clear trace=1 abs(2) check(last = 2) -- abs.cpp abs(2.0) check(last = 2) -- abs.cpp abs(-2) check(last = 2) -- abs.cpp abs(-2.0) check(last = 2) -- abs.cpp abs(a) check(last = abs(a)) -- abs.cpp abs(-a) check(last = abs(a)) -- abs.cpp abs(2*a) check(last = 2*abs(a)) -- abs.cpp abs(-2*a) check(last = 2*abs(a)) -- abs.cpp abs(2.0*a) check(last = 2*abs(a)) -- abs.cpp abs(-2.0*a) check(last = 2*abs(a)) -- abs.cpp abs(a-b)+abs(b-a) check(last = 2*abs(a-b)) -- abs.cpp abs(3 + 4 i) check(last = 5) -- abs.cpp abs((2,3,4)) check(last = 29^(1/2)) -- abs.cpp abs(a*b) check(last = abs(a)*abs(b)) -- abs.cpp abs(a/b) check(last = abs(a)/abs(b)) -- abs.cpp abs(1/a^b) check(last = 1/(abs(a^b))) -- abs.cpp P=(u*cos(v),u*sin(v),v) abs(cross(d(P,u),d(P,v))) check(last = (1+u^2)^(1/2)) -- abs.cpp clear trace=1 clear trace=1 adj(((a,b),(c,d))) check(last = ((d,-b),(-c,a))) -- adj.cpp adj(((1,2),(3,4))) check(last = ((4,-2),(-3,1))) -- adj.cpp adj(((2,3,-2,5),(6,-2,1,4),(5,10,3,-2),(-1,2,2,3))) check(last = ((-4,-177,-73,194),(-117,117,-99,-27),(310,-129,-44,-374),(-130,-51,71,-211))) -- adj.cpp clear trace=1 clear trace=1 clear trace=1 arccos(1) check(last = 0) -- arccos.cpp arccos(1/2) check(last = 1/3*pi) -- arccos.cpp arccos(0) check(last = 1/2*pi) -- arccos.cpp arccos(-1/2) check(last = 2/3*pi) -- arccos.cpp arccos(-1) check(last = pi) -- arccos.cpp arccos(cos(0)) check(last = 0) -- arccos.cpp arccos(cos(1/3*pi)) check(last = 1/3*pi) -- arccos.cpp arccos(cos(1/2*pi)) check(last = 1/2*pi) -- arccos.cpp arccos(cos(2/3*pi)) check(last = 2/3*pi) -- arccos.cpp arccos(cos(pi)) check(last = pi) -- arccos.cpp arccos(cos(x)) check(last = x) -- arccos.cpp arccos(1/sqrt(2)) check(last = 1/4*pi) -- arccos.cpp arccos(-1/sqrt(2)) check(last = 3/4*pi) -- arccos.cpp arccos(cos(1/4*pi)) check(last = 1/4*pi) -- arccos.cpp arccos(cos(3/4*pi)) check(last = 3/4*pi) -- arccos.cpp clear trace=1 arccosh(1.0) check(last = 0) -- arccosh.cpp arccosh(1) check(last = 0) -- arccosh.cpp arccosh(cosh(x)) check(last = x) -- arccosh.cpp clear trace=1 arcsin(-1) check(last = -1/2*pi) -- arcsin.cpp arcsin(-1/2) check(last = -1/6*pi) -- arcsin.cpp arcsin(0) check(last = 0) -- arcsin.cpp arcsin(1/2) check(last = 1/6*pi) -- arcsin.cpp arcsin(1) check(last = 1/2*pi) -- arcsin.cpp arcsin(sin(-1/2*pi)) check(last = -1/2*pi) -- arcsin.cpp arcsin(sin(-1/6*pi)) check(last = -1/6*pi) -- arcsin.cpp arcsin(sin(0)) check(last = 0) -- arcsin.cpp arcsin(sin(1/6*pi)) check(last = 1/6*pi) -- arcsin.cpp arcsin(sin(1/2*pi)) check(last = 1/2*pi) -- arcsin.cpp arcsin(sin(x)) check(last = x) -- arcsin.cpp arcsin(1/sqrt(2)) check(last = 1/4*pi) -- arcsin.cpp arcsin(-1/sqrt(2)) check(last = -1/4*pi) -- arcsin.cpp arcsin(sin(1/4*pi)) check(last = 1/4*pi) -- arcsin.cpp arcsin(sin(-1/4*pi)) check(last = -1/4*pi) -- arcsin.cpp clear trace=1 arcsinh(0.0) check(last = 0) -- arcsinh.cpp arcsinh(0) check(last = 0) -- arcsinh.cpp arcsinh(sinh(x)) check(last = x) -- arcsinh.cpp clear trace=1 arctan(x) check(last = arctan(x)) -- arctan.cpp arctan(-x) check(last = -arctan(x)) -- arctan.cpp arctan(0) check(last = 0) -- arctan.cpp arctan(tan(x)) check(last = x) -- arctan.cpp arctan(1/sqrt(3))-pi/6 check(last = 0) -- arctan.cpp arctan(1)-pi/4 check(last = 0) -- arctan.cpp arctan(sqrt(3))-pi/3 check(last = 0) -- arctan.cpp arctan(a-b) check(last = arctan(a-b)) -- arctan.cpp arctan(b-a) check(last = -arctan(a-b)) -- arctan.cpp arctan(tan(x)) check(last = x) -- arctan.cpp clear trace=1 arctanh(0.0) check(last = 0) -- arctanh.cpp arctanh(0) check(last = 0) -- arctanh.cpp arctanh(tanh(x)) check(last = x) -- arctanh.cpp clear trace=1 arg(1+i) check(last = 1/4*pi) -- arg.cpp arg(1-i) check(last = -1/4*pi) -- arg.cpp arg(-1+i) check(last = 3/4*pi) -- arg.cpp arg(-1-i) check(last = -3/4*pi) -- arg.cpp arg((-1)^(1/3)) check(last = 1/3*pi) -- arg.cpp arg(1+exp(i*pi/3)) check(last = 1/6*pi) -- arg.cpp arg((-1)^(1/6)*exp(i*pi/6)) check(last = 1/3*pi) -- arg.cpp arg(a) check(last = 0) -- arg.cpp arg(a*exp(b+i*pi/5)) check(last = 1/5*pi) -- arg.cpp arg(-1) check(last = -pi) -- arg.cpp arg(a) check(last = 0) -- arg.cpp arg(-a) check(last = -pi) -- arg.cpp arg(-(-1)^(1/3)) check(last = -2/3*pi) -- arg.cpp arg(-exp(i*pi/3)) check(last = -2/3*pi) -- arg.cpp arg(-i) check(last = -1/2*pi) -- arg.cpp arg((a+b*i)/(c+d*i)) check(last = arctan(b/a)-arctan(d/c)) -- arg.cpp clear trace=1 clear trace=1 (x+3)^3 check(last = x^3+9*x^2+27*x+27) -- bake.cpp factor check(last = (x+3)^3) -- bake.cpp clear trace=1 besselj(x,n) check(last = besselj(x,n)) -- besselj.cpp besselj(0,0) check(last = 1) -- besselj.cpp besselj(0,1) check(last = 0) -- besselj.cpp besselj(0,-1) check(last = 0) -- besselj.cpp besselj(x,1/2)-sqrt(2/pi/x)*sin(x) check(last = 0) -- besselj.cpp besselj(x,-1/2)-sqrt(2/pi/x)*cos(x) check(last = 0) -- besselj.cpp besselj(x,3/2)-sqrt(2/pi/x)*(sin(x)/x-cos(x)) check(last = 0) -- besselj.cpp besselj(x,-3/2)-sqrt(2/pi/x)*(-cos(x)/x-sin(x)) check(last = 0) -- besselj.cpp besselj(x,5/2)-sqrt(2/pi/x)*((3/x^2-1)*sin(x)-3/x*cos(x)) check(last = 0) -- besselj.cpp besselj(x,-5/2)-sqrt(2/pi/x)*((3/x^2-1)*cos(x)+3/x*sin(x)) check(last = 0) -- besselj.cpp besselj(x,3/2)-(1/x)*besselj(x,1/2)+besselj(x,-1/2) check(last = 0) -- besselj.cpp besselj(x,-3/2)+(1/x)*besselj(x,-1/2)+besselj(x,1/2) check(last = 0) -- besselj.cpp y=besselj(x,5/2) x^2*d(y,x,x)+x*d(y,x)+(x^2-(5/2)^2)*y check(last = 0) -- besselj.cpp y=quote(y) clear trace=1 bessely(x,n) check(last = bessely(x,n)) -- bessely.cpp clear trace=1 clear trace=1 clear trace=1 ceiling(a) check(last = ceiling(a)) -- ceiling.cpp ceiling(a+b) check(last = ceiling(a+b)) -- ceiling.cpp ceiling(5/2) check(last = 3) -- ceiling.cpp ceiling(4/2) check(last = 2) -- ceiling.cpp ceiling(3/2) check(last = 2) -- ceiling.cpp ceiling(2/2) check(last = 1) -- ceiling.cpp ceiling(1/2) check(last = 1) -- ceiling.cpp ceiling(0/2) check(last = 0) -- ceiling.cpp ceiling(-1/2) check(last = 0) -- ceiling.cpp ceiling(-2/2) check(last = -1) -- ceiling.cpp ceiling(-3/2) check(last = -1) -- ceiling.cpp ceiling(-4/2) check(last = -2) -- ceiling.cpp ceiling(-5/2) check(last = -2) -- ceiling.cpp ceiling(5/2.0) check(last = 3) -- ceiling.cpp ceiling(4/2.0) check(last = 2) -- ceiling.cpp ceiling(3/2.0) check(last = 2) -- ceiling.cpp ceiling(2/2.0) check(last = 1) -- ceiling.cpp ceiling(1/2.0) check(last = 1) -- ceiling.cpp ceiling(0.0) check(last = 0) -- ceiling.cpp ceiling(-1/2.0) check(last = 0) -- ceiling.cpp ceiling(-2/2.0) check(last = -1) -- ceiling.cpp ceiling(-3/2.0) check(last = -1) -- ceiling.cpp ceiling(-4/2.0) check(last = -2) -- ceiling.cpp ceiling(-5/2.0) check(last = -2) -- ceiling.cpp clear trace=1 choose(52,5) check(last = 2598960) -- choose.cpp choose(n,k) check(last = n!/(k!*(-k+n)!)) -- choose.cpp choose(0,k) check(last = 1/(k!*(-k)!)) -- choose.cpp choose(n,0) check(last = 1) -- choose.cpp choose(-1,k) check(last = 0) -- choose.cpp choose(n,-1) check(last = 0) -- choose.cpp clear trace=1 circexp(cos(x)) check(last = 1/2*exp(-i*x)+1/2*exp(i*x)) -- circexp.cpp circexp(sin(x)) check(last = 1/2*i*exp(-i*x)-1/2*i*exp(i*x)) -- circexp.cpp circexp(tan(x)) check(last = i*exp(-i*x)/(exp(-i*x)+exp(i*x))-i*exp(i*x)/(exp(-i*x)+exp(i*x))) -- circexp.cpp circexp(cosh(x)) check(last = 1/2*exp(x)+1/2*exp(-x)) -- circexp.cpp circexp(sinh(x)) check(last = 1/2*exp(x)-1/2*exp(-x)) -- circexp.cpp circexp(tanh(x)) check(last = -1/(1+exp(2*x))+exp(2*x)/(1+exp(2*x))) -- circexp.cpp circexp((cos(x),sin(x))) check(last = (1/2*exp(-i*x)+1/2*exp(i*x),1/2*i*exp(-i*x)-1/2*i*exp(i*x))) -- circexp.cpp circexp(cos(x)*sin(x))-expcos(x)*expsin(x) check(last = 0) -- circexp.cpp clear trace=1 clear trace=1 clock(exp(i pi/3)) check(last = (-1)^(1/3)) -- clock.cpp clock(exp(-i pi/3)) check(last = -(-1)^(2/3)) -- clock.cpp rect(clock(3+4*i)) check(last = 3+4*i) -- clock.cpp clear trace=1 coeff(40*x^3+30*x^2+20*x+10,3) check(last = 40) -- coeff.cpp coeff(40*x^3+30*x^2+20*x+10,2) check(last = 30) -- coeff.cpp coeff(40*x^3+30*x^2+20*x+10,1) check(last = 20) -- coeff.cpp coeff(40*x^3+30*x^2+20*x+10,0) check(last = 10) -- coeff.cpp coeff(a*t^3+b*t^2+c*t+d,t,3) check(last = a) -- coeff.cpp coeff(a*t^3+b*t^2+c*t+d,t,2) check(last = b) -- coeff.cpp coeff(a*t^3+b*t^2+c*t+d,t,1) check(last = c) -- coeff.cpp coeff(a*t^3+b*t^2+c*t+d,t,0) check(last = d) -- coeff.cpp clear trace=1 cofactor(((1,2),(3,4)),1,1) check(last = 4) -- cofactor.cpp cofactor(((1,2),(3,4)),1,2) check(last = -3) -- cofactor.cpp cofactor(((1,2),(3,4)),2,1) check(last = -2) -- cofactor.cpp cofactor(((1,2),(3,4)),2,2) check(last = 1) -- cofactor.cpp cofactor(((1,2,3),(4,5,6),(7,8,9)),1,2) check(last = 6) -- cofactor.cpp clear trace=1 condense(a/(a+b)+b/(a+b)) check(last = 1) -- condense.cpp psi(n) = exp(-r/n) laguerre(2r/n,n-1,1) psi(3) check(last = 3*exp(-1/3*r)-2*r*exp(-1/3*r)+2/9*r^2*exp(-1/3*r)) -- condense.cpp condense(last) check(last = exp(-1/3*r)*(3-2*r+2/9*r^2)) -- condense.cpp psi()=psi condense(-3 exp(-1/3 r + i phi) cos(theta) - 6 exp(-1/3 r + i phi) cos(theta) sin(theta)^2 + 12 exp(-1/3 r + i phi) cos(theta)^3) check(last = 3*exp(-1/3*r+i*phi)*(-1+4*cos(theta)^2-2*sin(theta)^2)*cos(theta)) -- condense.cpp clear trace=1 clear trace=1 clear trace=1 contract(0) check(last = 0) -- contract.cpp contract(0.0) check(last = 0) -- contract.cpp contract(((a,b),(c,d))) check(last = a+d) -- contract.cpp contract(((1,2),(3,4)),1,2) check(last = 5) -- contract.cpp A=((a11,a12),(a21,a22)) B=((b11,b12),(b21,b22)) contract(outer(A,B),2,3) check(last = ((a11*b11+a12*b21,a11*b12+a12*b22),(a21*b11+a22*b21,a21*b12+a22*b22))) -- contract.cpp A=quote(A) B=quote(B) clear trace=1 cos(x) check(last = cos(x)) -- cos.cpp cos(-x) check(last = cos(x)) -- cos.cpp cos(b-a) check(last = cos(a-b)) -- cos.cpp f(a,x)=1+cos(a/360*2*pi)-x f(0,1) check(last = 1) -- cos.cpp f(90,0) check(last = 1) -- cos.cpp f(180,-1) check(last = 1) -- cos.cpp f(270,0) check(last = 1) -- cos.cpp f(360,1) check(last = 1) -- cos.cpp f(-90,0) check(last = 1) -- cos.cpp f(-180,-1) check(last = 1) -- cos.cpp f(-270,0) check(last = 1) -- cos.cpp f(-360,1) check(last = 1) -- cos.cpp f(45,sqrt(2)/2) check(last = 1) -- cos.cpp f(135,-sqrt(2)/2) check(last = 1) -- cos.cpp f(225,-sqrt(2)/2) check(last = 1) -- cos.cpp f(315,sqrt(2)/2) check(last = 1) -- cos.cpp f(-45,sqrt(2)/2) check(last = 1) -- cos.cpp f(-135,-sqrt(2)/2) check(last = 1) -- cos.cpp f(-225,-sqrt(2)/2) check(last = 1) -- cos.cpp f(-315,sqrt(2)/2) check(last = 1) -- cos.cpp f(30,sqrt(3)/2) check(last = 1) -- cos.cpp f(150,-sqrt(3)/2) check(last = 1) -- cos.cpp f(210,-sqrt(3)/2) check(last = 1) -- cos.cpp f(330,sqrt(3)/2) check(last = 1) -- cos.cpp f(-30,sqrt(3)/2) check(last = 1) -- cos.cpp f(-150,-sqrt(3)/2) check(last = 1) -- cos.cpp f(-210,-sqrt(3)/2) check(last = 1) -- cos.cpp f(-330,sqrt(3)/2) check(last = 1) -- cos.cpp f(60,1/2) check(last = 1) -- cos.cpp f(120,-1/2) check(last = 1) -- cos.cpp f(240,-1/2) check(last = 1) -- cos.cpp f(300,1/2) check(last = 1) -- cos.cpp f(-60,1/2) check(last = 1) -- cos.cpp f(-120,-1/2) check(last = 1) -- cos.cpp f(-240,-1/2) check(last = 1) -- cos.cpp f(-300,1/2) check(last = 1) -- cos.cpp f=quote(f) cos(arccos(x)) check(last = x) -- cos.cpp cos(1/12*pi) check(last = cos(1/12*pi)) -- cos.cpp cos(arctan(4/3)) check(last = 3/5) -- cos.cpp cos(-arctan(4/3)) check(last = 3/5) -- cos.cpp cos(x-8/2*pi) check(last = cos(x)) -- cos.cpp cos(x-7/2*pi) check(last = -sin(x)) -- cos.cpp cos(x-6/2*pi) check(last = -cos(x)) -- cos.cpp cos(x-5/2*pi) check(last = sin(x)) -- cos.cpp cos(x-4/2*pi) check(last = cos(x)) -- cos.cpp cos(x-3/2*pi) check(last = -sin(x)) -- cos.cpp cos(x-2/2*pi) check(last = -cos(x)) -- cos.cpp cos(x-1/2*pi) check(last = sin(x)) -- cos.cpp cos(x+0/2*pi) check(last = cos(x)) -- cos.cpp cos(x+1/2*pi) check(last = -sin(x)) -- cos.cpp cos(x+2/2*pi) check(last = -cos(x)) -- cos.cpp cos(x+3/2*pi) check(last = sin(x)) -- cos.cpp cos(x+4/2*pi) check(last = cos(x)) -- cos.cpp cos(x+5/2*pi) check(last = -sin(x)) -- cos.cpp cos(x+6/2*pi) check(last = -cos(x)) -- cos.cpp cos(x+7/2*pi) check(last = sin(x)) -- cos.cpp cos(x+8/2*pi) check(last = cos(x)) -- cos.cpp clear trace=1 cosh(x) check(last = cosh(x)) -- cosh.cpp cosh(0) check(last = 1) -- cosh.cpp cosh(arccosh(x)) check(last = x) -- cosh.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 defint(x^2,y,0,sqrt(1-x^2),x,-1,1) check(last = 1/8*pi) -- defint.cpp z=2 P=(x,y,z) a=abs(cross(d(P,x),d(P,y))) defint(a,y,-sqrt(1-x^2),sqrt(1-x^2),x,-1,1) check(last = pi) -- defint.cpp z=x^2+2y P=(x,y,z) a=abs(cross(d(P,x),d(P,y))) defint(a,x,0,1,y,0,1) check(last = 3/2+5/8*log(5)) -- defint.cpp x=u*cos(v) y=u*sin(v) z=v S=(x,y,z) a=abs(cross(d(S,u),d(S,v))) defint(a,u,0,1,v,0,3pi) check(last = 3/2*pi*log(1+2^(1/2))+3*pi/(2^(1/2))) -- defint.cpp clear trace=1 clear trace=1 denominator(2/3) check(last = 3) -- denominator.cpp denominator(x) check(last = 1) -- denominator.cpp denominator(1/x) check(last = x) -- denominator.cpp denominator(a+b) check(last = 1) -- denominator.cpp denominator(1/a+1/b) check(last = a*b) -- denominator.cpp denominator(1/(x-1)/(x-2)) check(last = x^2-3*x+2) -- denominator.cpp clear trace=1 x=quote(x) f=quote(f) g=quote(g) d(a,x) check(last = 0) -- derivative.cpp d(x,x) check(last = 1) -- derivative.cpp d(x^2,x) check(last = 2*x) -- derivative.cpp d(log(x),x) check(last = 1/x) -- derivative.cpp d(exp(x),x) check(last = exp(x)) -- derivative.cpp d(a^x,x) check(last = a^x*log(a)) -- derivative.cpp d(x^x,x)-(x^x+x^x*log(x)) check(last = 0) -- derivative.cpp d(log(x^2+5),x)-(2*x/(5+x^2)) check(last = 0) -- derivative.cpp d(d(f(x),x),y) check(last = 0) -- derivative.cpp d(d(f(x),y),x) check(last = 0) -- derivative.cpp d(d(f(y),x),y) check(last = 0) -- derivative.cpp d(d(f(y),y),x) check(last = 0) -- derivative.cpp d((x*y*z,y,x+z),(x,y,z)) check(last = ((y*z,x*z,x*y),(0,1,0),(1,0,1))) -- derivative.cpp d(x+z,(x,y,z)) check(last = (1,0,1)) -- derivative.cpp d(cos(theta)^2,cos(theta)) check(last = 2*cos(theta)) -- derivative.cpp d(f()) check(last = d(f(),x)) -- derivative.cpp d(x^2) check(last = 2*x) -- derivative.cpp d(t^2) check(last = 2*t) -- derivative.cpp d(t^2 x^2) check(last = 2*t^2*x) -- derivative.cpp d(sin(x),x)-cos(x) check(last = 0) -- derivative.cpp d(cos(x),x)+sin(x) check(last = 0) -- derivative.cpp d(tan(x),x)-cos(x)^(-2) check(last = 0) -- derivative.cpp d(arcsin(x),x)-1/sqrt(1-x^2) check(last = 0) -- derivative.cpp d(arccos(x),x)+1/sqrt(1-x^2) check(last = 0) -- derivative.cpp d(arctan(x),x)-1/(1+x^2) check(last = 0) -- derivative.cpp d(arctan(y/x),x) check(last = -y/(x^2+y^2)) -- derivative.cpp d(arctan(y/x),y) check(last = x/(x^2+y^2)) -- derivative.cpp d(sinh(x),x)-cosh(x) check(last = 0) -- derivative.cpp d(cosh(x),x)-sinh(x) check(last = 0) -- derivative.cpp d(tanh(x),x)-cosh(x)^(-2) check(last = 0) -- derivative.cpp d(arcsinh(x),x)-1/sqrt(x^2+1) check(last = 0) -- derivative.cpp d(arccosh(x),x)-1/sqrt(x^2-1) check(last = 0) -- derivative.cpp d(arctanh(x),x)-1/(1-x^2) check(last = 0) -- derivative.cpp d(sin(cos(x)),x)+cos(cos(x))*sin(x) check(last = 0) -- derivative.cpp d(sin(x)^2,x)-2*sin(x)*cos(x) check(last = 0) -- derivative.cpp d(sin(cos(x)),cos(x))-cos(cos(x)) check(last = 0) -- derivative.cpp d(abs(x),x) check(last = sgn(x)) -- derivative.cpp d(sgn(x),x) check(last = 2*dirac(x)) -- derivative.cpp d(f(),x) check(last = d(f(),x)) -- derivative.cpp d(f(x),x) check(last = d(f(x),x)) -- derivative.cpp d(f(y),x) check(last = 0) -- derivative.cpp d(g(f(x)),f(x)) check(last = d(g(f(x)),f(x))) -- derivative.cpp d(g(f(x)),x) check(last = d(g(f(x)),x)) -- derivative.cpp d(erf(x))-2*exp(-x^2)/sqrt(pi) check(last = 0) -- derivative.cpp f=x^5*y^7 d(f) check(last = 5*x^4*y^7) -- derivative.cpp d(f,x) check(last = 5*x^4*y^7) -- derivative.cpp d(f,x,0) check(last = x^5*y^7) -- derivative.cpp d(f,x,1) check(last = 5*x^4*y^7) -- derivative.cpp d(f,x,2) check(last = 20*x^3*y^7) -- derivative.cpp d(f,2) check(last = 20*x^3*y^7) -- derivative.cpp d(f,2,y) check(last = 140*x^3*y^6) -- derivative.cpp d(f,x,x,y,y) check(last = 840*x^3*y^5) -- derivative.cpp f=quote(f) clear trace=1 clear trace=1 dirac(-x) check(last = dirac(x)) -- dirac.cpp clear trace=1 clear trace=1 divisors(12) check(last = (1,2,3,4,6,12)) -- divisors.cpp divisors(-12) check(last = (1,2,3,4,6,12)) -- divisors.cpp divisors(a) check(last = (1,a)) -- divisors.cpp divisors(-a) check(last = (1,a)) -- divisors.cpp divisors(+3*x+3) check(last = (1,3,1+x,3+3*x)) -- divisors.cpp divisors(+3*x-3) check(last = (1,3,-3+3*x,-1+x)) -- divisors.cpp divisors(-3*x+3) check(last = (1,3,1-x,3-3*x)) -- divisors.cpp divisors(-3*x-3) check(last = (1,3,1+x,3+3*x)) -- divisors.