void deriv705a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a,bc,bd,c;
do {
a = rndr(r);
bc = rndr(r);
bd = rndr(r);
c = rndr(r);
} while (!(a!=0 && bc<bd && bc>0 && bd>0 && (bc*bc)%(bd*bd)!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/(%s)^2)*arcsin(%s)",
polynomial(buf[0],2,
1, chprintf(buf[1],"arctg(%s)", memb(buf[2], 1,a,1,1,"x",false)),
c, ""
),
polynomial(buf[3],2, a*a,"",1,"x^2"),
fraction(buf[4], bc,1,bd)
);
sprintf(src, "y(x)=((arctg(x/a))/((a^2+x^2)^2))*arcsin(b)");
sprintf(answ[0], "y(x)`=((%s)/((%s)^3))*arcsin(%s)",
polynomial(buf[0],2,
a,"",
-4,polynomial(buf[1],2,
1,chprintf(buf[2],"x*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)),
-c,"x"
)
),
polynomial(buf[4],2, a*a,"", 1,"x^2"),
fraction(buf[5], bc,1,bd)
);
sprintf(answ[1], "y(x)`=((%s)/((%s)^4))*arcsin(%s)",
polynomial(buf[0],2,
a,"",
-2,polynomial(buf[1],2, 1,chprintf(buf[2],"x*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)), -c,"x")
),
polynomial(buf[4],2, a*a,"", 1,"x^2"),
fraction(buf[5], bc,1,bd)
);
sprintf(answ[2], "y(x)`=((%s)/((%s)^3))*arcsin(%s)",
polynomial(buf[0],2,
a*a,"",
-4,polynomial(buf[1],2, 1,chprintf(buf[2],"x^2*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)), -c,"x^2")
),
polynomial(buf[4],2, a*a,"", 1,"x^2"),
fraction(buf[5], bc,1,bd)
);
sprintf(answ[3], "y(x)`=((%s)/(sqrt(1-%s)*(%s)^4))",
polynomial(buf[0],2,
a,"",
-2,polynomial(buf[1],2, 1,chprintf(buf[2],"x*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)), -c,"x")
),
fraction(buf[5], bc*bc,1,bd*bd),
polynomial(buf[4],2, a*a,"", 1,"x^2")
);
}
void deriv702a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c, k;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
k = rndr(r);
} while (!(a!=0 && b!=0 && k!=0 && k!=2 && k!=1));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=(sin(%s)/(%s))*tg(%s)",
polynomial(buf[0],2, a,"x^2",b,""),
polynomial(buf[1],2, 1,"cos(x)^2", c,""),
memb(buf[2], 1,k,1,1,"pi", false)
);
sprintf(src, "y=(sin(a*x^2+b)/(cos(x)^2+c))*tg(pi/k)");
sprintf(answ[0], "y(x)`=tg(%s)*(((%s)*cos(%s)*(%s)+!(sin(2*x))*sin(%s))/((%s)^2))",
memb(buf[0], 1,k,1,1,"pi", false),
polynomial(buf[1],1, 2*a,"x"),
polynomial(buf[2],2, a,"x^2",b,""),
polynomial(buf[3],2, 1,"cos(x)^2", c,""),
polynomial(buf[4],2, a,"x^2",b,""),
polynomial(buf[5],2, 1,"cos(x)^2", c,"")
);
sprintf(answ[1], "y(x)`=tg(%s)*((%s)*cos(%s)-!(sin(2*x))*sin(%s))/((%s)^2))",
memb(buf[0], 1,k,1,1,"pi", false),
polynomial(buf[1],2, 1,"cos(x)^2", c,""),
polynomial(buf[2],2, a,"x^2",b,""),
polynomial(buf[3],2, a,"x^2",b,""),
polynomial(buf[4],2, 1,"cos(x)^2", c,"")
);
sprintf(answ[2], "y(x)`=(pi/(%s))*(%s)/((%s)^2))",
polynomial(buf[0],1, k*k,chprintf(buf[1],"cos(%s)^2", memb(buf[2], 1,k,1,1,"pi", false))),
polynomial(buf[3],2,
1,chprintf(buf[4], "sin(2*x)*sin(%s)", polynomial(buf[5],2, a,"x^2",b,"")),
-2*a, chprintf(buf[6], "x*(%s)*cos(%s)",
polynomial(buf[7],2, 1,"cos(x)^2", c,""),
polynomial(buf[8],2, a,"x^2", b,"")
)
),
polynomial(buf[9],2, 1,"cos(x)^2", c,"")
);
sprintf(answ[3], "y(x)`=tg(%s)*(((%s)*cos(%s)*(%s)-2*cos(x)*sin(%s))/((%s)^2))",
memb(buf[0], 1,k,1,1,"pi", false),
polynomial(buf[1],1, 2*a,"x"),
polynomial(buf[2],2, a,"x^2",b,""),
polynomial(buf[3],2, 1,"cos(x)^2", c,""),
polynomial(buf[4],2, a,"x^2",b,""),
polynomial(buf[5],2, 1,"cos(x)^2", c,"")
);
}
P serialize_member_name( const T& , P end, M memb )
{
const char* name = memb();
*(end++)='"';
for (; *name!='\0'; ++name) *(end++) = *name;
*(end++)='"';
*(end++) = ':';
return end;
}
