top level) = FAIL}

SSVGQUlMRyUqcHJvdGVjdGVkRw==

omega:=(1+I)/sqrt(2); omega^8; omega^4;

KiYsJiMiIiIiIiNGJSomRiRGJV4jRiVGJUYlRiUpRiZGJEYl

IiIi

ISIi

omega:=I; omega^8; omega^4;

XiMiIiI=

IiIi

IiIi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

4^4 mod 17; [4^i$i=0..3] mod 17;

IiIi

NyYiIiIiIiUiIzsiIzg=

A:=Matrix(4,(i,j)->4^((i-1)*(j-1)) mod 17);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKkdPQF4i

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

`mod`:=mods;

SSVtb2RzRyUqcHJvdGVjdGVkRw==

14&^8 mod 41;

IiIi

[14&^i$i=0..7]; map(x->x mod 41,%);

NyotSSMmXkc2IjYkIiM5IiIhLUYkNiRGJyIiIi1GJDYkRiciIiMtRiQ2JEYnIiIkLUYkNiRGJyIiJS1GJDYkRiciIiYtRiQ2JEYnIiInLUYkNiRGJyIiKA==

NyoiIiIiIzkhIiohIiQhIiIhIzkiIioiIiQ=

[(-9)&^i$i=0..3]; map(x->x mod 41,%);

NyYtSSMmXkc2IjYkISIqIiIhLUYkNiRGJyIiIi1GJDYkRiciIiMtRiQ2JEYnIiIk

NyYiIiIhIiohIiIiIio=

[(-1)&^i$i=0..1]; map(x->x mod 41,%);

NyQtSSMmXkc2IjYkISIiIiIhLUYkNiRGJyIiIg==

NyQiIiIhIiI=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:=5*x^6+x^5+3*x^3+x^2-4*x+1;

LC4qJiIiJiIiIilJInhHNiIiIidGJUYlKiQpRidGJEYlRiUqJiIiJEYlKUYnRi1GJUYlKiQpRiciIiNGJUYlKiYiIiVGJUYnRiUhIiJGJUYl

b:=5*y^3+y+1; c:=y^2+3*y-4; a=expand(subs(y=x^2,b+x*c));

LCgqJiIiJiIiIilJInlHNiIiIiRGJUYlRidGJUYlRiU=

LCgqJClJInlHNiIiIiMiIiJGKComIiIkRihGJUYoRigiIiUhIiI=

LywuKiYiIiYiIiIpSSJ4RzYiIiInRiZGJiokKUYoRiVGJkYmKiYiIiRGJilGKEYuRiZGJiokKUYoIiIjRiZGJiomIiIlRiZGKEYmISIiRiZGJkYj

d:=1; e:=5*z+1; b=expand(subs(z=y^2,d+y*e));

IiIi

LCYqJiIiJiIiIkkiekc2IkYlRiVGJUYl

LywoKiYiIiYiIiIpSSJ5RzYiIiIkRiZGJkYoRiZGJkYmRiM=

subs(z=1,d) mod 41; subs(z=1,e) mod 41;

IiIi

IiIn

subs(y=1,b) mod 41=1+1*6 mod 41; subs(y=-1,b) mod 41=1-1*6 mod 41;

LyIiKEYj

LyEiJkYj

subs(z=-1,d) mod 41; subs(z=-1,e) mod 41;

IiIi

ISIl

subs(y=-9,b) mod 41=1+(-9)*(-4) mod 41; subs(y=9,b) mod 41=1+9*(-4) mod 41;

LyEiJUYj

LyIiJ0Yj

subs(y=1,c) mod 41; subs(y=-1,c) mod 41; subs(y=-9,c) mod 41; subs(y=9,c) mod 41;

IiIh

ISIn

IiIq

ISM+

subs(x=3,a) mod 41=6+3*(-19) mod 41; subs(x=-3,a) mod 41=6+(-3)*(-19) mod 41;

LyEjNUYj

LyEjPkYj

[14&^i$i=0..7]; map(x->x mod 41,%); map(y->subs(x=y,a) mod 41,%);