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 erf(a) check(last = erf(a)) -- erf.cpp erf(0.0) check(abs(last) < 0.000001) -- erf.cpp float(erf(0)) check(abs(last) < 0.000001) -- erf.cpp float(erf(1)) check(abs(last - 0.842701) < 0.000001) -- erf.cpp clear trace=1 erfc(a) check(last = erfc(a)) -- erfc.cpp erfc(0.0)-1.0 check(abs(last) < 0.000001) -- erfc.cpp float(erfc(0))-1.0 check(abs(last) < 0.000001) -- erfc.cpp float(erfc(1)) check(abs(last - 0.157299) < 0.000001) -- erfc.cpp clear trace=1 clear trace=1 expand(1/(x+1)/(x+2)) check(last = 1/(x+1)-1/(x+2)) -- expand.cpp expand((2x^3-x+2)/(x^2-2x+1)) check(last = 4+2*x+5/(x-1)+3/(x^2-2*x+1)) -- expand.cpp expand(1/x^2/(x-1)) check(last = -1/(x^2)-1/x+1/(x-1)) -- expand.cpp p=5s+2 q=(s+1)(s+2)^2 expand(p/q) check(last = -3/(s+1)+3/(s+2)+8/(s^2+4*s+4)) -- expand.cpp q=(x-1)(x-2)^3 expand(1/q) check(last = 1/(x^3-6*x^2+12*x-8)+1/(x-2)-1/(x-1)-1/(x^2-4*x+4)) -- expand.cpp expand(1/(x+1/2)/(x+1/3)) check(last = -12/(2*x+1)+18/(3*x+1)) -- expand.cpp f=1/(x+1)/(x+2) g=1/(x+1)-1/(x+2) expand(((f,f),(f,f)))-((g,g),(g,g)) check(last = ((0,0),(0,0))) -- expand.cpp expand(1/(1+1/x)) check(last = 1-1/(x+1)) -- expand.cpp expand(1/x/(x+1)) check(last = 1/x-1/(x+1)) -- expand.cpp expand(1/x^2/(x+1)) check(last = x^(-2)-1/x+1/(x+1)) -- expand.cpp expand(1/x) check(last = 1/x) -- expand.cpp expand(1/x^2) check(last = x^(-2)) -- expand.cpp expand(1/(x^2-4x+4)) check(last = 1/(x^2-4*x+4)) -- expand.cpp clear trace=1 expcos(x) check(last = 1/2*exp(-i*x)+1/2*exp(i*x)) -- expcos.cpp clear trace=1 expsin(x) check(last = 1/2*i*exp(-i*x)-1/2*i*exp(i*x)) -- expsin.cpp clear trace=1 factor(0) check(last = 0) -- factor.cpp factor(1) check(last = 1) -- factor.cpp factor(2) check(last = 2) -- factor.cpp factor(3) check(last = 3) -- factor.cpp factor(4) check(last = 2^2) -- factor.cpp factor(5) check(last = 5) -- factor.cpp factor(6) check(last = 2*3) -- factor.cpp factor(7) check(last = 7) -- factor.cpp factor(8) check(last = 2^3) -- factor.cpp factor(9) check(last = 3^2) -- factor.cpp factor(10) check(last = 2*5) -- factor.cpp factor(100!) check(last = 2^97*3^48*5^24*7^16*11^9*13^7*17^5*19^5*23^4*29^3*31^3*37^2*41^2*43^2*47^2*53*59*61*67*71*73*79*83*89*97) -- factor.cpp factor(2*(2^30-35)) check(last = 2*1073741789) -- factor.cpp a=104729 factor(2*(a^2+6)) check(last = 2*10968163447) -- factor.cpp factor((a^2+6)^2) check(last = 10968163447*10968163447) -- factor.cpp factor((a^2+6)*(a^2+60)) check(last = 10968163501*10968163447) -- factor.cpp f=(x+1)(x+2)(y+3)(y+4) factor(f,x,y) check(last = (x+1)*(x+2)*(y+3)*(y+4)) -- factor.cpp factor(f,y,x) check(last = (x+1)*(x+2)*(y+3)*(y+4)) -- factor.cpp f=(x+1)(x+1)(y+2)(y+2) factor(f,x,y) check(last = (x+1)^2*(y+2)^2) -- factor.cpp factor(f,y,x) check(last = (x+1)^2*(y+2)^2) -- factor.cpp clear trace=1 clear trace=1 bake=0 factor((x+1)*(x+2)*(x+3),x) check(last = (1+x)*(2+x)*(3+x)) -- factorpoly.cpp factor((x+a)*(x^2+x+1),x) check(last = (1+x+x^2)*(a+x)) -- factorpoly.cpp factor(x*(x+1)*(x+2),x) check(last = x*(1+x)*(2+x)) -- factorpoly.cpp factor((-2*x+3)*(x+4),x) check(last = -(-3+2*x)*(4+x)) -- factorpoly.cpp (-2*x+3)*(x+4)+(-3+2*x)*(4+x) check(last = 0) -- factorpoly.cpp factor((x+1)*(-x^2+x+1),x) check(last = -(-1-x+x^2)*(1+x)) -- factorpoly.cpp factor((x+1/2)*(+x+1/3)*(+x+1/4),x) check(last = 1/24*(1+2*x)*(1+3*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(+x+1/3)*(+x+1/4)-1/24*(1+2*x)*(1+3*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x+1/3)*(+x-1/4),x) check(last = 1/24*(-1+4*x)*(1+2*x)*(1+3*x)) -- factorpoly.cpp (x+1/2)*(+x+1/3)*(+x-1/4)-1/24*(-1+4*x)*(1+2*x)*(1+3*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x+1/3)*(-x+1/4),x) check(last = -1/24*(-1+4*x)*(1+2*x)*(1+3*x)) -- factorpoly.cpp (x+1/2)*(+x+1/3)*(-x+1/4)+1/24*(-1+4*x)*(1+2*x)*(1+3*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x+1/3)*(-x-1/4),x) check(last = -1/24*(1+2*x)*(1+3*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(+x+1/3)*(-x-1/4)+1/24*(1+2*x)*(1+3*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x-1/3)*(+x+1/4),x) check(last = 1/24*(-1+3*x)*(1+2*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(+x-1/3)*(+x+1/4)-1/24*(-1+3*x)*(1+2*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x-1/3)*(+x-1/4),x) check(last = 1/24*(-1+3*x)*(-1+4*x)*(1+2*x)) -- factorpoly.cpp (x+1/2)*(+x-1/3)*(+x-1/4)-1/24*(-1+3*x)*(-1+4*x)*(1+2*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x-1/3)*(-x+1/4),x) check(last = -1/24*(-1+3*x)*(-1+4*x)*(1+2*x)) -- factorpoly.cpp (x+1/2)*(+x-1/3)*(-x+1/4)+1/24*(-1+3*x)*(-1+4*x)*(1+2*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(+x-1/3)*(-x-1/4),x) check(last = -1/24*(-1+3*x)*(1+2*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(+x-1/3)*(-x-1/4)+1/24*(-1+3*x)*(1+2*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x+1/3)*(+x+1/4),x) check(last = -1/24*(-1+3*x)*(1+2*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(-x+1/3)*(+x+1/4)+1/24*(-1+3*x)*(1+2*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x+1/3)*(+x-1/4),x) check(last = -1/24*(-1+3*x)*(-1+4*x)*(1+2*x)) -- factorpoly.cpp (x+1/2)*(-x+1/3)*(+x-1/4)+1/24*(-1+3*x)*(-1+4*x)*(1+2*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x+1/3)*(-x+1/4),x) check(last = 1/24*(-1+3*x)*(-1+4*x)*(1+2*x)) -- factorpoly.cpp (x+1/2)*(-x+1/3)*(-x+1/4)-1/24*(-1+3*x)*(-1+4*x)*(1+2*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x+1/3)*(-x-1/4),x) check(last = 1/24*(-1+3*x)*(1+2*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(-x+1/3)*(-x-1/4)-1/24*(-1+3*x)*(1+2*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x-1/3)*(+x+1/4),x) check(last = -1/24*(1+2*x)*(1+3*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(-x-1/3)*(+x+1/4)+1/24*(1+2*x)*(1+3*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x-1/3)*(+x-1/4),x) check(last = -1/24*(-1+4*x)*(1+2*x)*(1+3*x)) -- factorpoly.cpp (x+1/2)*(-x-1/3)*(+x-1/4)+1/24*(-1+4*x)*(1+2*x)*(1+3*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x-1/3)*(-x+1/4),x) check(last = 1/24*(-1+4*x)*(1+2*x)*(1+3*x)) -- factorpoly.cpp (x+1/2)*(-x-1/3)*(-x+1/4)-1/24*(-1+4*x)*(1+2*x)*(1+3*x) check(last = 0) -- factorpoly.cpp factor((x+1/2)*(-x-1/3)*(-x-1/4),x) check(last = 1/24*(1+2*x)*(1+3*x)*(1+4*x)) -- factorpoly.cpp (x+1/2)*(-x-1/3)*(-x-1/4)-1/24*(1+2*x)*(1+3*x)*(1+4*x) check(last = 0) -- factorpoly.cpp factor((+x+a)*(+x+b)*(+x+c),x) check(last = (a+x)*(b+x)*(c+x)) -- factorpoly.cpp (a+x)*(b+x)*(c+x)-(a+x)*(b+x)*(c+x) check(last = 0) -- factorpoly.cpp factor((+x+a)*(+x+b)*(+x-c),x) check(last = (a+x)*(b+x)*(-c+x)) -- factorpoly.cpp (+x+a)*(+x+b)*(+x-c)-(a+x)*(b+x)*(-c+x) check(last = 0) -- factorpoly.cpp factor((+x+a)*(+x+b)*(-x+c),x) check(last = -(a+x)*(b+x)*(-c+x)) -- factorpoly.cpp (+x+a)*(+x+b)*(-x+c)+(a+x)*(b+x)*(-c+x) check(last = 0) -- factorpoly.cpp factor((+x+a)*(+x+b)*(-x-c),x) check(last = -(a+x)*(b+x)*(c+x)) -- factorpoly.cpp (+x+a)*(+x+b)*(-x-c)+(a+x)*(b+x)*(c+x) check(last = 0) -- factorpoly.cpp factor((+a*x+b)*(+c*x+d),x) check(last = (b+a*x)*(d+c*x)) -- factorpoly.cpp (+a*x+b)*(+c*x+d)-(b+a*x)*(d+c*x) check(last = 0) -- factorpoly.cpp factor((+a*x+b)*(+c*x-d),x) check(last = (b+a*x)*(-d+c*x)) -- factorpoly.cpp (+a*x+b)*(+c*x-d)-(b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((+a*x+b)*(-c*x+d),x) check(last = -(b+a*x)*(-d+c*x)) -- factorpoly.cpp (+a*x+b)*(-c*x+d)+(b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((+a*x+b)*(-c*x-d),x) check(last = -(b+a*x)*(d+c*x)) -- factorpoly.cpp (+a*x+b)*(-c*x-d)+(b+a*x)*(d+c*x) check(last = 0) -- factorpoly.cpp factor((+a*x-b)*(+c*x+d),x) check(last = (d+c*x)*(-b+a*x)) -- factorpoly.cpp (+a*x-b)*(+c*x+d)-(d+c*x)*(-b+a*x) check(last = 0) -- factorpoly.cpp factor((+a*x-b)*(+c*x-d),x) check(last = (-b+a*x)*(-d+c*x)) -- factorpoly.cpp (+a*x-b)*(+c*x-d)-(-b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((+a*x-b)*(-c*x+d),x) check(last = -(-b+a*x)*(-d+c*x)) -- factorpoly.cpp (+a*x-b)*(-c*x+d)+(-b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((+a*x-b)*(-c*x-d),x) check(last = -(d+c*x)*(-b+a*x)) -- factorpoly.cpp (+a*x-b)*(-c*x-d)+(d+c*x)*(-b+a*x) check(last = 0) -- factorpoly.cpp factor((-a*x+b)*(+c*x+d),x) check(last = -(d+c*x)*(-b+a*x)) -- factorpoly.cpp (-a*x+b)*(+c*x+d)+(d+c*x)*(-b+a*x) check(last = 0) -- factorpoly.cpp factor((-a*x+b)*(+c*x-d),x) check(last = -(-b+a*x)*(-d+c*x)) -- factorpoly.cpp (-a*x+b)*(+c*x-d)+(-b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((-a*x+b)*(-c*x+d),x) check(last = (-b+a*x)*(-d+c*x)) -- factorpoly.cpp (-a*x+b)*(-c*x+d)-(-b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((-a*x+b)*(-c*x-d),x) check(last = (d+c*x)*(-b+a*x)) -- factorpoly.cpp (-a*x+b)*(-c*x-d)-(d+c*x)*(-b+a*x) check(last = 0) -- factorpoly.cpp factor((-a*x-b)*(+c*x+d),x) check(last = -(b+a*x)*(d+c*x)) -- factorpoly.cpp (-a*x-b)*(+c*x+d)+(b+a*x)*(d+c*x) check(last = 0) -- factorpoly.cpp factor((-a*x-b)*(+c*x-d),x) check(last = -(b+a*x)*(-d+c*x)) -- factorpoly.cpp (-a*x-b)*(+c*x-d)+(b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((-a*x-b)*(-c*x+d),x) check(last = (b+a*x)*(-d+c*x)) -- factorpoly.cpp (-a*x-b)*(-c*x+d)-(b+a*x)*(-d+c*x) check(last = 0) -- factorpoly.cpp factor((-a*x-b)*(-c*x-d),x) check(last = (b+a*x)*(d+c*x)) -- factorpoly.cpp (-a*x-b)*(-c*x-d)-(b+a*x)*(d+c*x) check(last = 0) -- factorpoly.cpp factor(x,x) check(last = x) -- factorpoly.cpp factor(x^2,x) check(last = x^2) -- factorpoly.cpp factor(x^3,x) check(last = x^3) -- factorpoly.cpp bake=1 y=(x+1)(x+2) factor(y,z) check(last = x^2+3*x+2) -- factorpoly.cpp factor(y,y) check(last = x^2+3*x+2) -- factorpoly.cpp y=x^2+exp(x) factor(y) check(last = x^2+exp(x)) -- factorpoly.