Лень двигатель прогресса. Генератор задач. Часть 2

type polynomial= record
st:integer;//степень многочлена
kof:array of real;//коэффициенты при x^i
function into(x:real):real;
class function operator+(a,b: polynomial): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]+b.kof[i];
end;
rez.st:=stn;
result:=rez;
end;
class function operator-(a,b: polynomial): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]-b.kof[i];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
result:=rez;
end;
class function operator*(a,b: polynomial): polynomial;
var i,j,stn:integer;
rez:polynomial;
begin
stn:=a.st+b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to a.st do
for j:=0 to b.st do
begin
rez.kof[i+j]:=rez.kof[i+j]+a.kof[i]*b.kof[j];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
result:=rez;
end;
class function operator*(a:integer; b: polynomial): polynomial;
var i:integer;
begin
for i:=0 to b.st do
b.kof[i]:=a*b.kof[i];
result:=b;
end;
class function operator in(a: polynomial; n:integer): polynomial;
var i:integer;
rez:polynomial;
begin
rez.st:=0;
setlength(rez.kof,1);
rez.kof[0]:=1;
for i:=1 to n do
rez:=rez*a;
result:=rez;
end;
procedure nw(x:integer);
function pltostr:string;//в строковую переменную
procedure derivative;//производная
procedure integral;//интеграл
end;

procedure polynomial.nw(x:integer);
var
i:integer;
begin
st:=x;
setlength(kof,st+1);
for i:=0 to st do
kof[i]:=random(-10,10);
while(kof[st]=0)do
kof[st]:=random(-10,10);
end;
procedure polynomial.integral;
var
i:integer;
begin
setlength(kof,st+2);
for i:=st downto 1 do
kof[i+1]:=kof[i]/i;
kof[0]:=0;
st:=st+1;
setlength(kof,st+1);
end;
procedure polynomial.derivative;
var
i:integer;
begin
for i:=1 to st do
kof[i-1]:=kof[i]*i;
st:=st-1;
setlength(kof,st+1);
end;

type polynomialwithroot= record
st:integer;//степень многочлена
root:array of integer;//корни многочлена
kof:array of integer;//коэффициенты при x^i
class function operator+(a,b: polynomialwithroot): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]+b.kof[i];
end;
rez.st:=stn;
result:=rez;
end;
class function operator+(a: polynomialwithroot; b:polynomial): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]+b.kof[i];
end;
rez.st:=stn;
result:=rez;
end;
class function operator+(b:polynomial; a: polynomialwithroot): polynomial;
// var i:integer;
// rez:polynomial;
begin
result:=a+b;
end;
class function operator-(a,b: polynomialwithroot): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]-b.kof[i];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
result:=rez;
end;
class function operator-(a:polynomialwithroot; b:polynomial): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]-b.kof[i];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
result:=rez;
end;
class function operator-(b:polynomial; a:polynomialwithroot): polynomial;
var i,stn:integer;
rez:polynomial;
begin
if(a.st>b.st)then stn:=a.st
else stn:=b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to stn do
begin
if(i<=a.st)then
rez.kof[i]:=rez.kof[i]+a.kof[i];
if(i<=b.st)then
rez.kof[i]:=rez.kof[i]-b.kof[i];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
result:=rez;
end;
class function operator*(a,b: polynomialwithroot): polynomialwithroot;
var i,j,stn:integer;
rez:polynomialwithroot;
begin
stn:=a.st+b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to a.st do
for j:=0 to b.st do
begin
rez.kof[i+j]:=rez.kof[i+j]+a.kof[i]*b.kof[j];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
setlength(rez.root,rez.st);
for i:=0 to a.st-1 do
rez.root[i]:=a.root[i];
for i:=0 to b.st-1 do
rez.root[a.st+i]:=b.root[i];
result:=rez;
end;
class function operator*(a:polynomialwithroot; b:polynomial): polynomial;
var i,j,stn:integer;
rez:polynomial;
begin
stn:=a.st+b.st;
setlength(rez.kof,stn+1);
for i:=0 to stn do
rez.kof[i]:=0;
for i:=0 to a.st do
for j:=0 to b.st do
begin
rez.kof[i+j]:=rez.kof[i+j]+a.kof[i]*b.kof[j];
end;
while(rez.kof[stn]=0)do
begin
setlength(rez.kof,stn);
stn:=stn-1;
end;
rez.st:=stn;
result:=rez;
end;
class function operator*(b:polynomial; a:polynomialwithroot): polynomial;
// var i,j,stn:integer;
// rez:polynomial;
begin
result:=a*b;
end;
class function operator in(a: polynomialwithroot; n:integer): polynomialwithroot;
var i:integer;
rez:polynomialwithroot;
begin
rez:=a;
for i:=2 to n do
rez:=rez*a;
result:=rez;
end;
procedure nw;
procedure roots(x:integer);
function pltostr:string;
end;
procedure polynomialwithroot.roots(x:integer);
var i:integer;
begin
st:=x;
setlength(root,st);
for i:=0 to st-1 do
begin
root[i]:=random(-5,5);
end;
nw;
end;
procedure polynomialwithroot.nw;
var
i,j,sum:integer;
tk:array of integer;
dop:integer;
begin
setlength(kof,st+1);
setlength(tk,st+1);
for i:=0 to st-1 do
kof[i]:=0;
for i:=0 to st-1 do
begin
for j:=0 to st do
tk[j]:=0;
while(tk[st]=0)do
begin
sum:=0;
for j:=0 to st-1 do
sum:=sum+tk[j];
if(sum=(i+1))then
begin
dop:=1;
for j:=0 to st-1 do
if(tk[j]=1)then
dop:=dop*root[j];
for j:=0 to i do
dop:=-dop;
kof[st-i-1]:=kof[st-i-1]+dop;
end;
tk[0]:=tk[0]+1;
for j:=0 to st-1 do
begin
tk[j+1]:=tk[j+1]+(tk[j] div 2);
tk[j]:=tk[j] mod 2;
end;
end;
end;
kof[st]:=1;
end;