NyotSSMmXkc2IjYkIiM5IiIhLUYkNiRGJyIiIi1GJDYkRiciIiMtRiQ2JEYnIiIkLUYkNiRGJyIiJS1GJDYkRiciIiYtRiQ2JEYnIiInLUYkNiRGJyIiKA==

NyoiIiIiIzkhIiohIiQhIiIhIzkiIioiIiQ=

NyoiIighIiIiIikhIz5GIyEiKCEjPSEjNQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

mFFT:=proc(a,x,omega,n,m) local A,B,C,b,c,i,j; if n=0 then return [a mod m] fi; b:=0; c:=0; for i from 0 to 2^(n-1)-1 do b:=b+coeff(a,x,2*i)*x^i; c:=c+coeff(a,x,2*i+1)*x^i; od; B:=mFFT(b,x,omega^2 mod m,n-1,m); C:=mFFT(c,x,omega^2 mod m,n-1,m); A:=[0$j=0..2^n-1]; for i from 0 to 2^(n-1)-1 do A[i+1]:=B[i+1]+omega&^i*C[i+1] mod m; A[i+1+2^(n-1)]:=B[i+1]-omega&^i*C[i+1] mod m; od; A; end;

Zio2J0kiYUc2IkkieEdGJUkmb21lZ2FHRiVJIm5HRiVJIm1HRiU2KUkiQUdGJUkiQkdGJUkiQ0dGJUkiYkdGJUkiY0dGJUkiaUdGJUkiakdGJUYlRiVDK0AkL0YoIiIhTzcjLUkkbW9kR0YlNiRGJEYpPkYuRjU+Ri9GNT8oRjBGNSIiIiwmKSIiIywmRihGPkY+ISIiRj5GPkZDSSV0cnVlRyUqcHJvdGVjdGVkR0MkPkYuLCZGLkY+KiYtSSZjb2VmZkdGRTYlRiRGJiwkKiZGQUY+RjBGPkY+Rj4pRiZGMEY+Rj4+Ri8sJkYvRj4qJi1GSzYlRiRGJiwmRk5GPkY+Rj5GPkZPRj5GPj5GLC1JJW1GRlRHRiU2J0YuRiYtRjk2JCokKUYnRkFGPkYpRkJGKT5GLS1GWDYnRi9GJkZaRkJGKT5GKzcjLUkiJEdGRTYkRjUvRjE7RjUsJilGQUYoRj5GPkZDPyhGMEY1Rj5GP0ZEQyQ+JkYrNiMsJkYwRj5GPkY+LUY5NiQsJiZGLEZob0Y+KiYtSSMmXkdGJTYkRidGMEY+JkYtRmhvRj5GPkYpPiZGKzYjLChGMEY+Rj5GPkZARj4tRjk2JCwmRl1wRj5GXnBGQ0YpRitGJUYlRiU=

debug(mFFT); mFFT(a,x,14,3,41); undebug(mFFT);

SSVtRkZURzYi

{--> enter mFFT, args = 5*x^6+x^5+3*x^3+x^2-4*x+1, x, 14, 3, 41

IiIh

IiIh

IiIi

ISIl

LCYiIiJGI0kieEc2IkYj

LCYiIiUhIiIqJiIiJCIiIkkieEc2IkYnRic=

LCYiIiJGI0kieEc2IkYj

LCgiIiUhIiIqJiIiJCIiIkkieEc2IkYnRicqJClGKCIiI0YnRic=

LCgiIiJGI0kieEc2IkYjKiYiIiZGIylGJCIiJEYjRiM=

LCgiIiUhIiIqJiIiJCIiIkkieEc2IkYnRicqJClGKCIiI0YnRic=

{--> enter mFFT, args = 1+x+5*x^3, x, 9, 2, 41

IiIh

IiIh

IiIi

IiIi

IiIi

LCYiIiJGIyomIiImRiNJInhHNiJGI0Yj

{--> enter mFFT, args = 1, x, 1, 1, 41

IiIh

IiIh

IiIi

IiIh

{--> enter mFFT, args = 1, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [1]}

NyMiIiI=

{--> enter mFFT, args = 0, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [0]}