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 float(x) check(last = x) -- float.cpp float(1/2) check(last = 0.5) -- float.cpp float(pi) check(abs(last - 3.14159) < 0.00001) -- float.cpp float(exp(1)) check(abs(last - 2.71828) < 0.00001) -- float.cpp x=(1/2,1/4) float(x) check(last = (0.5,0.25)) -- float.cpp x check(last = (1/2,1/4)) -- float.cpp x=quote(x) clear trace=1 floor(a) check(last = floor(a)) -- floor.cpp floor(a+b) check(last = floor(a+b)) -- floor.cpp floor(5/2) check(last = 2) -- floor.cpp floor(4/2) check(last = 2) -- floor.cpp floor(3/2) check(last = 1) -- floor.cpp floor(2/2) check(last = 1) -- floor.cpp floor(1/2) check(last = 0) -- floor.cpp floor(0/2) check(last = 0) -- floor.cpp floor(-1/2) check(last = -1) -- floor.cpp floor(-2/2) check(last = -1) -- floor.cpp floor(-3/2) check(last = -2) -- floor.cpp floor(-4/2) check(last = -2) -- floor.cpp floor(-5/2) check(last = -3) -- floor.cpp floor(5/2.0) check(last = 2) -- floor.cpp floor(4/2.0) check(last = 2) -- floor.cpp floor(3/2.0) check(last = 1) -- floor.cpp floor(2/2.0) check(last = 1) -- floor.cpp floor(1/2.0) check(last = 0) -- floor.cpp floor(0.0) check(last = 0) -- floor.cpp floor(-1/2.0) check(last = -1) -- floor.cpp floor(-2/2.0) check(last = -1) -- floor.cpp floor(-3/2.0) check(last = -2) -- floor.cpp floor(-4/2.0) check(last = -2) -- floor.cpp floor(-5/2.0) check(last = -3) -- floor.cpp -- for.cpp clear trace=1 x=0 y=2 for(k,1,9,x=sqrt(2+x),y=2y/x) float(y) check(abs(last - 3.14159) < 0.00001) for(i,1,3,j=i) check(i = sqrt(-1)) check(j = 3) t=0 A=2k for(k,1,3,t=t+A) check(t=12) clear trace=1 Gamma(a) check(last = Gamma(a)) -- gamma.cpp Gamma(x+1) check(last = x*Gamma(x)) -- gamma.cpp Gamma(1/2) check(last = pi^(1/2)) -- gamma.cpp Gamma(x-1)-Gamma(x)/(-1+x) check(last = 0) -- gamma.cpp Gamma(-x) check(last = -pi/(x*Gamma(x)*sin(pi*x))) -- gamma.cpp clear trace=1 gcd(30,42) check(last = 6) -- gcd.cpp gcd(42,30) check(last = 6) -- gcd.cpp gcd(-30,42) check(last = 6) -- gcd.cpp gcd(42,-30) check(last = 6) -- gcd.cpp gcd(30,-42) check(last = 6) -- gcd.cpp gcd(-42,30) check(last = 6) -- gcd.cpp gcd(-30,-42) check(last = 6) -- gcd.cpp gcd(-42,-30) check(last = 6) -- gcd.cpp gcd(x,x) check(last = x) -- gcd.cpp gcd(-x,x) check(last = x) -- gcd.cpp gcd(x,-x) check(last = x) -- gcd.cpp gcd(-x,-x) check(last = -x) -- gcd.cpp gcd(x^2,x^3) check(last = x^2) -- gcd.cpp gcd(x,y) check(last = 1) -- gcd.cpp gcd(y,x) check(last = 1) -- gcd.cpp gcd(x*y,y) check(last = y) -- gcd.cpp gcd(x*y,y^2) check(last = y) -- gcd.cpp gcd(x^2*y^2,x^3*y^3) check(last = x^2*y^2) -- gcd.cpp gcd(x^2,x^3) check(last = x^2) -- gcd.cpp gcd(x+y,x+z) check(last = 1) -- gcd.cpp gcd(x+y,x+y) check(last = x+y) -- gcd.cpp gcd(x+y,2*x+2*y) check(last = x+y) -- gcd.cpp gcd(-x-y,x+y) check(last = x+y) -- gcd.cpp gcd(4*x+4*y,6*x+6*y) check(last = 2*x+2*y) -- gcd.cpp gcd(4*x+4*y+4,6*x+6*y+6) check(last = 2+2*x+2*y) -- gcd.cpp gcd(4*x+4*y+4,6*x+6*y+12) check(last = 1) -- gcd.cpp gcd(27*t^3+y^3+9*t*y^2+27*t^2*y,t+y) check(last = 1) -- gcd.cpp gcd(2*a^2*x^2+a*x+a*b,a) check(last = a) -- gcd.cpp gcd(2*a^2*x^2+a*x+a*b,a^2) check(last = a) -- gcd.cpp gcd(2*a^2*x^2+2*a*x+2*a*b,a) check(last = a) -- gcd.cpp gcd(2*a^2*x^2+2*a*x+2*a*b,2*a) check(last = 2*a) -- gcd.cpp gcd(2*a^2*x^2+2*a*x+2*a*b,3*a) check(last = a) -- gcd.cpp gcd(2*a^2*x^2+2*a*x+2*a*b,4*a) check(last = 2*a) -- gcd.cpp gcd(x,x^2) check(last = x) -- gcd.cpp gcd(x,x^a) check(last = 1) -- gcd.cpp gcd(12,18,9) check(last = 3) -- gcd.cpp clear trace=1 clear trace=1 clear trace=1 hermite(x,n) check(last = hermite(x,n)) -- hermite.cpp hermite(x,0)-1 check(last = 0) -- hermite.cpp hermite(x,1)-2*x check(last = 0) -- hermite.cpp hermite(x,2)-(4*x^2-2) check(last = 0) -- hermite.cpp hermite(x,3)-(8*x^3-12*x) check(last = 0) -- hermite.cpp hermite(x,4)-(16*x^4-48*x^2+12) check(last = 0) -- hermite.cpp hermite(x,5)-(32*x^5-160*x^3+120*x) check(last = 0) -- hermite.cpp hermite(x,6)-(64*x^6-480*x^4+720*x^2-120) check(last = 0) -- hermite.cpp hermite(x,7)-(128*x^7-1344*x^5+3360*x^3-1680*x) check(last = 0) -- hermite.cpp hermite(x,8)-(256*x^8-3584*x^6+13440*x^4-13440*x^2+1680) check(last = 0) -- hermite.cpp hermite(x,9)-(512*x^9-9216*x^7+48384*x^5-80640*x^3+30240*x) check(last = 0) -- hermite.cpp hermite(x,10)-(1024*x^10-23040*x^8+161280*x^6-403200*x^4+302400*x^2-30240) check(last = 0) -- hermite.cpp hermite(a-b,10)-eval(subst(a-b,x,hermite(x,10))) check(last = 0) -- hermite.cpp clear trace=1 clear trace=1 clear trace=1 imag(a+i*b) check(last = b) -- imag.cpp imag(1+exp(i*pi/3)) check(last = 1/2*3^(1/2)) -- imag.cpp imag(i) check(last = 1) -- imag.cpp imag((-1)^(1/3)) check(last = 1/2*3^(1/2)) -- imag.cpp imag(-i) check(last = -1) -- imag.cpp clear trace=1 A=((A11,A12),(A21,A22)) A[1,1] check(last = A11) -- index.cpp A[1,2] check(last = A12) -- index.cpp A[2,1] check(last = A21) -- index.cpp A[2,2] check(last = A22) -- index.cpp A[1] check(last = (A11,A12)) -- index.cpp A[2] check(last = (A21,A22)) -- index.cpp A[1]=(B11,B12) A check(last = ((B11,B12),(A21,A22))) -- index.cpp A[2]=(B21,B22) A check(last = ((B11,B12),(B21,B22))) -- index.cpp A=((0,0),(0,0)) A[1,1] check(last = 0) -- index.cpp 1[2] check(last = 1) -- index.cpp clear trace=1 clear trace=1 inner(a,b) check(last = a*b) -- inner.cpp inner(a,(b1,b2)) check(last = (a*b1,a*b2)) -- inner.cpp inner((a1,a2),b) check(last = (a1*b,a2*b)) -- inner.cpp inner(((a11,a12),(a21,a22)),(x1,x2)) check(last = (a11*x1+a12*x2,a21*x1+a22*x2)) -- inner.cpp inner((1,2),(3,4)) check(last = 11) -- inner.cpp inner(inner((1,2),((3,4),(5,6))),(7,8)) check(last = 219) -- inner.cpp inner((1,2),inner(((3,4),(5,6)),(7,8))) check(last = 219) -- inner.cpp inner((1,2),((3,4),(5,6)),(7,8)) check(last = 219) -- inner.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 isprime(0) check(last = 0) -- isprime.cpp isprime(1) check(last = 0) -- isprime.cpp isprime(13) check(last = 1) -- isprime.cpp isprime(14) check(last = 0) -- isprime.cpp isprime(9007199254740991) check(last = 0) -- isprime.cpp isprime(2^53 - 111) check(last = 1) -- isprime.cpp isprime(2^50-71) check(last = 1) -- isprime.cpp isprime(2^40-87) check(last = 1) -- isprime.cpp clear trace=1 clear trace=1 clear trace=1 tty=1 integral(x^2+x)-(1/2*x^2+1/3*x^3) check(last = 0) -- itest.cpp #1 integral(A,X) check(last = A*X) -- itest.cpp #4 integral(A+B,X)-(A*X+B*X) check(last = 0) -- itest.cpp #9 integral(1/X,X) check(last = log(X)) -- itest.cpp #11 integral(exp(X),X) check(last = exp(X)) -- itest.cpp #12 integral(exp(A*X),X)-exp(A*X)/A check(last = 0) -- itest.cpp #14 integral(log(X),X)-X*log(X)+X check(last = 0) -- itest.cpp #15 integral(3^X*log(3),X) check(last = 3^X) -- itest.cpp #16 integral(1/(3+x^2),x)-3^(-1/2)*arctan(3^(-1/2)*x) check(last = 0) -- itest.cpp #17 integral(1/(a-x^2),x)-a^(-1/2)*arctanh(a^(-1/2)*x) check(last = 0) -- itest.cpp #19 integral(1/sqrt(a-x^2),x)-arcsin(a^(-1/2)*x) check(last = 0) -- itest.cpp #20 integral(1/sqrt(a+x^2),x)-(log(x+(a+x^2)^(1/2))) check(last = 0) -- itest.cpp #27 integral(1/(a+b*x),x)-(log(a+b*x)/b) check(last = 0) -- itest.cpp #28 integral(1/(A+B*X)^2,X)+1/B*1/(A+B*X) check(last = 0) -- itest.cpp #29 integral(1/(a+b*x)^3,x)+1/2*1/b*(a+b*x)^(-2) check(last = 0) -- itest.cpp #30 integral(X/(A+B*X),X)+A*B^(-2)*log(A+B*X)-X/B check(last = 0) -- itest.cpp #31 integral(X/(A+B*X)^2,X)-1/B^2*(log(A+B*X)+A/(A+B*X)) check(last = 0) -- itest.cpp #33 integral(X^2/(A+B*X),X)-1/B^2*(1/2*(A+B*X)^2-2*A*(A+B*X)+A^2*log(A+B*X)) check(last = 0) -- itest.cpp #34 integral(X^2/(A+B*X)^2,X)-1/B^3*(A+B*X-2*A*log(A+B*X)-A^2/(A+B*X)) check(last = 0) -- itest.cpp #35 integral(X^2/(A+B*X)^3,X)-1/B^3*(log(A+B*X)+2*A/(A+B*X)-1/2*A^2/(A+B*X)^2) check(last = 0) -- itest.cpp #37 integral(1/X*1/(A+B*X),X)+1/A*log((A+B*X)/X) check(last = 0) -- itest.cpp #38 integral(1/X*1/(A+B*X)^2,X)-1/A*1/(A+B*X)+1/A^2*log((A+B*X)/X) check(last = 0) -- itest.cpp #39 integral(1/X*1/(A+B*X)^3,X)-1/A^3*(1/2*((2*A+B*X)/(A+B*X))^2+log(X/(A+B*X))) check(last = 0) -- itest.cpp #40 integral(1/X^2*1/(A+B*X),X)+1/(A*X)-B/A^2*log((A+B*X)/X) check(last = 0) -- itest.cpp #41 integral(1/X^3*1/(A+B*X),X)-(2*B*X-A)/(2*A^2*X^2)-B^2/A^3*log(X/(A+B*X)) check(last = 0) -- itest.cpp #42 integral(1/X^2*1/(A+B*X)^2,X)+(A+2*B*X)/(A^2*X*(A+B*X))-2*B/A^3*log((A+B*X)/X) check(last = 0) -- itest.cpp #60 integral(1/(2+3*X^2),X)-1/sqrt(6)*arctan(1/2*X*sqrt(6)) check(last = 0) -- itest.cpp integral(1/(-2-3*X^2),X)-1/sqrt(6)*arctan(-1/2*X*sqrt(6)) check(last = 0) -- itest.cpp #61 integral(1/(2-3*X^2),X)-1/2*1/sqrt(6)*log((2+X*sqrt(6))/(2-X*sqrt(6))) check(last = 0) -- itest.cpp integral(1/(-2+3*X^2),X)-1/2*1/sqrt(6)*log((-2+X*sqrt(6))/(-2-X*sqrt(6))) check(last = 0) -- itest.cpp #63 integral(X/(A+B*X^2),X)-1/2*1/B*log(A+B*X^2) check(last = 0) -- itest.cpp #64 integral(X^2/(A+B*X^2),X)-X/B+A/B*integral(1/(A+B*X^2),X) check(last = 0) -- itest.cpp #65 integral(1/(A+B*X^2)^2,X)-X/(2*A*(A+B*X^2))-1/2*1/A*integral(1/(A+B*X^2),X) check(last = 0) -- itest.cpp #70 integral(1/X*1/(A+B*X^2),X)-1/2*1/A*log(X^2/(A+B*X^2)) check(last = 0) -- itest.cpp #71 integral(1/X^2*1/(A+B*X^2),X)+1/(A*X)+B/A*integral(1/(A+B*X^2),X) check(last = 0) -- itest.cpp #74 integral(1/(A+B*X^3),X)-1/3*1/A*(A/B)^(1/3)*(1/2*log(((A/B)^(1/3)+X)^3/(A+B*X^3))+sqrt(3)*arctan((2*X-(A/B)^(1/3))*(A/B)^(-1/3)/sqrt(3))) check(last = 0) -- itest.cpp #76 integral(X^2/(A+B*X^3),X)-1/3*1/B*log(A+B*X^3) check(last = 0) -- itest.cpp #77 integral(1/(2+3*X^4),X)-1/2*1/2*(2/3/4)^(1/4)*(1/2*log((X^2+2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2))/(X^2-2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2)))+arctan(2*(2/3/4)^(1/4)*X/(2*(2/3/4)^(1/2)-X^2))) check(last = 0) -- itest.cpp #78 integral(1/(2-3*X^4),X)-1/2*(2/3)^(1/4)/2*(1/2*log((X+(2/3)^(1/4))/(X-(2/3)^(1/4)))+arctan(X*(2/3)^(-1/4))) check(last = 0) -- itest.cpp #79 integral(X/(2+3*X^4),X)-1/2*1/3*1/sqrt(2/3)*arctan(X^2/sqrt(2/3)) check(last = 0) -- itest.cpp #80 integral(X/(2-3*X^4),X)+1/4*1/3*sqrt(3/2)*log((X^2-sqrt(2/3))/(X^2+sqrt(2/3))) check(last = 0) -- itest.cpp #81 integral(X^2/(2+3*X^4),X)-1/4*1/3*(2/3/4)^(-1/4)*(1/2*log((X^2-2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4))/(X^2+2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4)))+arctan(2*(2/3/4)^(1/4)*X/(2*sqrt(2/3/4)-X^2))) check(last = 0) -- itest.cpp #82 integral(X^2/(2-3*X^4),X)+1/4*1/3*(2/3)^(-1/4)*(log((X-(2/3)^(1/4))/(X+(2/3)^(1/4)))+2*arctan(X*(2/3)^(-1/4))) check(last = 0) -- itest.cpp #83 integral(X^3/(A+B*X^4),X)-1/4*1/B*log(A+B*X^4) check(last = 0) -- itest.cpp #124 integral(sqrt(A+B*X),X)-2/3/B*sqrt((A+B*X)^3) check(last = 0) -- itest.cpp #125 integral(X*sqrt(A+B*X),X)+2*(2*A-3*B*X)*sqrt((A+B*X)^3)/15*B^(-2) check(last = 0) -- itest.cpp #126 integral(X^2*sqrt(A+B*X),X)-2*(8*A^2-12*A*B*X+15*B^2*X^2)*sqrt((A+B*X)^3)/105*B^(-3) check(last = 0) -- itest.cpp #128 integral(sqrt(A+B*X)/X,X)-2*sqrt(A+B*X)-A*integral(1/X*1/sqrt(A+B*X),X) check(last = 0) -- itest.cpp #129 integral(sqrt(A+B*X)/X^2,X)+sqrt(A+B*X)/X-B/2*integral(1/X*1/sqrt(A+B*X),X) check(last = 0) -- itest.cpp #131 integral(1/sqrt(A+B*X),X)-2*sqrt(A+B*X)/B check(last = 0) -- itest.cpp #132 integral(X/sqrt(A+B*X),X)+2/3*(2*A-B*X)*sqrt(A+B*X)/B^2 check(last = 0) -- itest.cpp #133 integral(X^2/sqrt(A+B*X),X)-2/15*(8*A^2-4*A*B*X+3*B^2*X^2)*sqrt(A+B*X)/B^3 check(last = 0) -- itest.cpp #134 integral(1/X*1/sqrt(2+B*X),X)-1/sqrt(2)*log((sqrt(2+B*X)-sqrt(2))/(sqrt(2+B*X)+sqrt(2))) check(last = 0) -- itest.cpp #136 integral(1/X*1/sqrt(-2+B*X),X)-2/sqrt(2)*arctan(sqrt((-2+B*X)/2)) check(last = 0) -- itest.cpp #137 integral(1/X^2*1/sqrt(A+B*X),X)+sqrt(A+B*X)/A/X+1/2*B/A*integral(1/X*1/sqrt(A+B*X),X) check(last = 0) -- itest.cpp #156 integral(sqrt(X^2+A),X)-1/2*(X*sqrt(X^2+A)+A*log(X+sqrt(X^2+A))) check(last = 0) -- itest.cpp #157 integral(1/sqrt(X^2+A),X)-log(X+sqrt(X^2+A)) check(last = 0) -- itest.cpp #158 integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2) check(last = 0) -- itest.cpp #159 integral(1/X*1/sqrt(X^2+2),X)+1/sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X) check(last = 0) -- itest.cpp #160 integral(sqrt(X^2+2)/X,X)-sqrt(X^2+2)+sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X) check(last = 0) -- itest.cpp #161 integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2)) check(last = 0) -- itest.cpp #162 integral(X/sqrt(X^2+A),X)-sqrt(X^2+A) check(last = 0) -- itest.cpp #163 integral(X*sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3) check(last = 0) -- itest.cpp #164 integral(sqrt((X^2+A)^3),X)-1/4*(X*sqrt((X^2+A)^3)+3/2*A*X*sqrt(X^2+A)+3/2*A^2*log(X+sqrt(X^2+A))) check(last = 0) -- itest.cpp #165 integral(1/sqrt((X^2+A)^3),X)-X/A/sqrt(X^2+A) check(last = 0) -- itest.cpp #166 integral(X/sqrt((X^2+A)^3),X)+1/sqrt(X^2+A) check(last = 0) -- itest.cpp #167 integral(X*sqrt((X^2+A)^3),X)-1/5*sqrt((X^2+A)^5) check(last = 0) -- itest.cpp #168 integral(X^2*sqrt(X^2+A),X)-1/4*X*sqrt((X^2+A)^3)+1/8*A*X*sqrt(X^2+A)+1/8*A^2*log(X+sqrt(X^2+A)) check(last = 0) -- itest.cpp #169 integral(X^3*sqrt(X^2+7),X)-(1/5*X^2-2/15*7)*sqrt((X^2+7)^3) check(last = 0) -- itest.cpp #170 integral(X^3*sqrt(X^2-7),X)-(sqrt((X^2-7)^5)/5+7*sqrt((X^2-7)^3)/3) check(last = 0) -- itest.cpp #171 integral(X^2/sqrt(X^2+A),X)-1/2*X*sqrt(X^2+A)+1/2*A*log(X+sqrt(X^2+A)) check(last = 0) -- itest.cpp #172 integral(X^3/sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)+A*sqrt(X^2+A) check(last = 0) -- itest.cpp #173 integral(1/X^2*1/sqrt(X^2+A),X)+sqrt(X^2+A)/A/X check(last = 0) -- itest.cpp #174 integral(1/X^3*1/sqrt(X^2+2),X)+1/2*sqrt(X^2+2)/2/X^2-1/2*log((sqrt(2)+sqrt(X^2+2))/X)/(sqrt(2)^3) check(last = 0) -- itest.cpp #175 integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arcsec(X/(2^(1/2))) check(last = 0) -- itest.cpp #176+ integral(X^2*sqrt((X^2+2^2)^3),X)-1/6*X*sqrt((X^2+2^2)^5)+1/24*(2^2)*X*sqrt((X^2+2^2)^3)+1/16*(2^4)X*sqrt(X^2+2^2)+1/16*(2^6)*log(X+sqrt(X^2+2^2)) check(last = 0) -- itest.cpp #176- integral(X^2*sqrt((X^2-2^2)^3),X)-1/6*X*sqrt((X^2-2^2)^5)-1/24*(2^2)*X*sqrt((X^2-2^2)^3)+1/16*(2^4)X*sqrt(X^2-2^2)-1/16*(2^6)*log(X+sqrt(X^2-2^2)) check(last = 0) -- itest.cpp #177+ integral(X^3*sqrt((X^2+7^2)^3),X)-1/7*sqrt((X^2+7^2)^7)+1/5*(7^2)*sqrt((X^2+7^2)^5) check(last = 0) -- itest.cpp #177- integral(X^3*sqrt((X^2-7^2)^3),X)-1/7*sqrt((X^2-7^2)^7)-1/5*(7^2)*sqrt((X^2-7^2)^5) check(last = 0) -- itest.cpp #196 simplify(integral(1/(X-A)/sqrt(X^2-A^2),X)+sqrt(X^2-A^2)/A/(X-A)) check(last = 0) -- itest.cpp simplify(1/(X-A)/sqrt(X^2-A^2)-d(integral(1/(X-A)/sqrt(X^2-A^2),X),X)) check(last = 0) -- itest.cpp #197 integral(1/(X+A)/sqrt(X^2-A^2),X)-sqrt(X^2-A^2)/A/(X+A) check(last = 0) -- itest.cpp simplify(1/(X+A)/sqrt(X^2-A^2)-d(integral(1/(X+A)/sqrt(X^2-A^2),X),X)) check(last = 0) -- itest.cpp #200 integral(sqrt(7-X^2),X)-1/2*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7))) check(last = 0) -- itest.cpp #201 integral(1/sqrt(7-X^2),X)-arcsin(X/sqrt(7)) check(last = 0) -- itest.cpp #202 integral(1/X*1/sqrt(7-X^2),X)+1/sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X) check(last = 0) -- itest.cpp #203 integral(sqrt(7-X^2)/X,X)-sqrt(7-X^2)+sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X) check(last = 0) -- itest.cpp #204 integral(X/sqrt(A-X^2),X)+sqrt(A-X^2) check(last = 0) -- itest.cpp #205 integral(X*sqrt(A-X^2),X)+1/3*sqrt((A-X^2)^3) check(last = 0) -- itest.cpp #210 integral(X^2*sqrt(7-X^2),X)+1/4*X*sqrt((7-X^2)^3)-7/8*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7))) check(last = 0) -- itest.cpp #211 integral(X^3*sqrt(7-X^2),X)-(-1/5*X^2-2/15*7)*sqrt((7-X^2)^3) check(last = 0) -- itest.cpp #214 integral(X^2/sqrt(7-X^2),X)+X/2*sqrt(7-X^2)-7/2*arcsin(X/sqrt(7)) check(last = 0) -- itest.cpp #215 integral(1/X^2*1/sqrt(7-X^2),X)+sqrt(7-X^2)/7/X check(last = 0) -- itest.cpp #216 integral(sqrt(7-X^2)/X^2,X)+sqrt(7-X^2)/X+arcsin(X/sqrt(7)) check(last = 0) -- itest.cpp #217 integral(sqrt(7-X^2)/X^3,X)+1/2*sqrt(7-X^2)/X^2-1/2*log((sqrt(7)+sqrt(7-X^2))/X)/sqrt(7) check(last = 0) -- itest.cpp #218 integral(sqrt(7-X^2)/X^4,X)+1/3*sqrt((7-X^2)^3)/7/X^3 check(last = 0) -- itest.cpp #273 integral(sqrt(7*X^2+C),X)-X*sqrt(7*X^2+C)/2-C*log(X*sqrt(7)+sqrt(7*X^2+C))/2/sqrt(7) check(last = 0) -- itest.cpp #274 integral(sqrt(-7*X^2+C),X)-X*sqrt(-7*X^2+C)/2-C*arcsin(X*sqrt(7/C))/2/sqrt(7) check(last = 0) -- itest.cpp #290 integral(sin(A*X),X)+cos(A*X)/A check(last = 0) -- itest.cpp #291 integral(cos(A*X),X)-sin(A*X)/A check(last = 0) -- itest.cpp #292 integral(tan(A*X),X)+log(cos(A*X))/A check(last = 0) -- itest.cpp #293 integral(1/tan(A*X),X)-log(sin(A*X))/A check(last = 0) -- itest.cpp #294 integral(1/cos(A*X),X)-log(tan(pi/4+A*X/2))/A check(last = 0) -- itest.cpp #295 integral(1/sin(A*X),X)-log(tan(A*X/2))/A check(last = 0) -- itest.cpp #296 integral(sin(A*X)^2,X)-X/2+sin(2*A*X)/(4*A) check(last = 0) -- itest.cpp #297 integral(sin(A*X)^3,X)+cos(A*X)*(sin(A*X)^2+2)/(3*A) check(last = 0) -- itest.cpp #298 integral(sin(A*X)^4,X)-3/8*X+sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A) check(last = 0) -- itest.cpp #302 integral(cos(A*X)^2,X)-X/2-sin(2*A*X)/(4*A) check(last = 0) -- itest.cpp #303 integral(cos(A*X)^3,X)-sin(A*X)*(cos(A*X)^2+2)/(3*A) check(last = 0) -- itest.cpp #304 integral(cos(A*X)^4,X)-3/8*X-sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A) check(last = 0) -- itest.cpp #308 integral((1/sin(A*X))^2,X)+1/A*1/tan(A*X) check(last = 0) -- itest.cpp #312 integral((1/cos(A*X))^2,X)-tan(A*X)/A check(last = 0) -- itest.cpp #318 integral(sin(A*X)*cos(A*X),X)-sin(A*X)^2/(2*A) check(last = 0) -- itest.cpp #320 integral(sin(A*X)^2*cos(A*X)^2,X)+sin(4*A*X)/(32*A)-X/8 check(last = 0) -- itest.cpp #326 integral(sin(A*X)/cos(A*X)/cos(A*X),X)-1/(A*cos(A*X)) check(last = 0) -- itest.cpp #327 integral(sin(A*X)^2/cos(A*X),X)+sin(A*X)/A-log(tan(pi/4+A*X/2))/A check(last = 0) -- itest.cpp #328 integral(cos(A*X)/sin(A*X)^2,X)+1/(A*sin(A*X)) check(last = 0) -- itest.cpp #329 integral(1/sin(A*X)/cos(A*X),X)-log(tan(A*X))/A check(last = 0) -- itest.cpp #330 integral(1/sin(A*X)/cos(A*X)^2,X)-(1/cos(A*X)+log(tan(A*X/2)))/A check(last = 0) -- itest.cpp #332 integral(1/sin(A*X)^2/cos(A*X),X)-(log(tan(pi/4+A*X/2))-1/sin(A*X))/A check(last = 0) -- itest.cpp #333 integral(1/sin(A*X)^2/cos(A*X)^2,X)+2/(A*tan(2*A*X)) check(last = 0) -- itest.cpp #335 integral(sin(A+B*X),X)+cos(A+B*X)/B check(last = 0) -- itest.cpp #336 integral(cos(A+B*X),X)-sin(A+B*X)/B check(last = 0) -- itest.cpp #337+ integral(1/(1+sin(A*X)),X)+tan(pi/4-A*X/2)/A check(last = 0) -- itest.cpp #337b+ integral(1/(B+B*sin(A*X)),X)+tan(pi/4-A*X/2)/A/B check(last = 0) -- itest.cpp #337- integral(1/(1-sin(A*X)),X)-tan(pi/4+A*X/2)/A check(last = 0) -- itest.cpp #337b- integral(1/(B-B*sin(A*X)),X)-tan(pi/4+A*X/2)/A/B check(last = 0) -- itest.cpp #338 integral(1/(1+cos(A*X)),X)-tan(A*X/2)/A check(last = 0) -- itest.cpp #339 integral(1/(1-cos(A*X)),X)+1/(A*tan(A*X/2)) check(last = 0) -- itest.cpp #340 integral(1/(A+B*sin(X)),X)-1/sqrt(B^2-A^2)*log((A*tan(X/2)+B-sqrt(B^2-A^2))/(A*tan(X/2)+B+sqrt(B^2-A^2))) check(last = 0) -- itest.cpp #341 integral(1/(A+B*cos(X)),X)-1/sqrt(B^2-A^2)*log((sqrt(B^2-A^2)*tan(X/2)+A+B)/(sqrt(B^2-A^2)*tan(X/2)-A-B)) check(last = 0) -- itest.cpp #389 x*sin(A*x)-d(integral(x*sin(A*x))) check(last = 0) -- itest.cpp #390 x^2*sin(A*x)-d(integral(x^2*sin(A*x))) check(last = 0) -- itest.cpp #393 x*cos(A*x)-d(integral(x*cos(A*x))) check(last = 0) -- itest.cpp #394 x^2*cos(A*x)-d(integral(x^2*cos(A*x))) check(last = 0) -- itest.cpp #441 integral(arcsin(A*X),X)-X*arcsin(A*X)-sqrt(1-A^2*X^2)/A check(last = 0) -- itest.cpp #442 integral(arccos(A*X),X)-X*arccos(A*X)-sqrt(1-A^2*X^2)/A check(last = 0) -- itest.cpp #443 integral(arctan(A*X),X)-X*arctan(A*X)+log(1+A^2*X^2)/(2*A) check(last = 0) -- itest.cpp #485 integral(log(X),X)-X*log(X)+X check(last = 0) -- itest.cpp #485a integral(log(A*X),X)-X*log(A*X)+X check(last = 0) -- itest.cpp #486 integral(X*log(X),X)-1/2*X^2*log(X)+1/4*X^2 check(last = 0) -- itest.cpp #486a integral(X*log(A*X),X)-1/2*X^2*log(A*X)+1/4*X^2 check(last = 0) -- itest.cpp #487 integral(X^2*log(A*X),X)-1/3*X^3*log(A*X)+X^3/9 check(last = 0) -- itest.cpp #489 integral(log(X)^2,X)-X*log(X)^2+2*X*log(X)-2*X check(last = 0) -- itest.cpp #493 integral(1/X*1/log(A*X),X)-log(log(A*X)) check(last = 0) -- itest.cpp #499 integral(log(A*X+B),X)-(A*X+B)*log(A*X+B)/A+X check(last = 0) -- itest.cpp #500 integral(log(A*X+B)/X^2,X)-A*log(X)/B+(A*X+B)*log(A*X+B)/B/X check(last = 0) -- itest.cpp #554 integral(sinh(X),X)-cosh(X) check(last = 0) -- itest.cpp #555 integral(cosh(X),X)-sinh(X) check(last = 0) -- itest.cpp #556 integral(tanh(X),X)-log(cosh(X)) check(last = 0) -- itest.cpp #560 integral(X*sinh(X),X)-X*cosh(X)+sinh(X) check(last = 0) -- itest.cpp #562 integral(X*cosh(X),X)-X*sinh(X)+cosh(X) check(last = 0) -- itest.cpp #566 integral(sinh(X)^2,X)-sinh(2*X)/4+X/2 check(last = 0) -- itest.cpp #569 integral(tanh(X)^2,X)-X+tanh(X) check(last = 0) -- itest.cpp #572 integral(cosh(X)^2,X)-sinh(2*X)/4-X/2 check(last = 0) -- itest.cpp integral(exp(a*x^2))+i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2 check(last = 0) -- itest.cpp integral(exp(-x^2))-sqrt(pi)*erf(x)/2 check(last = 0) -- itest.cpp integral(exp(-3*x^2))-sqrt(pi/3)*erf(sqrt(3)*x)/2 check(last = 0) -- itest.cpp integral(1/x*1/(a+log(x)),x)-log(a+log(x)) check(last = 0) -- itest.cpp integral(exp(a*x+b*x)) check(last = exp((a+b)*x)/(a+b)) -- itest.cpp integral(x*exp(a*x)) check(last = -exp(a*x)/(a^2)+x*exp(a*x)/a) -- itest.cpp derivative check(last = x*exp(a*x)) -- itest.cpp integral(x*exp(a*x+b)) check(last = -exp(a*x+b)/(a^2)+x*exp(a*x+b)/a) -- itest.cpp derivative check(last = x*exp(a*x+b)) -- itest.cpp integral(x*exp(-a*x+b)) check(last = -exp(-a*x+b)/(a^2)-x*exp(-a*x+b)/a) -- itest.cpp derivative check(last = x*exp(-a*x+b)) -- itest.cpp integral(x^2*exp(a*x)) check(last = 2*exp(a*x)/(a^3)-2*x*exp(a*x)/(a^2)+x^2*exp(a*x)/a) -- itest.cpp derivative check(last = x^2*exp(a*x)) -- itest.cpp integral(x^2*exp(a*x+b)) check(last = 2*exp(a*x+b)/(a^3)-2*x*exp(a*x+b)/(a^2)+x^2*exp(a*x+b)/a) -- itest.cpp derivative check(last = x^2*exp(a*x+b)) -- itest.cpp integral(x^3*exp(a*x)) check(last = -6*exp(a*x)/(a^4)+6*x*exp(a*x)/(a^3)-3*x^2*exp(a*x)/(a^2)+x^3*exp(a*x)/a) -- itest.cpp derivative check(last = x^3*exp(a*x)) -- itest.cpp integral(x^3*exp(a*x+b)) check(last = -6*exp(a*x+b)/(a^4)+6*x*exp(a*x+b)/(a^3)-3*x^2*exp(a*x+b)/(a^2)+x^3*exp(a*x+b)/a) -- itest.cpp derivative check(last = x^3*exp(a*x+b)) -- itest.cpp -- itest.cpp integral(x^2*(1-x^2)^(3/2))-(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48 check(last = 0) -- itest.cpp integral(x^4*(1-x^2)^(3/2))-(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128 check(last = 0) -- itest.cpp integral(x^2*(1-x^2)^(5/2))-(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384 check(last = 0) -- itest.cpp clear trace=1 laguerre(x,n) check(last = laguerre(x,n,0)) -- laguerre.cpp laguerre(x,n,k) check(last = laguerre(x,n,k)) -- laguerre.cpp laguerre(x,0)-1 check(last = 0) -- laguerre.cpp laguerre(x,1)-(-x+1) check(last = 0) -- laguerre.cpp laguerre(x,2)-1/2*(x^2-4*x+2) check(last = 0) -- laguerre.cpp laguerre(x,3)-1/6*(-x^3+9*x^2-18*x+6) check(last = 0) -- laguerre.cpp laguerre(x,0,k)-1 check(last = 0) -- laguerre.cpp laguerre(x,1,k)-(-x+k+1) check(last = 0) -- laguerre.cpp laguerre(x,2,k)-1/2*(x^2-2*(k+2)*x+(k+1)*(k+2)) check(last = 0) -- laguerre.cpp laguerre(x,3,k)-1/6*(-x^3+3*(k+3)*x^2-3*(k+2)*(k+3)*x+(k+1)*(k+2)*(k+3)) check(last = 0) -- laguerre.cpp laguerre(a-b,10)-eval(subst(a-b,x,laguerre(x,10))) check(last = 0) -- laguerre.cpp clear trace=1 lcm(4,6) check(last = 12) -- lcm.cpp lcm(4*x,6*x*y) check(last = 12*x*y) -- lcm.cpp lcm(2,3,4) check(last = 12) -- lcm.cpp clear trace=1 clear trace=1 legendre(x,n) check(last = legendre(x,n,0)) -- legendre.cpp legendre(x,n,m) check(last = legendre(x,n,m)) -- legendre.cpp legendre(x,0)-1 check(last = 0) -- legendre.cpp legendre(x,1)-x check(last = 0) -- legendre.cpp legendre(x,2)-1/2*(3*x^2-1) check(last = 0) -- legendre.cpp legendre(x,3)-1/2*(5*x^3-3*x) check(last = 0) -- legendre.cpp legendre(x,4)-1/8*(35*x^4-30*x^2+3) check(last = 0) -- legendre.cpp legendre(x,5)-1/8*(63*x^5-70*x^3+15*x) check(last = 0) -- legendre.cpp legendre(x,6)-1/16*(231*x^6-315*x^4+105*x^2-5) check(last = 0) -- legendre.cpp legendre(x,0,0)-1 check(last = 0) -- legendre.cpp legendre(x,1,0)-x check(last = 0) -- legendre.cpp legendre(x,1,1)+(1-x^2)^(1/2) check(last = 0) -- legendre.cpp legendre(x,2,0)-1/2*(3*x^2-1) check(last = 0) -- legendre.cpp legendre(x,2,1)+3*x*(1-x^2)^(1/2) check(last = 0) -- legendre.cpp legendre(x,2,2)-3*(1-x^2) check(last = 0) -- legendre.cpp legendre(x,3,0)-1/2*x*(5*x^2-3) check(last = 0) -- legendre.cpp legendre(x,3,1)-3/2*(1-5*x^2)*(1-x^2)^(1/2) check(last = 0) -- legendre.cpp legendre(x,3,2)-15*x*(1-x^2) check(last = 0) -- legendre.cpp legendre(x,3,3)+15*(1-x^2)^(3/2) check(last = 0) -- legendre.cpp legendre(x,4,0)-1/8*(35*x^4-30*x^2+3) check(last = 0) -- legendre.cpp legendre(x,4,1)-5/2*x*(3-7*x^2)*(1-x^2)^(1/2) check(last = 0) -- legendre.cpp legendre(x,4,2)-15/2*(7*x^2-1)*(1-x^2) check(last = 0) -- legendre.cpp legendre(x,4,3)+105*x*(1-x^2)^(3/2) check(last = 0) -- legendre.cpp legendre(x,4,4)-105*(1-x^2)^2 check(last = 0) -- legendre.cpp legendre(x,5,0)-1/8*x*(63*x^4-70*x^2+15) check(last = 0) -- legendre.cpp legendre(cos(theta),0,0)-1 check(last = 0) -- legendre.cpp legendre(cos(theta),1,0)-cos(theta) check(last = 0) -- legendre.cpp legendre(cos(theta),1,1)+sin(theta) check(last = 0) -- legendre.cpp legendre(cos(theta),2,0)-1/2*(3*cos(theta)^2-1) check(last = 0) -- legendre.cpp legendre(cos(theta),2,1)+3*sin(theta)*cos(theta) check(last = 0) -- legendre.cpp legendre(cos(theta),2,2)-3*sin(theta)^2 check(last = 0) -- legendre.cpp legendre(cos(theta),3,0)-1/2*cos(theta)*(5*cos(theta)^2-3) check(last = 0) -- legendre.cpp legendre(cos(theta),3,1)+3/2*(5*cos(theta)^2-1)*sin(theta) check(last = 0) -- legendre.cpp legendre(cos(theta),3,2)-15*cos(theta)*sin(theta)^2 check(last = 0) -- legendre.cpp legendre(cos(theta),3,3)+15*sin(theta)^3 check(last = 0) -- legendre.cpp legendre(a-b,10)-eval(subst(a-b,x,legendre(x,10))) check(last = 0) -- legendre.cpp clear trace=1 clear trace=1 log(1) check(last = 0) -- log.cpp log(exp(1)) check(last = 1) -- log.cpp log(exp(x)) check(last = x) -- log.cpp exp(log(x)) check(last = x) -- log.cpp log(x^2) check(last = 2*log(x)) -- log.cpp log(1/x) check(last = -log(x)) -- log.cpp log(a^b) check(last = b*log(a)) -- log.cpp log(2) check(last = log(2)) -- log.cpp log(2.0) check(abs(last - 0.693147) < 0.00001) -- log.cpp float(log(2)) check(abs(last - 0.693147) < 0.00001) -- log.cpp log(a*b) check(last = log(a)+log(b)) -- log.cpp log(1/3)+log(3) check(last = 0) -- log.cpp log(-1) check(last = i*pi) -- log.cpp log(-1.0) check(last = i*pi) -- log.cpp clear trace=1 clear trace=1 mag(a+i*b) check(last = (a^2+b^2)^(1/2)) -- mag.cpp mag(exp(a+i*b)) check(last = exp(a)) -- mag.cpp mag(1) check(last = 1) -- mag.cpp mag(-1) check(last = 1) -- mag.cpp mag(1+exp(i*pi/3)) check(last = 3^(1/2)) -- mag.cpp mag((a+i*b)/(c+i*d)) check(last = (a^2+b^2)^(1/2)/((c^2+d^2)^(1/2))) -- mag.cpp mag(exp(i theta)) check(last = 1) -- mag.cpp mag(exp(-i theta)) check(last = 1) -- mag.cpp mag((-1)^theta) check(last = 1) -- mag.cpp mag((-1)^(-theta)) check(last = 1) -- mag.cpp mag(3*(-1)^theta) check(last = 3) -- mag.cpp mag(3*(-1)^(-theta)) check(last = 3) -- mag.cpp mag(-3*(-1)^theta) check(last = 3) -- mag.cpp mag(-3*(-1)^(-theta)) check(last = 3) -- mag.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear gdd=((-exp(2*Phi(r)),0,0,0),(0,exp(2*Lambda(r)),0,0),(0,0,r^2,0),(0,0,0,r^2*sin(theta)^2)) X=(t,r,theta,phi) guu=inv(gdd) gddd=d(gdd,X) GAMDDD=1/2*(gddd+transpose(gddd,2,3)-transpose(transpose(gddd,2,3),1,2)) GAMUDD=contract(outer(guu,GAMDDD),2,3) T1=d(GAMUDD,X) T2=contract(outer(GAMUDD,GAMUDD),2,4) RUDDD=transpose(T1,3,4)-T1+transpose(T2,2,3)-transpose(transpose(T2,2,3),3,4) RDD=contract(RUDDD,1,3) R=contract(contract(outer(guu,RDD),2,3),1,2) GDD=RDD-1/2*gdd*R Gtt=1/r^2*exp(2 Phi(r)) d(r (1 - exp(-2 Lambda(r))),r) Grr=-1/r^2*exp(2*Lambda(r))*(1-exp(-2*Lambda(r)))+2/r*d(Phi(r),r) Gthetatheta=r^2*exp(-2*Lambda(r))*(d(d(Phi(r),r),r)+d(Phi(r),r)^2+d(Phi(r),r)/r-d(Phi(r),r)*d(Lambda(r),r)-d(Lambda(r),r)/r) Gphiphi=sin(theta)^2*Gthetatheta T=((Gtt,0,0,0),(0,Grr,0,0),(0,0,Gthetatheta,0),(0,0,0,Gphiphi)) GDD-T check(last = ((0,0,0,0),(0,0,0,0),(0,0,0,0),(0,0,0,0))) -- mini-test.cpp clear z=1-x^2-y^2 F=(x*y^2*z,-2*x^3,y*z^2) S=(x,y,z) s=dot(F,cross(d(S,x),d(S,y))) defint(s,y,-sqrt(1-x^2),sqrt(1-x^2),x,-1,1) check(last = 1/48*pi) -- mini-test.cpp clear laplacian(f)=1/r^2*d(r^2*d(f,r),r)+1/(r^2*sin(theta))*d(sin(theta)*d(f,theta),theta)+1/(r*sin(theta))^2*d(f,phi,phi) n=7 l=3 m=1 R=r^l*exp(-r/n)*laguerre(2*r/n,n-l-1,2*l+1) Y=legendre(cos(theta),l,abs(m))*exp(i*m*phi) psi=R*Y E=psi/n^2 K=laplacian(psi) V=2*psi/r circexp(sin(theta)*(E-K-V)) check(last = 0) -- mini-test.cpp clear P=2x^3-y^3 Q=x^3+y^3 f=d(Q,x)-d(P,y) x=r*cos(theta) y=r*sin(theta) f=eval(f) defint(f*r,r,0,1,theta,0,2pi) check(last = 3/2*pi) -- mini-test.cpp clear x=cos(t) y=sin(t) P=2x^3-y^3 Q=x^3+y^3 f=P*d(x,t)+Q*d(y,t) f=circexp(f) defint(f,t,0,2pi) check(last = 3/2*pi) -- mini-test.cpp clear z=9-x^2-y^2 F=(3y,4z,-6x) S=(x,y,z) f=dot(curl(F),cross(d(S,x),d(S,y))) x=r*cos(theta) y=r*sin(theta) f=eval(f) defint(f*r,r,0,3,theta,0,2pi) check(last = -27*pi) -- mini-test.cpp clear x=3*cos(t) y=3*sin(t) z=9-x^2-y^2 P=3y Q=4z R=-6x f=P*d(x,t)+Q*d(y,t)+R*d(z,t) f=circexp(f) defint(f,t,0,2pi) check(last = -27*pi) -- mini-test.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 mod(2.0,3.0) check(last = 2) -- mod.cpp mod(-2.0,3.0) check(last = -2) -- mod.cpp mod(2.0,-3.0) check(last = 2) -- mod.cpp mod(-2.0,-3.0) check(last = -2) -- mod.cpp mod(2,3) check(last = 2) -- mod.cpp mod(-2,3) check(last = -2) -- mod.cpp mod(2,-3) check(last = 2) -- mod.cpp mod(-2,-3) check(last = -2) -- mod.cpp mod(a,b) check(last = mod(a,b)) -- mod.cpp -- mod.cpp -- mod.cpp -- mod.cpp -- mod.cpp mod(15,8.0) check(last = 7) -- mod.cpp clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 0*a check(last = 0) -- multiply.cpp a*0 check(last = 0) -- multiply.cpp 1*a check(last = a) -- multiply.cpp a*1 check(last = a) -- multiply.cpp a*a check(last = a^2) -- multiply.cpp a^2*a check(last = a^3) -- multiply.cpp a*a^2 check(last = a^3) -- multiply.cpp a^2*a^2 check(last = a^4) -- multiply.cpp 2^a*2^(3-a) check(last = 8) -- multiply.cpp sqrt(2)/2 check(last = 2^(-1/2)) -- multiply.cpp 2/sqrt(2) check(last = 2^(1/2)) -- multiply.cpp -sqrt(2)/2 check(last = -1/(2^(1/2))) -- multiply.cpp 2^(1/2-a)*2^a/10 check(last = 1/(5*2^(1/2))) -- multiply.cpp i/4 check(last = 1/4*i) -- multiply.cpp 1/(4 i) check(last = -1/4*i) -- multiply.cpp 1.0 pi 1/2 check(last = 0.5*pi) -- multiply.cpp 1.0 1/2 pi check(last = 0.5*pi) -- multiply.cpp clear trace=1 nroots(x) check(last = 0) -- nroots.cpp --nroots((1+i)*x^2+1) --check(last = (-0.17178-0.727673*i,0.17178+0.727673*i)) -- nroots.cpp --nroots(sqrt(2)*exp(i*pi/4)*x^2+1) --check(last = (-0.17178-0.727673*i,0.17178+0.727673*i)) -- nroots.cpp clear trace=1 numerator(2/3) check(last = 2) -- numerator.cpp numerator(x) check(last = x) -- numerator.cpp numerator(1/x) check(last = 1) -- numerator.cpp numerator(a+b) check(last = a+b) -- numerator.cpp numerator(1/a+1/b) check(last = a+b) -- numerator.cpp clear trace=1 outer(a,b) check(last = a*b) -- outer.cpp outer(a,(b1,b2)) check(last = (a*b1,a*b2)) -- outer.cpp outer((a1,a2),b) check(last = (a1*b,a2*b)) -- outer.cpp H33=hilbert(3) H44=hilbert(4) H55=hilbert(5) H3344=outer(H33,H44) H4455=outer(H44,H55) H33444455=outer(H33,H44,H44,H55) simplify(inner(H3344,H4455)-contract(H33444455,4,5)) check(last = 0) -- outer.cpp clear trace=1 clear trace=1 polar(1+i) check(last = 2^(1/2)*exp(1/4*i*pi)) -- polar.cpp polar(-1+i) check(last = 2^(1/2)*exp(3/4*i*pi)) -- polar.cpp polar(-1-i) check(last = 2^(1/2)*exp(-3/4*i*pi)) -- polar.cpp polar(1-i) check(last = 2^(1/2)*exp(-1/4*i*pi)) -- polar.cpp rect(polar(3+4*i)) check(last = 3+4*i) -- polar.cpp rect(polar(-3+4*i)) check(last = -3+4*i) -- polar.cpp rect(polar(3-4*i)) check(last = 3-4*i) -- polar.cpp rect(polar(-3-4*i)) check(last = -3-4*i) -- polar.cpp clear trace=1 clear trace=1 2^(1/2) check(last = 2^(1/2)) -- power.cpp 2^(3/2) check(last = 2*2^(1/2)) -- power.cpp (-2)^(1/2) check(last = i*2^(1/2)) -- power.cpp 3^(4/3) check(last = 3*3^(1/3)) -- power.cpp 3^(-4/3) check(last = 1/(3*3^(1/3))) -- power.cpp 3^(5/3) check(last = 3*3^(2/3)) -- power.cpp 3^(2/3)-9^(1/3) check(last = 0) -- power.cpp 3^(10/3) check(last = 27*3^(1/3)) -- power.cpp 3^(-10/3) check(last = 1/(27*3^(1/3))) -- power.cpp (1/3)^(10/3) check(last = 1/(27*3^(1/3))) -- power.cpp (1/3)^(-10/3) check(last = 27*3^(1/3)) -- power.cpp 27^(2/3) check(last = 9) -- power.cpp 27^(-2/3) check(last = 1/9) -- power.cpp 102^(1/2) check(last = 2^(1/2)*3^(1/2)*17^(1/2)) -- power.cpp 32^(1/3) check(last = 2*2^(2/3)) -- power.cpp 9999^(1/2) check(last = 3*11^(1/2)*101^(1/2)) -- power.cpp 10000^(1/3) check(last = 10*2^(1/3)*5^(1/3)) -- power.cpp sqrt(1000000) check(last = 1000) -- power.cpp sqrt(-1000000) check(last = 1000*i) -- power.cpp sqrt(2^60) check(last = 1073741824) -- power.cpp 6^(1/3) 3^(2/3) check(last = 3*2^(1/3)) -- power.cpp 1/(2+3*i) check(last = 2/13-3/13*i) -- power.cpp 1/(2+3*i)^2 check(last = -5/169-12/169*i) -- power.cpp (-1+3i)/(2-i) check(last = -1+i) -- power.cpp (0.0)^(0.0) check(last = 1) -- power.cpp (-4.0)^(1.5) check(last = -8*i) -- power.cpp (-4.0)^(0.5) check(last = 2*i) -- power.cpp (-4.0)^(-0.5) check(last = -0.5*i) -- power.cpp (-4.0)^(-1.5) check(last = 0.125*i) -- power.cpp (1+i)^2 check(last = 2*i) -- power.cpp (1+i)^(-2) check(last = -1/2*i) -- power.cpp (1+i)^(1/2) check(last = (-1)^(1/8)*2^(1/4)) -- power.cpp (1+i)^(-1/2) check(last = -(-1)^(7/8)/(2^(1/4))) -- power.cpp --(1+i)^(0.5) --check(last = 1.09868+0.45509*i) -- power.cpp --(1+i)^(-0.5) --check(last = 0.776887-0.321797*i) -- power.cpp exp(i*pi/2) check(last = i) -- power.cpp exp(i*pi) check(last = -1) -- power.cpp exp(i*3*pi/2) check(last = -i) -- power.cpp exp(i*2*pi) check(last = 1) -- power.cpp exp(i*5*pi/2) check(last = i) -- power.cpp exp(i*3*pi) check(last = -1) -- power.cpp exp(i*7*pi/2) check(last = -i) -- power.cpp exp(i*4*pi) check(last = 1) -- power.cpp exp(A+i*pi/2) check(last = i*exp(A)) -- power.cpp exp(A+i*pi) check(last = -exp(A)) -- power.cpp exp(A+i*3*pi/2) check(last = -i*exp(A)) -- power.cpp exp(A+i*2*pi) check(last = exp(A)) -- power.cpp exp(A+i*5*pi/2) check(last = i*exp(A)) -- power.cpp exp(A+i*3*pi) check(last = -exp(A)) -- power.cpp exp(A+i*7*pi/2) check(last = -i*exp(A)) -- power.cpp exp(A+i*4*pi) check(last = exp(A)) -- power.cpp exp(-i*pi/2) check(last = -i) -- power.cpp exp(-i*pi) check(last = -1) -- power.cpp exp(-i*3*pi/2) check(last = i) -- power.cpp exp(-i*2*pi) check(last = 1) -- power.cpp exp(-i*5*pi/2) check(last = -i) -- power.cpp exp(-i*3*pi) check(last = -1) -- power.cpp exp(-i*7*pi/2) check(last = i) -- power.cpp exp(-i*4*pi) check(last = 1) -- power.cpp exp(A-i*pi/2) check(last = -i*exp(A)) -- power.cpp exp(A-i*pi) check(last = -exp(A)) -- power.cpp exp(A-i*3*pi/2) check(last = i*exp(A)) -- power.cpp exp(A-i*2*pi) check(last = exp(A)) -- power.cpp exp(A-i*5*pi/2) check(last = -i*exp(A)) -- power.cpp exp(A-i*3*pi) check(last = -exp(A)) -- power.cpp exp(A-i*7*pi/2) check(last = i*exp(A)) -- power.cpp exp(A-i*4*pi) check(last = exp(A)) -- power.cpp -- product.cpp clear trace=1 check(product(n,1,4,n)=24) check(n=quote(n)) A=2n check(product(n,1,4,A)=384) check(product(i,1,3,i)=6) check(i=sqrt(-1)) clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 clear trace=1 quotient(x^2+1,x+1)-x+1 check(last = 0) -- quotient.cpp quotient(a*x^2+b*x+c,d*x+e)-(-a*e/(d^2)+a*x/d+b/d) check(last = 0) -- quotient.cpp clear trace=1 rationalize(a/b+c/d) check(last = (a*d+b*c)/(b*d)) -- rationalize.cpp rationalize(t*y/(t+y)+2*t^2*y*(2*t+y)^(-2)) check(last = t*y*(6*t^2+y^2+6*t*y)/((t+y)*(2*t+y)^2)) -- rationalize.cpp rationalize(x^(-2*a)+x^(-4*a)) check(last = (1+x^(2*a))/(x^(4*a))) -- rationalize.cpp rationalize(x^(1/3)+x^(2/3)) check(last = x^(1/3)*(1+x^(1/3))) -- rationalize.cpp clear trace=1 real(a+i*b) check(last = a) -- real.cpp real(1+exp(i*pi/3)) check(last = 3/2) -- real.cpp real(i) check(last = 0) -- real.cpp real((-1)^(1/3)) check(last = 1/2) -- real.cpp clear trace=1 rect(a+i*b) check(last = a+i*b) -- rect.cpp rect(exp(a+i*b)) check(last = i*exp(a)*sin(b)+exp(a)*cos(b)) -- rect.cpp rect(1+exp(i*pi/3)) check(last = 3/2+1/2*i*3^(1/2)) -- rect.cpp