void deriv701a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, m, n, c, d;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
d = rndr(r);
m = rndr(range(2, 4));
n = rndr(range(2, 4));
} while (!(c>0 && d>0 && m*n>2 && a!=b && a!=0 && b!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=(%s)/(%s)",
memb(buf[0], 1,1,m,1, polynomial(buf[1],2, a,"x", b,""), false),
memb(buf[2], 1,1,1,n, polynomial(buf[3],2, c,"x", d,""), false)
);
sprintf(src, "y=((a*x+b)^m)/root(n,c*x+d)");
sprintf(answ[0], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, a*c*(m*n-1),"x", a*m*n*d-c*b,""),
memb(buf[3], n,1,n+1,n, polynomial(buf[4],2, c,"x",d,""), false)
);
sprintf(answ[1], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], m,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, a*c,"x", -c*b,""),
memb(buf[3], n,1,2,n, polynomial(buf[4],2, c,"x",d,""), false)
);
sprintf(answ[2], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], m,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, m*a-c,"x", d*b,""),
memb(buf[3], n,1,n+1,n, polynomial(buf[4],2, c,"x",d,""), false)
);
sprintf(answ[3], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, a*c,"x", a*d-c*b,""),
memb(buf[3], n,1,2,n, polynomial(buf[4],2, c,"x",d,""), false)
);
}
void deriv703a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a!=0 && c!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=((%s)/sqrt(%s))*arctg(%d)",
polynomial(buf[0],2,
1,chprintf(buf[1], "arcsin(%s)", memb(buf[2], 1,a,1,1,"x", false)),
c,""
),
polynomial(buf[3],2, a*a,"", -1,"x^2"),
b
);
sprintf(src, "y(x)=((arcsin(x/a)+c)/sqrt(a^2-x^2))*arctg(b)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*arctg(%d)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a,"", -1,"x^2"),
b
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*arctg(%d)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a,"", -1,"x^2"),
b
);
sprintf(answ[2], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a*(1+b*b),"", -(1+b*b),"x^2")
);
sprintf(answ[3], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
2,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a*(1+b*b),"", -(1+b*b),"x^2")
);
}
void deriv707a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a!=0 && b>1));
char arctgxac[BUFSZ];
polynomial(arctgxac,2,
1,chprintf(buf[0],"arctg(%s)", memb(buf[1], 1,a,1,1, "x", false)),
c,""
);
char xarctgxac[BUFSZ];
sprintf(xarctgxac, "x*(%s)", arctgxac);
char a2x2[BUFSZ];
polynomial(a2x2,2, a*a,"",1,"x^2");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/sqrt(%s))*ln(%d)", arctgxac, a2x2, b);
sprintf(src, "y(x)=((arctg(x/a)+c)/sqrt(a*x^2+b))*ln(b)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*ln(%d)",
polynomial(buf[0],2, a,"", -1,xarctgxac),
a2x2,
b
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*ln(%d)",
polynomial(buf[0],2, a,"", -2,xarctgxac),
a2x2,
b
);
sprintf(answ[2], "y(x)`=((%s)/(%s))*ln(%d)",
polynomial(buf[0],2, a,"", -1,xarctgxac),
a2x2,
b
);
sprintf(answ[3], "y(x)`=((%s)/(%s))",
polynomial(buf[0],2, a,"", -1,xarctgxac),
polynomial(buf[1],1, b,a2x2)
);
}
bool OsiConicCut::consistent (const OsiConicSolverInterface & si) const {
// check whether the members are actually existing variables in si
int max_index = si.getNumCols()-1;
for (int i=0; i<size_; ++i) {
if (members_[i]>max_index) {
return false;
}
}
// return false if a member is repeating
std::set<int> memb (members_, members_+size_);
if (memb.size()!=size_) {
memb.clear();
return false;
}
memb.clear();
// todo(aykut): consistency of other data elements?
return true;
}
P unserialize_member_name( T& , P beg, P end, M memb, bool& unserialized )
{
const char* name = memb();
P start = beg;
if ( !parser::is_string(beg, end) )
throw expected_of("\"", std::distance(beg, end));
++beg;
unserialized = true;
for ( ; beg!=end && *name!='\0' && *beg==*name && *beg!='"'; ++name, ++beg)
{
if (*name!=*beg)
{
unserialized = false;
break;
}
}
if (beg==end)
throw unexpected_end_fragment();
if (*beg!='"' || *name!='\0')
unserialized = false;
if ( !unserialized ) return start;
++beg;
beg = parser::parse_space(beg, end);
if (beg==end)
throw unexpected_end_fragment();
if (*beg!=':')
throw expected_of(":", std::distance(beg, end));
++beg;
beg = parser::parse_space(beg, end);
if (beg==end)
throw unexpected_end_fragment();
return beg;
}
void deriv706a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, n;
do {
a = rndr(r);
n = rndr(r);
} while (!(a!=0 && n>0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=arctg(%s)/(%s)",
memb(buf[0], 1,a,1,1,"x", false),
memb(buf[1], 1,1,n,1, polynomial(buf[2],2, a*a,"",1,"x^2"), false)
);
sprintf(src, "y(x)=arctg(x/a)/(a^2+x^2)^n");
char xarctg[BUFSZ];
sprintf(xarctg, "x*arctg(%s)", memb(buf[0], 1,a,1,1, "x", false));
sprintf(answ[0], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a,"", -2*n,xarctg),
memb(buf[1], 1,1,n+1,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[1], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a*a,"", -4*n,xarctg),
memb(buf[1], 1,1,n+1,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[2], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a,polynomial(buf[1],2, a*a,"", 1,"x^2"), -2*n,xarctg),
memb(buf[2], 1,1,n,1, polynomial(buf[3],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[3], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a*a,"", -2*n,xarctg),
memb(buf[1], 1,1,n,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
}
void deriv704a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, n;
do {
a = rndr(r);
n = rndr(r);
} while (!(a!=0 && n>1));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=(%s)/sqrt(%s)",
memb(buf[0], 1,1,n,1, chprintf(buf[1],"arccos(%s)", memb(buf[2], 1,a,1,1, "x", false)), false),
polynomial(buf[3],2, a*a,"", -1,"x^2")
);
sprintf(src, "y(x)=arccos(x/a)^n/sqrt(a^2-x^2)");
sprintf(answ[0], "y(x)`=((%s)*(%s))/sqrt((%s)^3)",
memb(buf[0], 1,1,n-1,1, chprintf(buf[1],"arccos(%s)", memb(buf[2], 1,a,1,1, "x", false)), false),
polynomial(buf[3],2,
1,chprintf(buf[4], "x*arccos(%s)", memb(buf[5], 1,a,1,1,"x", false)),
-n, chprintf(buf[6], "sqrt(%s)", polynomial(buf[7],2,a*a,"",-1,"x^2"))
),
polynomial(buf[7],2, a*a,"", -1,"x^2")
);
sprintf(answ[1], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2,
2*a, chprintf(buf[1], "x*(%s)", memb(buf[2], 1,1,n,1, chprintf(buf[3],"arccos(%s)", memb(buf[4],1,a,1,1,"x", false)), false)),
-n,chprintf(buf[5], "sqrt(%s)*(%s)",
polynomial(buf[6],2, a*a,"", -1,"x^2"),
memb(buf[7], 1,1,n-1,1, chprintf(buf[8],"arccos(%s)", memb(buf[9],1,a,1,1,"x", false)), false)
)
),
polynomial(buf[10],2, a*a,"", -1,"x^2")
);
sprintf(answ[2], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,n-1,1, chprintf(buf[1], "arccos(%s)", memb(buf[2], 1,a,1,1,"x", false)), false),
polynomial(buf[3],2,
n,chprintf(buf[4],"sqrt(%s)", polynomial(buf[5],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[6],"x*arccos(%s)", memb(buf[7], 1,a,1,1,"x", false))
),
memb(buf[8], a,1,1,1, chprintf(buf[9],"sqrt((%s)^3)", polynomial(buf[10],2,a*a,"",-1,"x^2")), false)
);
sprintf(answ[3], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,n-1,1, chprintf(buf[1], "arccos(%s)", memb(buf[2], 1,a,1,1,"x", false)), false),
polynomial(buf[3],2,
-n*a, polynomial(buf[5],2, a*a,"", -1,"x^2"),
1,chprintf(buf[6],"x*arccos(%s)", memb(buf[7], 1,a,1,1,"x", false))
),
polynomial(buf[10],2,a*a,"",-1,"x^2")
);
}