NyMiIiE=

NyQiIiFGIw==

IiIi

IiIi

NyQiIiJGIw==

<-- exit mFFT (now in mFFT) = [1, 1]}

NyQiIiJGIw==

{--> enter mFFT, args = 1+5*x, x, 1, 1, 41

IiIh

IiIh

IiIi

IiIm

{--> enter mFFT, args = 1, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [1]}

NyMiIiI=

{--> enter mFFT, args = 5, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [5]}

NyMiIiY=

NyQiIiFGIw==

IiIn

ISIl

NyQiIichIiU=

<-- exit mFFT (now in mFFT) = [6, -4]}

NyQiIichIiU=

NyYiIiFGI0YjRiM=

IiIo

ISIm

ISIl

IiIn

NyYiIighIiUhIiYiIic=

<-- exit mFFT (now in mFFT) = [7, -4, -5, 6]}

NyYiIighIiUhIiYiIic=

{--> enter mFFT, args = -4+3*x+x^2, x, 9, 2, 41

IiIh

IiIh

ISIl

IiIk

LCZJInhHNiIiIiIiIiUhIiI=

IiIk

{--> enter mFFT, args = x-4, x, 1, 1, 41

IiIh

IiIh

ISIl

IiIi

{--> enter mFFT, args = 4, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [-4]}

NyMhIiU=

{--> enter mFFT, args = 1, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [1]}

NyMiIiI=

NyQiIiFGIw==

ISIk

ISIm

NyQhIiQhIiY=

<-- exit mFFT (now in mFFT) = [-3, -5]}

NyQhIiQhIiY=

{--> enter mFFT, args = 3, x, 1, 1, 41

IiIh

IiIh

IiIk

IiIh

{--> enter mFFT, args = 3, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [3]}

NyMiIiQ=

{--> enter mFFT, args = 0, x, 1, 0, 41 <-- exit mFFT (now in mFFT) = [0]}

NyMiIiE=

NyQiIiFGIw==

IiIk

IiIk

NyQiIiRGIw==

<-- exit mFFT (now in mFFT) = [3, 3]}

NyQiIiRGIw==

NyYiIiFGI0YjRiM=

IiIh

ISIn

IiIq

ISM+

NyYiIiEiIiohIichIz4=

<-- exit mFFT (now in mFFT) = [0, 9, -6, -19]}

NyYiIiEiIiohIichIz4=

NyoiIiFGI0YjRiNGI0YjRiNGIw==

IiIo

IiIo

ISIi

ISIo

IiIp

ISM9

ISM+

ISM1

NyoiIighIiIiIikhIz5GIyEiKCEjPSEjNQ==

<-- exit mFFT (now at top level) = [7, -1, 8, -19, 7, -7, -18, -10]}

NyoiIighIiIiIikhIz5GIyEiKCEjPSEjNQ==

SSVtRkZURzYi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

`mod`:=modp;

SSVtb2RwRyUqcHJvdGVjdGVkRw==

4^4 mod 17; [4^i$i=0..3] mod 17;

IiIi

NyYiIiIiIiUiIzsiIzg=

A:=Matrix(4,(i,j)->4^((i-1)*(j-1)) mod 17);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKissTV4i

B:=Matrix(4,(i,j)->4^(-((i-1)*(j-1))) mod 17);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKmM9Tl4i

evalm(A&*B); map(x->x mod 17,%);

PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIjIiIkIiQqRzYkRidGJyIkaCQ2JEYnRiYiI002JEYqRiciJFUlNiRGJkYmRic2JEYrRipGLDYkRitGKyIkOSY2JEYmRidGMDYkRidGK0YsNiRGK0YnRiw2JEYrRiZGMDYkRipGJkYwNiRGJkYqRjA2JEYqRipGLjYkRidGKkYyNiRGJkYrRjA=

PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIjIiIkIiIhNiRGJ0YnRic2JEYnRiZGLDYkRipGJ0YsNiRGJkYmRic2JEYrRipGLDYkRitGK0YnNiRGJkYnRiw2JEYnRitGLDYkRitGJ0YsNiRGK0YmRiw2JEYqRiZGLDYkRiZGKkYsNiRGKkYqRic2JEYnRipGLDYkRiZGK0Ys