z=(a+b*i)/(c+d*i) rect(z)-real(z)-i*imag(z) check(last = 0) -- rect.cpp z=quote(z) clear trace=1 roots(x) check(last = 0) -- roots.cpp roots(x^2) check(last = 0) -- roots.cpp roots(x^3) check(last = 0) -- roots.cpp roots(2 x) check(last = 0) -- roots.cpp roots(2 x^2) check(last = 0) -- roots.cpp roots(2 x^3) check(last = 0) -- roots.cpp roots(6+11*x+6*x^2+x^3) check(last = (-3,-2,-1)) -- roots.cpp roots(a*x^2+b*x+c) check(last = (-b/(2*a)-(-4*a*c+b^2)^(1/2)/(2*a),-b/(2*a)+(-4*a*c+b^2)^(1/2)/(2*a))) -- roots.cpp roots(3+7*x+5*x^2+x^3) check(last = (-3,-1)) -- roots.cpp roots(x^3+x^2+x+1) check(last = (-1,-i,i)) -- roots.cpp -- roots.cpp roots(x^2==1) check(last = (-1,1)) -- roots.cpp roots(3 x + 12 == 24) check(last = 4) -- roots.cpp y=roots(x^2+b*x+c/k)[1] y^2+b*y+c/k check(last = 0) -- roots.cpp y=roots(x^2+b*x+c/k)[2] y^2+b*y+c/k check(last = 0) -- roots.cpp y=roots(a*x^2+b*x+c/4)[1] a*y^2+b*y+c/4 check(last = 0) -- roots.cpp y=roots(a*x^2+b*x+c/4)[2] a*y^2+b*y+c/4 check(last = 0) -- roots.cpp y=quote(y) clear trace=1 clear trace=1 clear trace=1 sgn(-3) check(last = -1) -- sgn.cpp sgn(0) check(last = 0) -- sgn.cpp sgn(3) check(last = 1) -- sgn.cpp clear trace=1 clear trace=1 simplify(A) check(last = A) -- simplify.cpp simplify(A+B) check(last = A+B) -- simplify.cpp simplify(A B) check(last = A*B) -- simplify.cpp simplify(A^B) check(last = A^B) -- simplify.cpp simplify(A/(A+B)+B/(A+B)) check(last = 1) -- simplify.cpp simplify((A-B)/(B-A)) check(last = -1) -- simplify.cpp A=((A11,A12),(A21,A22)) simplify(det(A) inv(A) - adj(A)) check(last = 0) -- simplify.cpp A=quote(A) simplify(-3 exp(-1/3 r + i phi) cos(theta) / sin(theta) + 3 exp(-1/3 r + i phi) cos(theta) sin(theta) + 3 exp(-1/3 r + i phi) cos(theta)^3 / sin(theta)) check(last = 0) -- simplify.cpp simplify((A^2 C^2 + A^2 D^2 + B^2 C^2 + B^2 D^2)/(A^2+B^2)/(C^2+D^2)) check(last = 1) -- simplify.cpp simplify(d(arctan(y/x),y)) check(last = x/(x^2+y^2)) -- simplify.cpp simplify(d(arctan(y/x),x)) check(last = -y/(x^2+y^2)) -- simplify.cpp simplify(1-sin(x)^2) check(last = cos(x)^2) -- simplify.cpp simplify(1-cos(x)^2) check(last = sin(x)^2) -- simplify.cpp simplify(sin(x)^2-1) check(last = -cos(x)^2) -- simplify.cpp simplify(cos(x)^2-1) check(last = -sin(x)^2) -- simplify.cpp F=quote(F) simplify(n!/n)-(n-1)! check(last = 0) -- simplify.cpp simplify(n/n!)-1/(n-1)! check(last = 0) -- simplify.cpp simplify(rationalize((n+k+1)/(n+k+1)!))-1/(n+k)! check(last = 0) -- simplify.cpp simplify(condense((n+1)*n!))-(n+1)! check(last = 0) -- simplify.cpp simplify(1/((n+1)*n!))-1/(n+1)! check(last = 0) -- simplify.cpp simplify((n+1)!/n!)-n-1 check(last = 0) -- simplify.cpp simplify(n!/(n+1)!)-1/(n+1) check(last = 0) -- simplify.cpp simplify(binomial(n+1,k)/binomial(n,k)) check(last = (1+n)/(1-k+n)) -- simplify.cpp simplify(binomial(n,k)/binomial(n+1,k)) check(last = (1-k+n)/(1+n)) -- simplify.cpp F(nn,kk)=kk*binomial(nn,kk) simplify((F(n,k)+F(n,k-1))/F(n+1,k))-n/(n+1) check(last = 0) -- simplify.cpp F=quote(F) simplify((n+1)/(n+1)!)-1/n! check(last = 0) -- simplify.cpp simplify(a*b+a*c) check(last = a*(b+c)) -- simplify.cpp x=simplify(a*b+a*c) x check(last = a*b+a*c) -- simplify.cpp clear trace=1 sin(x) check(last = sin(x)) -- sin.cpp sin(-x) check(last = -sin(x)) -- sin.cpp sin(b-a) check(last = -sin(a-b)) -- sin.cpp f(a,x)=1+sin(a/360*2*pi)-x f(0,0) check(last = 1) -- sin.cpp f(90,1) check(last = 1) -- sin.cpp f(180,0) check(last = 1) -- sin.cpp f(270,-1) check(last = 1) -- sin.cpp f(360,0) check(last = 1) -- sin.cpp f(-90,-1) check(last = 1) -- sin.cpp f(-180,0) check(last = 1) -- sin.cpp f(-270,1) check(last = 1) -- sin.cpp f(-360,0) check(last = 1) -- sin.cpp f(45,sqrt(2)/2) check(last = 1) -- sin.cpp f(135,sqrt(2)/2) check(last = 1) -- sin.cpp f(225,-sqrt(2)/2) check(last = 1) -- sin.cpp f(315,-sqrt(2)/2) check(last = 1) -- sin.cpp f(-45,-sqrt(2)/2) check(last = 1) -- sin.cpp f(-135,-sqrt(2)/2) check(last = 1) -- sin.cpp f(-225,sqrt(2)/2) check(last = 1) -- sin.cpp f(-315,sqrt(2)/2) check(last = 1) -- sin.cpp f(30,1/2) check(last = 1) -- sin.cpp f(150,1/2) check(last = 1) -- sin.cpp f(210,-1/2) check(last = 1) -- sin.cpp f(330,-1/2) check(last = 1) -- sin.cpp f(-30,-1/2) check(last = 1) -- sin.cpp f(-150,-1/2) check(last = 1) -- sin.cpp f(-210,1/2) check(last = 1) -- sin.cpp f(-330,1/2) check(last = 1) -- sin.cpp f(60,sqrt(3)/2) check(last = 1) -- sin.cpp f(120,sqrt(3)/2) check(last = 1) -- sin.cpp f(240,-sqrt(3)/2) check(last = 1) -- sin.cpp f(300,-sqrt(3)/2) check(last = 1) -- sin.cpp f(-60,-sqrt(3)/2) check(last = 1) -- sin.cpp f(-120,-sqrt(3)/2) check(last = 1) -- sin.cpp f(-240,sqrt(3)/2) check(last = 1) -- sin.cpp f(-300,sqrt(3)/2) check(last = 1) -- sin.cpp f=quote(f) sin(arcsin(x)) check(last = x) -- sin.cpp sin(1/12*pi) check(last = sin(1/12*pi)) -- sin.cpp sin(arctan(4/3)) check(last = 4/5) -- sin.cpp sin(-arctan(4/3)) check(last = -4/5) -- sin.cpp sin(x-8/2*pi) check(last = sin(x)) -- sin.cpp sin(x-7/2*pi) check(last = cos(x)) -- sin.cpp sin(x-6/2*pi) check(last = -sin(x)) -- sin.cpp sin(x-5/2*pi) check(last = -cos(x)) -- sin.cpp sin(x-4/2*pi) check(last = sin(x)) -- sin.cpp sin(x-3/2*pi) check(last = cos(x)) -- sin.cpp sin(x-2/2*pi) check(last = -sin(x)) -- sin.cpp sin(x-1/2*pi) check(last = -cos(x)) -- sin.cpp sin(x+0/2*pi) check(last = sin(x)) -- sin.cpp sin(x+1/2*pi) check(last = cos(x)) -- sin.cpp sin(x+2/2*pi) check(last = -sin(x)) -- sin.cpp sin(x+3/2*pi) check(last = -cos(x)) -- sin.cpp sin(x+4/2*pi) check(last = sin(x)) -- sin.cpp sin(x+5/2*pi) check(last = cos(x)) -- sin.cpp sin(x+6/2*pi) check(last = -sin(x)) -- sin.cpp sin(x+7/2*pi) check(last = -cos(x)) -- sin.cpp sin(x+8/2*pi) check(last = sin(x)) -- sin.cpp clear trace=1 sinh(x) check(last = sinh(x)) -- sinh.cpp sinh(0) check(last = 0) -- sinh.cpp sinh(arcsinh(x)) check(last = x) -- sinh.cpp clear trace=1 clear trace=1 clear trace=1 sum(n,0,10,(-1/3)^n) check(last = 44287/59049) -- sum.cpp sum(i,1,3,i) check(sum(k,1,3,k) = 6) check(i = sqrt(-1)) check(sum(k,1,3,2k) = 12) A=2k check(sum(k,1,3,A) = 12) clear trace=1 clear trace=1 tan(x) check(last = tan(x)) -- tan.cpp tan(-x) check(last = -tan(x)) -- tan.cpp tan(b-a) check(last = -tan(a-b)) -- tan.cpp f(a,x)=1+tan(a/360*2*pi)-x f(0,0) check(last = 1) -- tan.cpp f(180,0) check(last = 1) -- tan.cpp f(360,0) check(last = 1) -- tan.cpp f(-180,0) check(last = 1) -- tan.cpp f(-360,0) check(last = 1) -- tan.cpp f(45,1) check(last = 1) -- tan.cpp f(135,-1) check(last = 1) -- tan.cpp f(225,1) check(last = 1) -- tan.cpp f(315,-1) check(last = 1) -- tan.cpp f(-45,-1) check(last = 1) -- tan.cpp f(-135,1) check(last = 1) -- tan.cpp f(-225,-1) check(last = 1) -- tan.cpp f(-315,1) check(last = 1) -- tan.cpp f(30,sqrt(3)/3) check(last = 1) -- tan.cpp f(150,-sqrt(3)/3) check(last = 1) -- tan.cpp f(210,sqrt(3)/3) check(last = 1) -- tan.cpp f(330,-sqrt(3)/3) check(last = 1) -- tan.cpp f(-30,-sqrt(3)/3) check(last = 1) -- tan.cpp f(-150,sqrt(3)/3) check(last = 1) -- tan.cpp f(-210,-sqrt(3)/3) check(last = 1) -- tan.cpp f(-330,sqrt(3)/3) check(last = 1) -- tan.cpp f(60,sqrt(3)) check(last = 1) -- tan.cpp f(120,-sqrt(3)) check(last = 1) -- tan.cpp f(240,sqrt(3)) check(last = 1) -- tan.cpp f(300,-sqrt(3)) check(last = 1) -- tan.cpp f(-60,-sqrt(3)) check(last = 1) -- tan.cpp f(-120,sqrt(3)) check(last = 1) -- tan.cpp f(-240,-sqrt(3)) check(last = 1) -- tan.cpp f(-300,sqrt(3)) check(last = 1) -- tan.cpp f=quote(f) tan(arctan(x)) check(last = x) -- tan.cpp tan(1/12*pi) check(last = tan(1/12*pi)) -- tan.cpp clear trace=1 tanh(x) check(last = tanh(x)) -- tanh.cpp tanh(0) check(last = 0) -- tanh.cpp tanh(arctanh(x)) check(last = x) -- tanh.cpp clear trace=1 taylor(1/(5+4*cos(x)),x,6,0)-(1/9+2/81*x^2+5/1458*x^4+49/131220*x^6) check(last = 0) -- taylor.cpp taylor(1/(5+4*cos(x)),x,6)-(1/9+2/81*x^2+5/1458*x^4+49/131220*x^6) check(last = 0) -- taylor.cpp clear trace=1 #test_tensor a=(1,2,3) b=(4,5,6) c=(7,8,9) rank((a,b,c)) check(last = 2) -- tensor.cpp (a,b,c) check(last = ((1,2,3),(4,5,6),(7,8,9))) -- tensor.cpp ((1,0),(0,0)) check(last = ((1,0),(0,0))) -- tensor.cpp a=quote(a) b=quote(b) c=quote(c) clear trace=1 a=1 check(last = 1) -- test.cpp 1>=2 check(last = 0) -- test.cpp 2>=1 check(last = 1) -- test.cpp 1>1 check(last = 0) -- test.cpp 1>2 check(last = 0) -- test.cpp 2>1 check(last = 1) -- test.cpp 1<=1 check(last = 1) -- test.cpp 1<=2 check(last = 1) -- test.cpp 2<=1 check(last = 0) -- test.cpp 1<1 check(last = 0) -- test.cpp 1<2 check(last = 1) -- test.cpp 2<1 check(last = 0) -- test.cpp test(0,A,B) check(last = B) -- test.cpp test(1,A,B) check(last = A) -- test.cpp test(0,A,0,B) check(last = 0) -- test.cpp test(0,A,0,B,C) check(last = C) -- test.cpp not(1) check(last = 0) -- test.cpp not(0) check(last = 1) -- test.cpp not(a=a) check(last = 0) -- test.cpp and(1,1) check(last = 1) -- test.cpp and(1,0) check(last = 0) -- test.cpp or(1,0) check(last = 1) -- test.cpp or(0,0) check(last = 0) -- test.cpp (0,0)==0 check(last = 1) -- test.cpp 1