type sinx= record
x:polynomial;
s:string;
procedure nw;
procedure derivative;//производная
end;
type cosx= record
x:polynomial;
s:string;
procedure nw;
procedure derivative;//производная
end;
type tgx= record
x:polynomial;
s:string;
procedure nw;
procedure derivative;//производная
end;
type ctgx= record
x:polynomial;
s:string;
procedure nw;
procedure derivative;//производная
end;

type lnx=record
s:string;
x:polynomial;
procedure nw;
procedure derivative;
end;
type ex=record
s:string;
f,x:polynomial;
procedure nw;
procedure derivative;
end;

type tex=record
namefl:string;
procedure newtex(s:string);
procedure add(s:string);
procedure closetex;
procedure createpdf;
procedure openpdf;
end;

implementation

procedure tex.newtex(s:string);
var
t:text;
begin
namefl:=s;
assign(t,s+’.tex’);
rewrite(t);
writeln(t,’\documentclass[12pt]{article}’);
writeln(t,’\usepackage{amsmath}’);
writeln(t,’%\usepackage[rus]{babel}’);
writeln(t,’%\usepackage[cp1251]{inputenc}’);
writeln(t,’\begin{document}’);
close(t);
end;
procedure tex.add(s:string);
var
t:text;
begin
assign(t,namefl+’.tex’);
append(t);
writeln(t,’\[‘);
writeln(t,s);
writeln(t,’\]’);
close(t);
end;
procedure tex.closetex;
var
t:text;
begin
assign(t,namefl+’.tex’);
append(t);
writeln(t,’\end{document}’);
close(t);
end;
procedure tex.createpdf;
var
p:System.Diagnostics.Process;
begin
p:=new System.Diagnostics.Process();
p.StartInfo.FileName:=’pdflatex’;
p.StartInfo.Arguments:=namefl+’.tex’;
p.Start();
end;
procedure tex.openpdf;
var
p:System.Diagnostics.Process;
begin
p:=new System.Diagnostics.Process();
p.StartInfo.FileName:=namefl+’.pdf’;
p.Start();
end;

unit taskMath;

interface
uses mathUnit;

type taskderivative=record
task:string;
answer:string;
end;
type tasklimits=record
task:string;
answer:string;
end;

function taskintegral1(var s:string):string;

function tasklimits1(var s:string):string;
function tasklimits2(var s:string):string;
function tasklimits3(var s:string):string;
function tasklimits4(var s:string):string;

function taskderivative1(var s:string):string;
function taskderivative2(var s:string):string;

procedure rand(var x:taskderivative);
procedure rand(var x:tasklimits);

implementation

function correct(s:string):string;
var i:integer;
begin
for i:=1 to length(s) do
case s[i] of
‘{‘:s[i]:='(‘;
‘}’:s[i]:=’)’;
end;
result:=s;
end;

function tasklimits1(var s:string):string;
var
p1,p2:polynomialwithroot;
i:integer;
x:integer;
rez:string;
k1,k2,r1,r2:integer;
begin
randomize;
p1.roots(random(1,3));
p2.roots(random(1,3));
i:=random(p1.st)-1;
for i:=i downto 0 do
p2.root[random(p2.st)]:=p1.root[random(p1.st)];
i:=random(p1.st)+random(p2.st);
if(i>p1.st-1)then
begin
x:=p2.root[i-(p1.st-1)];
end
else
x:=p1.root[i];
p1.nw;
p2.nw;
rez:=’Find:\;lim_{x\to\!’+inttostr(x)+’}\quad \frac{‘+p1.pltostr+’}{‘+p2.pltostr+’}’;
k1:=0;
k2:=0;
r1:=1;
r2:=1;
s:=’При\; сокращении\;(x-‘+inttostr(x)+’)\; получается\;’;
for i:=0 to p1.st-1 do
if(p1.kof[i]=x)then
inc(k1)
else
r1:=r1*(x-p1.kof[i]);
for i:=0 to p2.st-1 do
if(p2.kof[i]=x)then
inc(k2)
else
r2:=r2*(x-p2.kof[i]);
if(k1>k2)then
s:=’0′;// s:=s+’нуль’;
if(k2>k1)then
s:=’inf’;//s:=s+’нуль\; в\; знаменателе\; и\; получается\; бесконечность’;
if(k1=k2)then
s:=inttostr(r1)+’/’+inttostr(r2);//s:=s+’число\;’+floattostr(r1/r2);
s:=correct(s);
result:=rez;
end;
function tasklimits2(var s:string):string;
var
f:polynomialwithroot;
g,x:polynomial;
st:integer;
rez,answ:string;
begin
f.roots(random(1,2));
g.nw(random(1,2));
x.nw(random(1,2));
st:=f.root[random(0,f.st-1)];
rez:=’Find:\;lim_{x\to\!’+inttostr(st)+’}\quad \frac{‘+(f*g).pltostr+’}{‘+(f*x).pltostr+’}’;
s:=floattostr(g.into(st))+’/’+floattostr(x.into(st));
s:=correct(s);
result:=rez;
end;
function tasklimits3(var s:string):string;
var
f,g:sqrnpolynomial;
x:polynomial;
rez,answ:string;
begin
f.nw(random(1,4),2);
g.nw(f.x.st,2);
x:=f.x-g.x;
rez:=’Find:\;lim_{x\to\infty}\quad ‘+f.s+’-‘+g.s;
if(x.st+1=f.x.st)then
s:=floattostr(x.kof[x.st])+’/’+floattostr(g.x.kof[g.x.st]+f.x.kof[g.x.st])
else
s:=’0′;
s:=correct(s);
result:=rez;
end;
function tasklimits4(var s:string):string;
var
f,g:polynomialwithroot;
kf1,kf2:polynomial;
a,i,j,num:integer;
rez,add:string;
begin
f.roots(random(1,2));
g.roots(random((f.st),3));
num:=random(1,f.st-1);
for i:=0 to num-1 do
g.root[i]:=f.root[i];
g.nw;
// writeln(num);
sleep(1000);
num:=0;
for i:=0 to f.st-1 do
for j:=0 to g.st-1 do
if(f.kof[i]=g.kof[j])then num+=1;
// writeln(num);
// sleep(1000);
kf1.nw(random(1,2));
kf2.nw(0);
a:=random(2,5);
add:=’\frac{‘+(kf1+kf2).pltostr+’}{‘+kf1.pltostr+’}’;
for i:=1 to length(s) do
if(add[i]=’x’)then add[i]:=’n’;
rez:=’Find \; x,\; when: \;lim_{n\to\infty}\quad ‘+
add+’\frac{(‘+f.pltostr+’)^{n^’+inttostr(a)+’}}{(‘+g.pltostr+’)^{n^’+inttostr(a)+’}}=e^{‘+floattostr(kf2.kof[0])+’}’;
s:=inttostr(num);
result:=rez;
end;

function taskintegral1(var s:string):string;
var
tr1:sinx;
tr2:cosx;
tr3:tgx;
tr4:ctgx;
f,g:polynomial;
r:integer;
rez:string;
begin
rez:=’Find\;\int ‘;
r:=random(1,5);
case r of
1:begin
tr1.x.nw(random(1,3));
tr1.nw;
s:=tr1.s;
tr1.derivative;
rez:=rez+tr1.s+’\;dx’;
end;
2:begin
tr2.x.nw(random(1,3));
tr2.nw;
s:=tr2.s;
tr2.derivative;
rez:=rez+tr2.s+’\;dx’;
end;
3:begin
tr3.x.nw(random(1,3));
tr3.nw;
s:=tr3.s;
tr3.derivative;
rez:=rez+tr3.s+’\;dx’;
end;
4:begin
tr4.x.nw(random(1,3));
tr4.nw;
s:=tr4.s;
tr4.derivative;
rez:=rez+tr4.s+’\;dx’;
end;
5:begin
r:=random(1,2);
f.nw(random(1,3));
rez:=rez+'(‘+f.pltostr+’)’;
while(r<>0)do
begin
g.nw(random(1,3));
f:=f*g;
rez:=rez+'(‘+g.pltostr+’)’;
r:=r-1;
end;
f.integral;
s:=correct(f.pltostr);
rez:=rez+’\;dx’;
end;
end;
s:=correct(s);
result:=rez;
end;

function taskderivative1(var s:string):string;
var
sinx1,sinx2:sinx;
cosx1,cosx2:cosx;
tgx1,tgx2:tgx;
ctgx1,ctgx2:ctgx;
f,g:polynomial;
r:integer;
rez:string;
bg,answ:string;
begin
randomize;
sinx1.x.nw(random(1,3));
sinx1.nw;
sinx2:=sinx1;
sinx2.derivative;

tgx1.x.nw(random(1,3));
tgx1.nw;
tgx2:=tgx1;
tgx2.derivative;

cosx1.x.nw(random(1,3));
cosx1.nw;
cosx2:=cosx1;
cosx2.derivative;

ctgx1.x.nw(random(1,3));
ctgx1.nw;
ctgx2:=ctgx1;
ctgx2.derivative;

r:=random(1,4);
case r of
1:begin
rez:=rez+sinx1.s;
answ:=sinx2.s;
end;
2:begin
rez:=rez+cosx1.s;
answ:=cosx2.s;
end;
3:begin
rez:=rez+tgx1.s;
answ:='(‘+tgx2.x.pltostr+’)/(cos(‘+tgx1.x.pltostr+’)^2)’;
end;
4:begin
rez:=rez+ctgx1.s;
answ:='(‘+(-1*ctgx2.x).pltostr+’))/(sin(‘+ctgx1.x.pltostr+’)^2)’;
end;
end;
bg:=rez;
rez:=’Find\; \frac{d}{dx}\;(‘+rez;
rez:=rez+’)’;
r:=random(1,2);
f.nw(random(1,3));
while(r>0)do
begin
g.nw(random(1,3));
rez:=rez+'(‘;
rez:=rez+g.pltostr;
rez:=rez+’)’;
f:=f*g;
r:=r-1;
end;
rez:=rez+’)’;
answ:='(‘+answ+’)*(‘+g.pltostr+’)+(‘;
g.derivative;
answ:=answ+bg+’)*(‘+g.pltostr+’)’;
s:=answ;
s:=correct(s);
result:=rez;
end;
function taskderivative2(var s:string):string;
var
sinx1,sinx2:sinx;
cosx1,cosx2:cosx;
tgx1,tgx2:tgx;
ctgx1,ctgx2:ctgx;
f,g,st:polynomial;
r:integer;
rez:string;
answ,bg:string;
begin
randomize;
sinx1.x.nw(random(1,3));
sinx1.nw;
sinx2:=sinx1;
sinx2.derivative;

tgx1.x.nw(random(1,3));
tgx1.nw;
tgx2:=tgx1;
tgx2.derivative;

cosx1.x.nw(random(1,3));
cosx1.nw;
cosx2:=cosx1;
cosx2.derivative;

ctgx1.x.nw(random(1,3));
ctgx1.nw;
ctgx2:=ctgx1;
ctgx2.derivative;

r:=random(1,4);
case r of
1:begin
rez:=rez+sinx1.s;
answ:=sinx2.s;
end;
2:begin
rez:=rez+cosx1.s;
answ:=cosx2.s;
end;
3:begin
rez:=rez+tgx1.s;
answ:='(‘+tgx2.x.pltostr+’)/(cos(‘+tgx1.x.pltostr+’)^2)’;
end;
4:begin
rez:=rez+ctgx1.s;
answ:='(‘+(-1*ctgx2.x).pltostr+’))/(sin(‘+ctgx1.x.pltostr+’)^2)’;
end;
end;
bg:=rez;
rez:=’Find\; \frac{d}{dx}\;(‘+rez;
rez:=rez+’)^{‘;
f.nw(random(1,3));
rez:=rez+f.pltostr+’}’;
st:=f;
st.derivative;
answ:='((‘+bg+’)^{‘+f.pltostr+’})*((‘+st.pltostr+’)*ln(‘+bg+’)+(‘+f.pltostr+’)*(‘+answ+’)/(‘+bg+’)’;
s:=answ;
s:=correct(s);
result:=rez;
end;
procedure rand(var x:taskderivative);
var
r:integer;
begin
randomize;
r:=random(1,2);
case r of
1:x.task:=taskderivative1(x.answer);
2:x.task:=taskderivative2(x.answer);
end;
end;
procedure rand(var x:tasklimits);
var
r:integer;
begin
randomize;
r:=random(1,4);
case r of
1:x.task:=tasklimits1(x.answer);
2:x.task:=tasklimits2(x.answer);
3:x.task:=tasklimits3(x.answer);
4:x.task:=tasklimits4(x.answer);
end;
end;

end.