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

`mod`:=mods;

SSVtb2RzRyUqcHJvdGVjdGVkRw==

mFFT_Multiply:=proc(a,b,x,omega,n,m) local A,B,c,C,i; A:=mFFT(a,x,omega,n,m); B:=mFFT(b,x,omega,n,m); c:=0; for i from 0 to 2^n-1 do c:=c+A[i+1]*B[i+1]*x^i mod m; od; C:=mFFT(c,x,omega,n,m); c:=0; for i from 0 to 2^n-1 do c:=c+C[i+1]/2^n*x^i mod m; od; c; end;

Zio2KEkiYUc2IkkiYkdGJUkieEdGJUkmb21lZ2FHRiVJIm5HRiVJIm1HRiU2J0kiQUdGJUkiQkdGJUkiY0dGJUkiQ0dGJUkiaUdGJUYlRiVDKj5GLC1JJW1GRlRHRiU2J0YkRidGKEYpRio+Ri0tRjQ2J0YmRidGKEYpRio+Ri4iIiE/KEYwRjoiIiIsJikiIiNGKUY8RjwhIiJJJXRydWVHJSpwcm90ZWN0ZWRHPkYuLUkkbW9kR0YlNiQsJkYuRjwqKCZGLDYjLCZGMEY8RjxGPEY8JkYtRkpGPClGJ0YwRjxGPEYqPkYvLUY0NidGLkYnRihGKUYqRjk/KEYwRjpGPEY9RkE+Ri4tRkU2JCwmRi5GPCooJkYvRkpGPEY+RkBGTUY8RjxGKkYuRiVGJUYl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:=3*x^3+x^2-4*x+1; b:=x^3+2*x^2+5*x-3;

LCoqJiIiJCIiIilJInhHNiJGJEYlRiUqJClGJyIiI0YlRiUqJiIiJUYlRidGJSEiIkYlRiU=

LCoqJClJInhHNiIiIiQiIiJGKComIiIjRigpRiVGKkYoRigqJiIiJkYoRiVGKEYoRichIiI=

debug(mFFT_Multiply); mFFT_Multiply(a,b,x,14,3,41); expand(a*b);

SS5tRkZUX011bHRpcGx5RzYi

{--> enter mFFT_Multiply, args = 3*x^3+x^2-4*x+1, x^3+2*x^2+5*x-3, x, 14, 3, 41

NyoiIiIiIiohIz4hIz0iIiQiIzsiIz4hIiQ=

NyoiIiZGIyIiISIjOSEiKCEiJyEjNSIjOw==

IiIh

IiIm

LCYiIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJA==

LCYiIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJA==

LCgiIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJComIiInRiQpRiciIiRGJCEiIg==

LCoiIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJComIiInRiQpRiciIiRGJCEiIiomIiM/RiQpRidGJkYkRiQ=

LCwiIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJComIiInRiQpRiciIiRGJCEiIiomIiM/RiQpRidGJkYkRiQqJiIjOUYkKUYnRiNGJEYt

LC4iIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJComIiInRiQpRiciIiRGJCEiIiomIiM/RiQpRidGJkYkRiQqJiIjOUYkKUYnRiNGJEYtKiYiIzpGJClGJ0YqRiRGJA==

LDAiIiYiIiIqJiIiJUYkSSJ4RzYiRiRGJComIiInRiQpRiciIiRGJCEiIiomIiM/RiQpRidGJkYkRiQqJiIjOUYkKUYnRiNGJEYtKiYiIzpGJClGJ0YqRiRGJComIiIoRiQpRidGOEYkRi0=

NyoiIzwiIiEhIzwiIzohIz4hIichIiUiIzg=

IiIh

ISIk

ISIk

LCYiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiY=

LCgiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYm

LCoiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYmKiYiIzhGJilGKCIiJUYmRiY=

LCwiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYmKiYiIzhGJilGKCIiJUYmRiYqJiIjNkYmKUYoIiImRiZGJA==

LC4iIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYmKiYiIzhGJilGKCIiJUYmRiYqJiIjNkYmKUYoIiImRiZGJComIiM/RiYpRigiIidGJkYm

LDAiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYmKiYiIzhGJilGKCIiJUYmRiYqJiIjNkYmKUYoIiImRiZGJComIiM/RiYpRigiIidGJkYmKiYiIzxGJilGKEYsRiZGJg==

LDAiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYmKiYiIzhGJilGKCIiJUYmRiYqJiIjNkYmKUYoIiImRiZGJComIiM/RiYpRigiIidGJkYmKiYiIzxGJilGKEYsRiZGJg==

<-- exit mFFT_Multiply (now at top level) = -3+3*x^2+7*x^3+13*x^4-11*x^5+20*x^6+17*x^7}

LDAiIiQhIiIqJkYjIiIiKUkieEc2IiIiI0YmRiYqJiIiKEYmKUYoRiNGJkYmKiYiIzhGJilGKCIiJUYmRiYqJiIjNkYmKUYoIiImRiZGJComIiM/RiYpRigiIidGJkYmKiYiIzxGJilGKEYsRiZGJg==

LDAqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIihGJSlGJyIiJkYlRiUqJiIjOEYlKUYnIiIlRiVGJSomIiM2RiUpRidGJEYlISIiKiYiI0BGJSlGJyIiI0YlRjUqJiIjPEYlRidGJUYlRiRGNQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

14&^8 mod 41; 14&^4 mod 41;

IiIi

ISIi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

with(numtheory);

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

2.^31/ln(2.^31)/phi(2^20);

JCIrJyoqPWkhPiEiKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

15&^8 mod 41; 15&^20 mod 41;

IiM9

ISIi

evalf(3./Pi^2);

JCIrM2JqUkkhIzU=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:='a'; powcreate(a(n)=1,a(0)=1,a(1)=-2,a(2)=3,a(3)=0,a(4)=1,a(5)=-1,a(6)=2); tpsform(a,x,8); convert(%,polynom);

SSJhRzYi

KzNJInhHNiIiIiIiIiEhIiNGJSIiJCIiI0YlIiIlISIiIiImRikiIidGJSIiKC1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiKQ==

LDAiIiJGIyomIiIjRiNJInhHNiJGIyEiIiomIiIkRiMpRiZGJUYjRiMqJClGJiIiJUYjRiMqJClGJiIiJkYjRigqJkYlRiMpRiYiIidGI0YjKiQpRiYiIihGI0Yj

tpsform(a,x,1); convert(%,polynom); y:=powpoly(1/%,x); two:=powpoly(2,x);

KydJInhHNiIiIiIiIiEtSSJPRyUqcHJvdGVjdGVkRzYjRiVGJQ==

IiIi

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

multiply(y,subtract(two,multiply(y,a))); tpsform(%,x,2); convert(%,polynom); y:=powpoly(%,x);

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

KylJInhHNiIiIiIiIiEiIiNGJS1JIk9HJSpwcm90ZWN0ZWRHNiNGJUYn

LCYiIiJGIyomIiIjRiNJInhHNiJGI0Yj

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

multiply(y,subtract(two,multiply(y,a))); tpsform(%,x,4); convert(%,polynom); y:=powpoly(%,x);

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

Ky1JInhHNiIiIiIiIiEiIiNGJUYlRichIiUiIiQtSSJPRyUqcHJvdGVjdGVkRzYjRiUiIiU=

LCoiIiJGIyomIiIjRiNJInhHNiJGI0YjKiQpRiZGJUYjRiMqJiIiJUYjKUYmIiIkRiMhIiI=

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

multiply(y,subtract(two,multiply(y,a))); tpsform(%,x,8); convert(%,polynom); y:=powpoly(%,x);

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

KzVJInhHNiIiIiIiIiEiIiNGJUYlRichIiUiIiQhIzciIiUhIzgiIiYiIioiIiciI2QiIigtSSJPRyUqcHJvdGVjdGVkRzYjRiUiIik=

LDIiIiJGIyomIiIjRiNJInhHNiJGI0YjKiQpRiZGJUYjRiMqJiIiJUYjKUYmIiIkRiMhIiIqJiIjN0YjKUYmRitGI0YuKiYiIzhGIylGJiIiJkYjRi4qJiIiKkYjKUYmIiInRiNGIyomIiNkRiMpRiYiIihGI0Yj

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

multiply(y,a); tpsform(%,x,8);

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

KydJInhHNiIiIiIiIiEtSSJPRyUqcHJvdGVjdGVkRzYjRiUiIik=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

FastNewtonInversion:=proc(a,x,n) local y,yy,k,two; tpsform(a,x,1); yy:=convert(1/%,polynom); y:=powpoly(yy,x); two:=powpoly(2,x); for k to n do multiply(y,subtract(two,multiply(y,a))); tpsform(%,x,2^k); yy:=convert(%,polynom); y:=powpoly(yy,x); od; yy; end;

Zio2JUkiYUc2IkkieEdGJUkibkdGJTYmSSJ5R0YlSSN5eUdGJUkia0dGJUkkdHdvR0YlRiVGJUMoLV9JKnBvd3Nlcmllc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUkodHBzZm9ybUdGJTYlRiRGJiIiIj5GKi1JKGNvbnZlcnRHRjI2JCokSSIlR0YlISIiSShwb2x5bm9tR0YyPkYpLV9GMEkocG93cG9seUdGJTYkRipGJj5GLC1GQTYkIiIjRiY/KEYrRjZGNkYnSSV0cnVlR0YyQyYtX0YwSSltdWx0aXBseUdGJTYkRiktX0YwSSlzdWJ0cmFjdEdGJTYkRiwtRkw2JEYpRiQtRi82JUY8RiYpRkdGKz5GKi1GOTYkRjxGPkY/RipGJUYlRiU=

FastNewtonInversion(a,x,3);

LDIiIiJGIyomIiIjRiNJInhHNiJGI0YjKiQpRiZGJUYjRiMqJiIiJUYjKUYmIiIkRiMhIiIqJiIjN0YjKUYmRitGI0YuKiYiIzhGIylGJiIiJkYjRi4qJiIiKkYjKUYmIiInRiNGIyomIiNkRiMpRiYiIihGI0Yj

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

G:=(1-2*t*x+x^2)^(-1/2); series(G,x);

KiQpLCgiIiJGJSooIiIjRiVJInRHNiJGJUkieEdGKUYlISIiKiQpRipGJ0YlRiUjRiVGJ0Yr

KzFJInhHNiIiIiIiIiFJInRHRiRGJSwmI0YlIiIjISIiKiYjIiIkRipGJSlGJ0YqRiVGJUYqLCYqJkYtRiVGJ0YlRisqJiMiIiZGKkYlKUYnRi5GJUYlRi4sKCNGLiIiKUYlKiYjIiM6IiIlRiVGL0YlRisqJiMiI05GOEYlKUYnRjxGJUYlRjwsKComI0Y7RjhGJUYnRiVGJSomI0Y/RjxGJUY1RiVGKyomIyIjakY4RiUpRidGNEYlRiVGNC1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiJw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

P:=(1-2*t*x+x^2)*y^2-1; PP:=diff(P,y); y0:=1;

LCYqJiwoIiIiRiUqKCIiI0YlSSJ0RzYiRiVJInhHRilGJSEiIiokKUYqRidGJUYlRiUpSSJ5R0YpRidGJUYlRiVGKw==

LCQqKCIiIyIiIiwoRiVGJSooRiRGJUkidEc2IkYlSSJ4R0YpRiUhIiIqJClGKkYkRiVGJUYlSSJ5R0YpRiVGJQ==

IiIi

y1:=series(y0-subs(y=y0,P)/subs(y=y0,PP),x,2); y1:=convert(y1,polynom);

KylJInhHNiIiIiIiIiFJInRHRiRGJS1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiIw==

LCYiIiJGIyomSSJ0RzYiRiNJInhHRiZGI0Yj

y2:=series(y1-subs(y=y1,P)/subs(y=y1,PP),x,4); y2:=convert(y2,polynom);

Ky1JInhHNiIiIiIiIiFJInRHRiRGJSwmI0YlIiIjISIiKiYjIiIkRipGJSlGJ0YqRiVGJUYqLCgqJClGJ0YuRiVGJUYnRisqKEYpRiUsJiomRi5GJUYvRiVGJUYlRitGJUYnRiVGJUYuLUkiT0clKnByb3RlY3RlZEc2I0YlIiIl

LCoiIiJGIyomSSJ0RzYiRiNJInhHRiZGI0YjKiYsJiNGIyIiIyEiIiomIyIiJEYrRiMpRiVGK0YjRiNGIylGJ0YrRiNGIyomLCgqJClGJUYvRiNGI0YlRiwqKEYqRiMsJiomRi9GI0YwRiNGI0YjRixGI0YlRiNGI0YjKUYnRi9GI0Yj

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:=4+x+2*x^2+3*x^3;

LCoiIiUiIiJJInhHNiJGJComIiIjRiQpRiVGKEYkRiQqJiIiJEYkKUYlRitGJEYk

P:=y^2-a; y0:=-2; y0:=2;

LCwqJClJInlHNiIiIiMiIiJGKCIiJSEiIkkieEdGJkYqKiZGJ0YoKUYrRidGKEYqKiYiIiRGKClGK0YvRihGKg==

ISIj

IiIj

yy:=series(2-(4-a)/4,x,2); yy:=convert(yy,polynom);

KylJInhHNiIiIiMiIiEjIiIiIiIlRigtSSJPRyUqcHJvdGVjdGVkRzYjRihGJQ==

LCYiIiMiIiIqJiNGJCIiJUYkSSJ4RzYiRiRGJA==

yy:=series(yy-(yy^2-a)/2/yy,x,4); yy:=convert(yy,polynom);

Ky1JInhHNiIiIiMiIiEjIiIiIiIlRigjIiNKIiNrRiUjIiRgJCIkNyYiIiQtSSJPRyUqcHJvdGVjdGVkRzYjRihGKQ==

LCoiIiMiIiIqJiNGJCIiJUYkSSJ4RzYiRiRGJComIyIjSiIja0YkKUYoRiNGJEYkKiYjIiRgJCIkNyZGJClGKCIiJEYkRiQ=

series(yy^2,x,4);

Ky1JInhHNiIiIiUiIiEiIiJGJyIiI0YoIiIkRiktSSJPRyUqcHJvdGVjdGVkRzYjRidGJQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

NewtonSolve:=proc(P,y,x,y0,n) local yy,k,PP; PP:=diff(P,y); yy:=y0; for k to n do yy:=series(yy-subs(y=yy,P)/subs(y=yy,PP),x,2^k); yy:=convert(yy,polynom); od; yy; end;

Zio2J0kiUEc2IkkieUdGJUkieEdGJUkjeTBHRiVJIm5HRiU2JUkjeXlHRiVJImtHRiVJI1BQR0YlRiVGJUMmPkYtLUklZGlmZkclKnByb3RlY3RlZEc2JEYkRiY+RitGKD8oRiwiIiJGNkYpSSV0cnVlR0YyQyQ+RistSSdzZXJpZXNHRjI2JSwmRitGNiomLUklc3Vic0dGMjYkL0YmRitGJEY2LUZANiRGQkYtISIiRkVGJykiIiNGLD5GKy1JKGNvbnZlcnRHRjI2JEYrSShwb2x5bm9tR0YyRitGJUYlRiU=

NewtonSolve(P,y,x,2,3);

LDIiIiMiIiIqJiNGJCIiJUYkSSJ4RzYiRiRGJComIyIjSiIja0YkKUYoRiNGJEYkKiYjIiRgJCIkNyZGJClGKCIiJEYkRiQqJiMiJXRCIiYlUTtGJClGKEYnRiQhIiIqJiMiJjgmPiInczU4RiQpRigiIiZGJEY6KiYjIidIbTgiKF9yNCNGJClGKCIiJ0YkRjoqJiMiKCwjejoiKTtzeDtGJClGKCIiKEYkRiQ=

series(%^2,x,8);

Ky1JInhHNiIiIiUiIiEiIiJGJyIiI0YoIiIkRiktSSJPRyUqcHJvdGVjdGVkRzYjRiciIik=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn