Results of Elementary Functions
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DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|
4.2.E8 | log[a](z)=(ln(z))/(ln(a)) |
Log[a,z]=Divide[Log[z],Log[a]] |
Successful | Successful | - | - | |
4.2.E9 | log[a](z)=(log[b](z))/(log[b](a)) |
Log[a,z]=Divide[Log[b,z],Log[b,a]] |
Successful | Successful | - | - | |
4.2.E10 | log[a](b)=(1)/(log[b](a)) |
Log[a,b]=Divide[1,Log[b,a]] |
Successful | Successful | - | - | |
4.2.E12 | ln(exp(1))= 1 |
Log[E]= 1 |
Successful | Successful | - | - | |
4.2.E13 | int((1)/(t), t = 1..exp(1))= 1 |
Integrate[Divide[1,t], {t, 1, E}]= 1 |
Successful | Successful | - | - | |
4.2.E14 | log[exp(1)](z)= ln(z) |
Log[E,z]= Log[z] |
Successful | Successful | - | - | |
4.2.E15 | log[10](z)=(ln(z))/(ln(10)) |
Log[10,z]=Divide[Log[z],Log[10]] |
Successful | Successful | - | - | |
4.2.E15 | (ln(z))/(ln(10))=(log[10](exp(1)))* ln(z) |
Divide[Log[z],Log[10]]=(Log[10,E])* Log[z] |
Successful | Successful | - | - | |
4.2.E16 | ln(z)=(ln(10))* log[10](z) |
Log[z]=(Log[10])* Log[10,z] |
Successful | Successful | - | - | |
4.2.E20 | exp(z + 2*Pi*I)= exp(z) |
Exp[z + 2*Pi*I]= Exp[z] |
Successful | Successful | - | - | |
4.2.E21 | exp(- z)= 1/ exp(z) |
Exp[- z]= 1/ Exp[z] |
Successful | Successful | - | - | |
4.2.E22 | abs(exp(z))= exp(Re(z)) |
Abs[Exp[z]]= Exp[Re[z]] |
Successful | Successful | - | - | |
4.2.E23 | argument(exp(z))= Im(z)+ 2*k*Pi |
Arg[Exp[z]]= Im[z]+ 2*k*Pi |
Failure | Failure | Fail -18.84955592 <- {z = 2^(1/2)+I*2^(1/2), k = 3} -18.84955592 <- {z = 2^(1/2)-I*2^(1/2), k = 3} -18.84955592 <- {z = -2^(1/2)-I*2^(1/2), k = 3} -18.84955592 <- {z = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
-18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} -18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} -18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} -18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.2.E24 | exp(z)= exp(x)*cos(y)+ I*exp(x)*sin(y) |
Exp[z]= Exp[x]*Cos[y]+ I*Exp[x]*Sin[y] |
Failure | Failure | Fail -.8272584772+1.775573363*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1} 1.772639846+1.591201978*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2} 3.332514076+3.679324696*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3} -3.350888586-2.154747662*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1} ... skip entries to safe data |
Fail
Complex[-0.8272584783533998, 1.7755733643246545] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.7726398453192989, 1.591201979498678] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[3.332514075382279, 3.679324697962366] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-3.3508885868787868, -2.154747660864471] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.2.E26 | (z)^(a)= exp(a*ln(z)) |
(z)^(a)= Exp[a*Log[z]] |
Successful | Failure | - | Successful | |
4.2.E28 | (z)^(a)= exp(a*ln(z)) |
(z)^(a)= Exp[a*Log[z]] |
Successful | Successful | - | - | |
4.2.E29 | abs((z)^(a))=(abs(z))^(Re(a))* exp(-(Im(a))* argument(z)) |
Abs[(z)^(a)]=(Abs[z])^(Re[a])* Exp[-(Im[a])* Arg[z]] |
Failure | Failure | Successful | Successful | |
4.2.E30 | argument((z)^(a))=(Re(a))* argument(z)+(Im(a))* ln(abs(z)) |
Arg[(z)^(a)]=(Re[a])* Arg[z]+(Im[a])* Log[Abs[z]] |
Failure | Failure | Fail -6.283185309 <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} 6.283185309 <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} 6.283185309 <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} -6.283185309 <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} |
Fail
-6.283185307179586 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} 6.283185307179586 <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} 6.283185307179586 <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} -6.283185307179586 <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} | |
4.2#Ex2 | argument((z)^(a))= a*argument(z) |
Arg[(z)^(a)]= a*Arg[z] |
Failure | Failure | Fail .980258143-1.110720734*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)} .9802581426+1.110720734*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)} .980258144+3.332162204*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} -5.302927166-3.332162204*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data |
Fail
Complex[0.9802581434685473, -1.1107207345395915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.9802581434685472, 1.1107207345395915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[0.9802581434685469, 3.332162203618774] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.302927163711039, -3.332162203618774] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.2.E32 | exp(z)= exp(z) |
Exp[z]= Exp[z] |
Successful | Successful | - | - | |
4.2.E33 | exp(z)=(exp(z))* exp(2*k*z*Pi*I) |
Exp[z]=(Exp[z])* Exp[2*k*z*Pi*I] |
Failure | Failure | Fail .6414354628+4.062928650*I <- {z = 2^(1/2)+I*2^(1/2), k = 3} -.1544020768e13-.1710664597e12*I <- {z = 2^(1/2)-I*2^(1/2), k = 3} .8993679173e11+.1849553851e11*I <- {z = -2^(1/2)-I*2^(1/2), k = 3} .3791252193e-1+.2401424313*I <- {z = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
Complex[0.6414354615731531, 4.062928651501303] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-1.5440207807554412*^12, -1.710664745395911*^11] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[8.993679264986926*^10, 1.8495537828408436*^10] <- {Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.03791252182632387, 0.24014243117514714] <- {Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.2.E36 | - Pi < = Im((1)/(a)*ln(w)) |
- Pi < = Im[Divide[1,a]*Log[w]] |
Failure | Failure | Successful | Successful | |
4.2.E36 | Im((1)/(a)*ln(w))< = Pi |
Im[Divide[1,a]*Log[w]]< = Pi |
Failure | Failure | Successful | Successful | |
4.4.E1 | ln(1)= 0 |
Log[1]= 0 |
Successful | Successful | - | - | |
4.4.E2 | ln(- 1 + I*0)= + Pi*I |
Log[- 1 + I*0]= + Pi*I |
Successful | Successful | - | - | |
4.4.E2 | ln(- 1 - I*0)= - Pi*I |
Log[- 1 - I*0]= - Pi*I |
Failure | Failure | Fail 6.283185308*I <- {} |
Fail
Complex[0.0, 6.283185307179586] <- {} | |
4.4.E3 | ln(+ I)= +(1)/(2)*Pi*I |
Log[+ I]= +Divide[1,2]*Pi*I |
Successful | Successful | - | - | |
4.4.E3 | ln(- I)= -(1)/(2)*Pi*I |
Log[- I]= -Divide[1,2]*Pi*I |
Successful | Successful | - | - | |
4.4.E5 | exp(+ Pi*I)= - 1 |
Exp[+ Pi*I]= - 1 |
Successful | Successful | - | - | |
4.4.E5 | exp(- Pi*I)= - 1 |
Exp[- Pi*I]= - 1 |
Successful | Successful | - | - | |
4.4.E6 | exp(+ Pi*I/ 2)= + I |
Exp[+ Pi*I/ 2]= + I |
Successful | Successful | - | - | |
4.4.E6 | exp(- Pi*I/ 2)= - I |
Exp[- Pi*I/ 2]= - I |
Successful | Successful | - | - | |
4.4.E7 | exp(2*Pi*k*I)= 1 |
Exp[2*Pi*k*I]= 1 |
Successful | Failure | - | Successful | |
4.4.E8 | exp(+ Pi*I/ 3)=(1)/(2)+ I*(sqrt(3))/(2) |
Exp[+ Pi*I/ 3]=Divide[1,2]+ I*Divide[Sqrt[3],2] |
Successful | Successful | - | - | |
4.4.E8 | exp(- Pi*I/ 3)=(1)/(2)- I*(sqrt(3))/(2) |
Exp[- Pi*I/ 3]=Divide[1,2]- I*Divide[Sqrt[3],2] |
Successful | Successful | - | - | |
4.4.E9 | exp(+ 2*Pi*I/ 3)= -(1)/(2)+ I*(sqrt(3))/(2) |
Exp[+ 2*Pi*I/ 3]= -Divide[1,2]+ I*Divide[Sqrt[3],2] |
Successful | Successful | - | - | |
4.4.E9 | exp(- 2*Pi*I/ 3)= -(1)/(2)- I*(sqrt(3))/(2) |
Exp[- 2*Pi*I/ 3]= -Divide[1,2]- I*Divide[Sqrt[3],2] |
Successful | Successful | - | - | |
4.4.E10 | exp(+ Pi*I/ 4)=(1)/(sqrt(2))+ I*(1)/(sqrt(2)) |
Exp[+ Pi*I/ 4]=Divide[1,Sqrt[2]]+ I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - | |
4.4.E10 | exp(- Pi*I/ 4)=(1)/(sqrt(2))- I*(1)/(sqrt(2)) |
Exp[- Pi*I/ 4]=Divide[1,Sqrt[2]]- I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - | |
4.4.E11 | exp(+ 3*Pi*I/ 4)= -(1)/(sqrt(2))+ I*(1)/(sqrt(2)) |
Exp[+ 3*Pi*I/ 4]= -Divide[1,Sqrt[2]]+ I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - | |
4.4.E11 | exp(- 3*Pi*I/ 4)= -(1)/(sqrt(2))- I*(1)/(sqrt(2)) |
Exp[- 3*Pi*I/ 4]= -Divide[1,Sqrt[2]]- I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - | |
4.4.E12 | (I)^(+ I)= exp(- Pi/ 2) |
(I)^(+ I)= Exp[- Pi/ 2] |
Successful | Successful | - | - | |
4.4.E12 | (I)^(- I)= exp(+ Pi/ 2) |
(I)^(- I)= Exp[+ Pi/ 2] |
Successful | Successful | - | - | |
4.4.E13 | limit((x)^(- a)* ln(x), x = infinity)= 0 |
Limit[(x)^(- a)* Log[x], x -> Infinity]= 0 |
Successful | Failure | - | Successful | |
4.4.E14 | limit((x)^(a)* ln(x), x = 0)= 0 |
Limit[(x)^(a)* Log[x], x -> 0]= 0 |
Failure | Failure | Skip | Successful | |
4.4.E19 | limit((sum((1)/(k), k = 1..n))- ln(n), n = infinity)= gamma |
Limit[(Sum[Divide[1,k], {k, 1, n}])- Log[n], n -> Infinity]= EulerGamma |
Successful | Successful | - | - | |
4.5.E1 | (x)/(1 + x)< ln(1 + x) |
Divide[x,1 + x]< Log[1 + x] |
Failure | Failure | Skip | Successful | |
4.5.E1 | ln(1 + x)< x |
Log[1 + x]< x |
Failure | Failure | Skip | Successful | |
4.5.E2 | x < - ln(1 - x) |
x < - Log[1 - x] |
Failure | Failure | Skip | Successful | |
4.5.E2 | - ln(1 - x)<(x)/(1 - x) |
- Log[1 - x]<Divide[x,1 - x] |
Failure | Failure | Skip | Successful | |
4.5.E3 | abs(ln(1 - x))<(3)/(2)*x |
Abs[Log[1 - x]]<Divide[3,2]*x |
Failure | Failure | Error | Successful | |
4.5.E4 | ln(x)< = x - 1 |
Log[x]< = x - 1 |
Failure | Failure | Successful | Successful | |
4.5.E5 | ln(x)< = a*((x)^(1/ a)- 1) |
Log[x]< = a*((x)^(1/ a)- 1) |
Failure | Failure | Successful | Successful | |
4.5.E6 | abs(ln(1 + z))< = - ln(1 -abs(z)) |
Abs[Log[1 + z]]< = - Log[1 -Abs[z]] |
Failure | Failure | Successful | Successful | |
4.7.E1 | diff(ln(z), z)=(1)/(z) |
D[Log[z], z]=Divide[1,z] |
Successful | Successful | - | - | |
4.7.E2 | diff(ln(z), z)=(1)/(z) |
D[Log[z], z]=Divide[1,z] |
Successful | Successful | - | - | |
4.7.E3 | diff(ln(z), [z$(n)])=(- 1)^(n - 1)*factorial(n - 1)*(z)^(- n) |
D[Log[z], {z, n}]=(- 1)^(n - 1)*(n - 1)!*(z)^(- n) |
Failure | Failure | Successful | Successful | |
4.7.E4 | diff(ln(z), [z$(n)])=(- 1)^(n - 1)*factorial(n - 1)*(z)^(- n) |
D[Log[z], {z, n}]=(- 1)^(n - 1)*(n - 1)!*(z)^(- n) |
Failure | Failure | Successful | Successful | |
4.7.E7 | diff(exp(z), z)= exp(z) |
D[Exp[z], z]= Exp[z] |
Successful | Successful | - | - | |
4.7.E8 | diff(exp(a*z), z)= a*exp(a*z) |
D[Exp[a*z], z]= a*Exp[a*z] |
Successful | Successful | - | - | |
4.7.E9 | diff((a)^(z), z)= (a)^(z)* ln(a) |
D[(a)^(z), z]= (a)^(z)* Log[a] |
Successful | Failure | - | Successful | |
4.7.E10 | diff((z)^(a), z)= a*(z)^(a - 1) |
D[(z)^(a), z]= a*(z)^(a - 1) |
Successful | Successful | - | - | |
4.7.E14 | diff(w, [z$(2)])= a*w |
D[w, {z, 2}]= a*w |
Failure | Failure | Skip | Successful | |
4.8.E1 | ln(z[1]*z[2])= ln(z[1])+ ln(z[2]) |
Log[Subscript[z, 1]*Subscript[z, 2]]= Log[Subscript[z, 1]]+ Log[Subscript[z, 2]] |
Failure | Failure | Fail .4e-9+6.283185307*I <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)} .4e-9+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2)} 0.+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)} 0.-6.283185307*I <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, -6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.8.E2 | ln(z[1]*z[2])= ln(z[1])+ ln(z[2]) |
Log[Subscript[z, 1]*Subscript[z, 2]]= Log[Subscript[z, 1]]+ Log[Subscript[z, 2]] |
Failure | Failure | Skip | Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} | |
4.8.E3 | ln((z[1])/(z[2]))= ln(z[1])- ln(z[2]) |
Log[Divide[Subscript[z, 1],Subscript[z, 2]]]= Log[Subscript[z, 1]]- Log[Subscript[z, 2]] |
Failure | Failure | Fail 0.+6.283185307*I <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)} 0.+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2)} 0.+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)} 0.-6.283185307*I <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)} |
Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, -6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} | |
4.8.E4 | ln((z[1])/(z[2]))= ln(z[1])- ln(z[2]) |
Log[Divide[Subscript[z, 1],Subscript[z, 2]]]= Log[Subscript[z, 1]]- Log[Subscript[z, 2]] |
Failure | Failure | Skip | Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} | |
4.8.E5 | ln((z)^(n))= n*ln(z) |
Log[(z)^(n)]= n*Log[z] |
Failure | Failure | Fail 0.+6.283185307*I <- {z = -2^(1/2)-I*2^(1/2), n = 3} 0.-6.283185307*I <- {z = -2^(1/2)+I*2^(1/2), n = 3} |
Fail
Complex[0.0, 6.283185307179586] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, -6.283185307179586] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.8.E6 | ln((z)^(n))= n*ln(z) |
Log[(z)^(n)]= n*Log[z] |
Failure | Failure | Skip | Successful | |
4.8.E7 | ln((1)/(z))= - ln(z) |
Log[Divide[1,z]]= - Log[z] |
Failure | Failure | Skip | Successful | |
4.8.E8 | ln(exp(z))= z + 2*k*Pi*I |
Log[Exp[z]]= z + 2*k*Pi*I |
Failure | Failure | Fail 0.-18.84955592*I <- {z = 2^(1/2)+I*2^(1/2), k = 3} 0.-18.84955592*I <- {z = 2^(1/2)-I*2^(1/2), k = 3} 0.-18.84955592*I <- {z = -2^(1/2)-I*2^(1/2), k = 3} 0.-18.84955592*I <- {z = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.8.E9 | ln(exp(z))= z |
Log[Exp[z]]= z |
Failure | Failure | Skip | Successful | |
4.8.E10 | exp(ln(z))= exp(ln(z)) |
Exp[Log[z]]= Exp[Log[z]] |
Successful | Successful | - | - | |
4.8.E10 | exp(ln(z))= z |
Exp[Log[z]]= z |
Successful | Successful | - | - | |
4.8.E11 | ln((a)^(z))= z*ln(a)+ 2*k*Pi*I |
Log[(a)^(z)]= z*Log[a]+ 2*k*Pi*I |
Failure | Failure | Fail 0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3} 0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 3} 0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), k = 3} 0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), k = 3} ... skip entries to safe data |
Fail
Complex[1.1102230246251565*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.3877787807814457*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[4.440892098500626*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.8.E12 | ln((a)^(z))= z*ln(a)+ 2*k*Pi*I |
Log[(a)^(z)]= z*Log[a]+ 2*k*Pi*I |
Failure | Failure | Fail 0.-6.283185308*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1} 0.-12.56637062*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2} 0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3} 0.-6.283185308*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1} ... skip entries to safe data |
Fail
Complex[1.1102230246251565*^-16, -6.283185307179586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.1102230246251565*^-16, -12.566370614359172] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.1102230246251565*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0, -6.283185307179586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.8.E13 | ln((a)^(x))= x*ln(a) |
Log[(a)^(x)]= x*Log[a] |
Failure | Failure | Successful | Successful | |
4.10.E1 | int((1)/(z), z)= ln(z) |
Integrate[Divide[1,z], z]= Log[z] |
Successful | Successful | - | - | |
4.10.E2 | int(ln(z), z)= z*ln(z)- z |
Integrate[Log[z], z]= z*Log[z]- z |
Successful | Successful | - | - | |
4.10.E3 | int((z)^(n)* ln(z), z)=((z)^(n + 1))/(n + 1)*ln(z)-((z)^(n + 1))/((n + 1)^(2)) |
Integrate[(z)^(n)* Log[z], z]=Divide[(z)^(n + 1),n + 1]*Log[z]-Divide[(z)^(n + 1),(n + 1)^(2)] |
Successful | Successful | - | - | |
4.10.E4 | int((1)/(z*ln(z)), z)= ln(ln(z)) |
Integrate[Divide[1,z*Log[z]], z]= Log[Log[z]] |
Successful | Successful | - | - | |
4.10.E5 | int((ln(t))/(1 - t), t = 0..1)= -((Pi)^(2))/(6) |
Integrate[Divide[Log[t],1 - t], {t, 0, 1}]= -Divide[(Pi)^(2),6] |
Successful | Successful | - | - | |
4.10.E6 | int((ln(t))/(1 + t), t = 0..1)= -((Pi)^(2))/(12) |
Integrate[Divide[Log[t],1 + t], {t, 0, 1}]= -Divide[(Pi)^(2),12] |
Successful | Successful | - | - | |
4.10.E8 | int(exp(a*z), z)=(exp(a*z))/(a) |
Integrate[Exp[a*z], z]=Divide[Exp[a*z],a] |
Successful | Successful | - | - | |
4.10.E9 | int((1)/(exp(a*z)+ b), z)=(1)/(a*b)*(a*z - ln(exp(a*z)+ b)) |
Integrate[Divide[1,Exp[a*z]+ b], z]=Divide[1,a*b]*(a*z - Log[Exp[a*z]+ b]) |
Failure | Successful | Skip | - | |
4.10.E10 | int((exp(a*z)- 1)/(exp(a*z)+ 1), z)=(2)/(a)*ln(exp(a*z/ 2)+ exp(- a*z/ 2)) |
Integrate[Divide[Exp[a*z]- 1,Exp[a*z]+ 1], z]=Divide[2,a]*Log[Exp[a*z/ 2]+ Exp[- a*z/ 2]] |
Failure | Failure | Skip | Fail
Complex[-4.442882938158366, -4.442882938158366] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[4.442882938158366, -4.442882938158366] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[4.442882938158366, 4.442882938158366] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-4.442882938158366, 4.442882938158366] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} | |
4.10.E11 | int(exp(- c*(x)^(2)), x = - infinity..infinity)=sqrt((Pi)/(c)) |
Integrate[Exp[- c*(x)^(2)], {x, - Infinity, Infinity}]=Sqrt[Divide[Pi,c]] |
Successful | Failure | - | Skip | |
4.10.E12 | int((x*exp(x))/(exp(x)- 1), x = 0..ln(2))=((Pi)^(2))/(12) |
Integrate[Divide[x*Exp[x],Exp[x]- 1], {x, 0, Log[2]}]=Divide[(Pi)^(2),12] |
Successful | Successful | - | - | |
4.10.E13 | int((1)/(exp(x)+ 1), x = 0..infinity)= ln(2) |
Integrate[Divide[1,Exp[x]+ 1], {x, 0, Infinity}]= Log[2] |
Successful | Successful | - | - | |
4.12.E6 | phi*(x)= ln(x + 1) |
\[Phi]*(x)= Log[x + 1] |
Failure | Failure | Skip | Successful | |
4.12.E9 | psi*(x)= ell + subs( temp=x, diff( ln(temp), temp$(ell) ) ) |
\[Psi]*(x)= \[ScriptL]+ (D[Log[temp], {temp, \[ScriptL]}]/.temp-> x) |
Failure | Failure | Fail .454653676+2.121320343*I <- {psi = 2^(1/2)+I*2^(1/2), ell = 1, x = 3/2} .565764787+2.121320343*I <- {psi = 2^(1/2)+I*2^(1/2), ell = 2, x = 3/2} -1.471272250+2.121320343*I <- {psi = 2^(1/2)+I*2^(1/2), ell = 3, x = 3/2} .454653676-2.121320343*I <- {psi = 2^(1/2)-I*2^(1/2), ell = 1, x = 3/2} ... skip entries to safe data |
Fail
Complex[0.45465367689297564, 2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 1], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.5657647880040868, 2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 2], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-1.4712722490329502, 2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 3], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.45465367689297564, -2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 1], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.13.E1 | W*exp(W)= x |
W*Exp[W]= x |
Failure | Failure | Fail -5.838722068+6.652975529*I <- {W = 2^(1/2)+I*2^(1/2), x = 1} -6.838722068+6.652975529*I <- {W = 2^(1/2)+I*2^(1/2), x = 2} -7.838722068+6.652975529*I <- {W = 2^(1/2)+I*2^(1/2), x = 3} -5.838722068-6.652975529*I <- {W = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data |
Fail
Complex[-5.838722072781763, 6.652975531039188] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[-6.838722072781763, 6.652975531039188] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[-7.838722072781763, 6.652975531039188] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[-5.838722072781763, -6.652975531039188] <- {Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]} ... skip entries to safe data | |
4.13#Ex1 | LambertW(0, - 1/ exp(1))= LambertW(-1, - 1/ exp(1)) |
ProductLog[0, - 1/ E]= ProductLog[-1, - 1/ E] |
Successful | Successful | - | - | |
4.13#Ex1 | LambertW(-1, - 1/ exp(1))= - 1 |
ProductLog[-1, - 1/ E]= - 1 |
Successful | Successful | - | - | |
4.13#Ex2 | LambertW(0, 0)= 0 |
ProductLog[0, 0]= 0 |
Successful | Successful | - | - | |
4.13#Ex3 | LambertW(0, exp(1))= 1 |
ProductLog[0, E]= 1 |
Successful | Successful | - | - | |
4.13#Ex4 | U + ln(U)= x |
U + Log[U]= x |
Failure | Failure | Fail 1.107360742+2.199611725*I <- {U = 2^(1/2)+I*2^(1/2), x = 1} .107360742+2.199611725*I <- {U = 2^(1/2)+I*2^(1/2), x = 2} -.892639258+2.199611725*I <- {U = 2^(1/2)+I*2^(1/2), x = 3} 1.107360742-2.199611725*I <- {U = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data |
Fail
Complex[1.1073607429330403, 2.199611725770543] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[0.10736074293304043, 2.199611725770543] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[-0.8926392570669596, 2.199611725770543] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[1.1073607429330403, -2.199611725770543] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]} ... skip entries to safe data | |
4.13#Ex5 | U = U*(x) |
U = U*(x) |
Failure | Failure | Fail -1.414213562-1.414213562*I <- {U = 2^(1/2)+I*2^(1/2), x = 2} -2.828427124-2.828427124*I <- {U = 2^(1/2)+I*2^(1/2), x = 3} -1.414213562+1.414213562*I <- {U = 2^(1/2)-I*2^(1/2), x = 2} -2.828427124+2.828427124*I <- {U = 2^(1/2)-I*2^(1/2), x = 3} ... skip entries to safe data |
Fail
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]} ... skip entries to safe data | |
4.13#Ex5 | U*(x)= LambertW(exp(x)) |
U*(x)= ProductLog[Exp[x]] |
Failure | Failure | Fail .414213562+1.414213562*I <- {U = 2^(1/2)+I*2^(1/2), x = 1} 1.271281525+2.828427124*I <- {U = 2^(1/2)+I*2^(1/2), x = 2} 2.034700655+4.242640686*I <- {U = 2^(1/2)+I*2^(1/2), x = 3} .414213562-1.414213562*I <- {U = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data |
Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[1.2712815257485788, 2.8284271247461903] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[2.0347006555499627, 4.242640687119286] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]} ... skip entries to safe data | |
4.13.E4 | diff(LambertW(x), =)*(exp(- LambertW($0)))/(1 + LambertW($0)) |
D[ProductLog[x], =]*Divide[Exp[- ProductLog[$0]],1 + ProductLog[$0]] |
Error | Error | - | - | |
4.13.E5 | LambertW(0, x)= sum((- 1)^(n - 1)*((n)^(n - 2))/(factorial(n - 1))*(x)^(n), n = 1..infinity) |
ProductLog[0, x]= Sum[(- 1)^(n - 1)*Divide[(n)^(n - 2),(n - 1)!]*(x)^(n), {n, 1, Infinity}] |
Failure | Successful | Skip | - | |
4.13.E6 | LambertW(- exp(- 1 -((t)^(2)/ 2)))= sum((- 1)^(n - 1)* c[n]*(t)^(n), n = 0..infinity) |
ProductLog[- Exp[- 1 -((t)^(2)/ 2)]]= Sum[(- 1)^(n - 1)* Subscript[c, n]*(t)^(n), {n, 0, Infinity}] |
Failure | Failure | Skip | Successful | |
4.14.E1 | sin(z)=(exp(I*z)- exp(- I*z))/(2*I) |
Sin[z]=Divide[Exp[I*z]- Exp[- I*z],2*I] |
Successful | Successful | - | - | |
4.14.E2 | cos(z)=(exp(I*z)+ exp(- I*z))/(2) |
Cos[z]=Divide[Exp[I*z]+ Exp[- I*z],2] |
Successful | Successful | - | - | |
4.14.E3 | cos(z)+ I*sin(z)= exp(+ I*z) |
Cos[z]+ I*Sin[z]= Exp[+ I*z] |
Successful | Successful | - | - | |
4.14.E3 | cos(z)- I*sin(z)= exp(- I*z) |
Cos[z]- I*Sin[z]= Exp[- I*z] |
Successful | Successful | - | - | |
4.14.E4 | tan(z)=(sin(z))/(cos(z)) |
Tan[z]=Divide[Sin[z],Cos[z]] |
Successful | Successful | - | - | |
4.14.E5 | csc(z)=(1)/(sin(z)) |
Csc[z]=Divide[1,Sin[z]] |
Successful | Successful | - | - | |
4.14.E6 | sec(z)=(1)/(cos(z)) |
Sec[z]=Divide[1,Cos[z]] |
Successful | Successful | - | - | |
4.14.E7 | cot(z)=(cos(z))/(sin(z)) |
Cot[z]=Divide[Cos[z],Sin[z]] |
Successful | Successful | - | - | |
4.14.E7 | (cos(z))/(sin(z))=(1)/(tan(z)) |
Divide[Cos[z],Sin[z]]=Divide[1,Tan[z]] |
Successful | Successful | - | - | |
4.14.E8 | sin(z + 2*k*Pi)= sin(z) |
Sin[z + 2*k*Pi]= Sin[z] |
Failure | Failure | Successful | Successful | |
4.14.E9 | cos(z + 2*k*Pi)= cos(z) |
Cos[z + 2*k*Pi]= Cos[z] |
Failure | Failure | Successful | Successful | |
4.14.E10 | tan(z + k*Pi)= tan(z) |
Tan[z + k*Pi]= Tan[z] |
Failure | Failure | Successful | Successful | |
4.15.E1 | cos(x + I*y)= sin(x +(1)/(2)*Pi + I*y) |
Cos[x + I*y]= Sin[x +Divide[1,2]*Pi + I*y] |
Successful | Successful | - | - | |
4.15.E2 | cot(x + I*y)= - tan(x +(1)/(2)*Pi + I*y) |
Cot[x + I*y]= - Tan[x +Divide[1,2]*Pi + I*y] |
Successful | Successful | - | - | |
4.15.E3 | sec(x + I*y)= csc(x +(1)/(2)*Pi + I*y) |
Sec[x + I*y]= Csc[x +Divide[1,2]*Pi + I*y] |
Successful | Successful | - | - | |
4.17.E1 | limit((sin(z))/(z), z = 0)= 1 |
Limit[Divide[Sin[z],z], z -> 0]= 1 |
Successful | Successful | - | - | |
4.17.E2 | limit((tan(z))/(z), z = 0)= 1 |
Limit[Divide[Tan[z],z], z -> 0]= 1 |
Successful | Successful | - | - | |
4.17.E3 | limit((1 - cos(z))/((z)^(2)), z = 0)=(1)/(2) |
Limit[Divide[1 - Cos[z],(z)^(2)], z -> 0]=Divide[1,2] |
Successful | Successful | - | - | |
4.18.E1 | (2*x)/(Pi)< = sin(x) |
Divide[2*x,Pi]< = Sin[x] |
Failure | Failure | Skip | Successful | |
4.18.E1 | sin(x)< = x |
Sin[x]< = x |
Failure | Failure | Skip | Successful | |
4.18.E2 | x < = tan(x) |
x < = Tan[x] |
Failure | Failure | Skip | Successful | |
4.18.E3 | cos(x)< =(sin(x))/(x) |
Cos[x]< =Divide[Sin[x],x] |
Failure | Failure | Skip | Successful | |
4.18.E3 | (sin(x))/(x)< = 1 |
Divide[Sin[x],x]< = 1 |
Failure | Failure | Skip | Successful | |
4.18.E4 | Pi <(sin(Pi*x))/(x*(1 - x)) |
Pi <Divide[Sin[Pi*x],x*(1 - x)] |
Failure | Failure | Successful | Successful | |
4.18.E4 | (sin(Pi*x))/(x*(1 - x))< = 4 |
Divide[Sin[Pi*x],x*(1 - x)]< = 4 |
Failure | Failure | Successful | Successful | |
4.18.E5 | abs(sinh(y))< =abs(sin(z))<= cosh(y) |
Abs[Sinh[y]]< =Abs[Sin[z]]<= Cosh[y] |
Failure | Failure | Error | Successful | |
4.18.E6 | abs(sinh(y))< =abs(cos(z))<= cosh(y) |
Abs[Sinh[y]]< =Abs[Cos[z]]<= Cosh[y] |
Failure | Failure | Error | Successful | |
4.18.E7 | abs(csc(z))< = csch(abs(y)) |
Abs[Csc[z]]< = Csch[Abs[y]] |
Failure | Failure | Fail .4602792559 <= .2757205648 <- {z = 2^(1/2)+I*2^(1/2), y = 2} .4602792559 <= .9982156967e-1 <- {z = 2^(1/2)+I*2^(1/2), y = 3} .4602792559 <= .2757205648 <- {z = 2^(1/2)-I*2^(1/2), y = 2} .4602792559 <= .9982156967e-1 <- {z = 2^(1/2)-I*2^(1/2), y = 3} ... skip entries to safe data |
Successful | |
4.18.E8 | abs(cos(z))< = cosh(abs(z)) |
Abs[Cos[z]]< = Cosh[Abs[z]] |
Failure | Failure | Successful | Successful | |
4.18.E9 | abs(sin(z))< = sinh(abs(z)) |
Abs[Sin[z]]< = Sinh[Abs[z]] |
Failure | Failure | Successful | Successful | |
4.18#Ex1 | abs(cos(z))< 2 |
Abs[Cos[z]]< 2 |
Failure | Failure | Successful | Successful | |
4.18#Ex2 | abs(sin(z))< =(6)/(5)*abs(z) |
Abs[Sin[z]]< =Divide[6,5]*Abs[z] |
Failure | Failure | Successful | Successful | |
4.19.E7 | ln((sin(z))/(z))= sum(((- 1)^(n)* (2)^(2*n - 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity) |
Log[Divide[Sin[z],z]]= Sum[Divide[(- 1)^(n)* (2)^(2*n - 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}] |
Failure | Failure | Skip | Successful | |
4.19.E8 | ln(cos(z))= sum(((- 1)^(n)* (2)^(2*n - 1)*((2)^(2*n)- 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity) |
Log[Cos[z]]= Sum[Divide[(- 1)^(n)* (2)^(2*n - 1)*((2)^(2*n)- 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}] |
Failure | Failure | Skip | Successful | |
4.19.E9 | ln((tan(z))/(z))= sum(((- 1)^(n - 1)* (2)^(2*n)*((2)^(2*n - 1)- 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity) |
Log[Divide[Tan[z],z]]= Sum[Divide[(- 1)^(n - 1)* (2)^(2*n)*((2)^(2*n - 1)- 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}] |
Failure | Failure | Skip | Successful | |
4.20.E1 | diff(sin(z), z)= cos(z) |
D[Sin[z], z]= Cos[z] |
Successful | Successful | - | - | |
4.20.E2 | diff(cos(z), z)= - sin(z) |
D[Cos[z], z]= - Sin[z] |
Successful | Successful | - | - | |
4.20.E3 | diff(tan(z), z)= (sec(z))^(2) |
D[Tan[z], z]= (Sec[z])^(2) |
Successful | Successful | - | - | |
4.20.E4 | diff(csc(z), z)= - csc(z)*cot(z) |
D[Csc[z], z]= - Csc[z]*Cot[z] |
Successful | Successful | - | - | |
4.20.E5 | diff(sec(z), z)= sec(z)*tan(z) |
D[Sec[z], z]= Sec[z]*Tan[z] |
Successful | Successful | - | - | |
4.20.E6 | diff(cot(z), z)= - (csc(z))^(2) |
D[Cot[z], z]= - (Csc[z])^(2) |
Successful | Successful | - | - | |
4.20.E7 | diff(sin(z), [z$(n)])= sin(z +(1)/(2)*n*Pi) |
D[Sin[z], {z, n}]= Sin[z +Divide[1,2]*n*Pi] |
Successful | Successful | - | - | |
4.20.E8 | diff(cos(z), [z$(n)])= cos(z +(1)/(2)*n*Pi) |
D[Cos[z], {z, n}]= Cos[z +Divide[1,2]*n*Pi] |
Successful | Successful | - | - | |
4.20.E9 | diff(w, [z$(2)])+ (a)^(2)* w = 0 |
D[w, {z, 2}]+ (a)^(2)* w = 0 |
Failure | Failure | Fail -5.656854245+5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data |
Fail
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.20.E10 | (diff(w, z))^(2)+ (a)^(2)* (w)^(2)= 1 |
(D[w, z])^(2)+ (a)^(2)* (w)^(2)= 1 |
Failure | Failure | Fail -16.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)} 14.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)} -16.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)} 14.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data |
Fail
-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} 15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} -17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} 15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.20.E11 | diff(w, z)- (a)^(2)* (w)^(2)= 1 |
D[w, z]- (a)^(2)* (w)^(2)= 1 |
Failure | Failure | Fail 14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)} -16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)} 14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)} -16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data |
Fail
15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} -17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} 15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} -17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.20.E12 | w = A*cos(a*z)+ B*sin(a*z) |
w = A*Cos[a*z]+ B*Sin[a*z] |
Failure | Failure | Skip | Skip | |
4.20.E13 | w =(1/ a)* sin(a*z + c) |
w =(1/ a)* Sin[a*z + c] |
Failure | Failure | Fail -43.99146068+34.43827298*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)} 1.560620374+.384416402*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)} -.552876601+4.108989171*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} 2.401710418+1.589052846*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data |
Fail
Complex[-43.991460739515965, 34.43827305491785] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.5606203716754656, 0.38441640190707305] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.5528766038746884, 4.1089891749071095] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[2.4017104180648507, 1.5890528479992119] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.20.E14 | w =(1/ a)* tan(a*z + c) |
w =(1/ a)* Tan[a*z + c] |
Failure | Failure | Fail 1.060642513+1.060651152*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)} 1.097992560+1.014214371*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)} 1.770353735+1.772853405*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} 1.045061232+1.116024928*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data |
Fail
Complex[1.0606425136739976, 1.0606511525471942] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.0979925605963208, 1.0142143722877455] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[1.7703537351803704, 1.7728534052480869] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.0450612330665354, 1.11602492841073] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data | |
4.21.E1 | sin(u)+ cos(u)=sqrt(2)*sin(u +(1)/(4)*Pi) |
Sin[u]+ Cos[u]=Sqrt[2]*Sin[u +Divide[1,4]*Pi] |
Successful | Successful | - | - | |
4.21.E1 | sin(u)- cos(u)=sqrt(2)*sin(u -(1)/(4)*Pi) |
Sin[u]- Cos[u]=Sqrt[2]*Sin[u -Divide[1,4]*Pi] |
Successful | Successful | - | - | |
4.21.E1 | sqrt(2)*sin(u +(1)/(4)*Pi)= +sqrt(2)*cos(u -(1)/(4)*Pi) |
Sqrt[2]*Sin[u +Divide[1,4]*Pi]= +Sqrt[2]*Cos[u -Divide[1,4]*Pi] |
Successful | Successful | - | - | |
4.21.E1 | sqrt(2)*sin(u -(1)/(4)*Pi)= -sqrt(2)*cos(u +(1)/(4)*Pi) |
Sqrt[2]*Sin[u -Divide[1,4]*Pi]= -Sqrt[2]*Cos[u +Divide[1,4]*Pi] |
Successful | Successful | - | - | |
4.21.E2 | sin(u + v)= sin(u)*cos(v)+ cos(u)*sin(v) |
Sin[u + v]= Sin[u]*Cos[v]+ Cos[u]*Sin[v] |
Successful | Successful | - | - | |
4.21.E2 | sin(u - v)= sin(u)*cos(v)- cos(u)*sin(v) |
Sin[u - v]= Sin[u]*Cos[v]- Cos[u]*Sin[v] |
Successful | Successful | - | - | |
4.21.E3 | cos(u + v)= cos(u)*cos(v)- sin(u)*sin(v) |
Cos[u + v]= Cos[u]*Cos[v]- Sin[u]*Sin[v] |
Successful | Successful | - | - | |
4.21.E3 | cos(u - v)= cos(u)*cos(v)+ sin(u)*sin(v) |
Cos[u - v]= Cos[u]*Cos[v]+ Sin[u]*Sin[v] |
Successful | Successful | - | - | |
4.21.E4 | tan(u + v)=(tan(u)+ tan(v))/(1 - tan(u)*tan(v)) |
Tan[u + v]=Divide[Tan[u]+ Tan[v],1 - Tan[u]*Tan[v]] |
Successful | Successful | - | - | |
4.21.E4 | tan(u - v)=(tan(u)- tan(v))/(1 + tan(u)*tan(v)) |
Tan[u - v]=Divide[Tan[u]- Tan[v],1 + Tan[u]*Tan[v]] |
Successful | Successful | - | - | |
4.21.E5 | cot(u + v)=(+ cot(u)*cot(v)- 1)/(cot(u)+ cot(v)) |
Cot[u + v]=Divide[+ Cot[u]*Cot[v]- 1,Cot[u]+ Cot[v]] |
Successful | Successful | - | - | |
4.21.E5 | cot(u - v)=(- cot(u)*cot(v)- 1)/(cot(u)- cot(v)) |
Cot[u - v]=Divide[- Cot[u]*Cot[v]- 1,Cot[u]- Cot[v]] |
Successful | Successful | - | - | |
4.21.E6 | sin(u)+ sin(v)= 2*sin((u + v)/(2))*cos((u - v)/(2)) |
Sin[u]+ Sin[v]= 2*Sin[Divide[u + v,2]]*Cos[Divide[u - v,2]] |
Successful | Successful | - | - | |
4.21.E7 | sin(u)- sin(v)= 2*cos((u + v)/(2))*sin((u - v)/(2)) |
Sin[u]- Sin[v]= 2*Cos[Divide[u + v,2]]*Sin[Divide[u - v,2]] |
Successful | Successful | - | - | |
4.21.E8 | cos(u)+ cos(v)= 2*cos((u + v)/(2))*cos((u - v)/(2)) |
Cos[u]+ Cos[v]= 2*Cos[Divide[u + v,2]]*Cos[Divide[u - v,2]] |
Successful | Successful | - | - | |
4.21.E9 | cos(u)- cos(v)= - 2*sin((u + v)/(2))*sin((u - v)/(2)) |
Cos[u]- Cos[v]= - 2*Sin[Divide[u + v,2]]*Sin[Divide[u - v,2]] |
Successful | Successful | - | - | |
4.21.E10 | tan(u)+ tan(v)=(sin(u + v))/(cos(u)*cos(v)) |
Tan[u]+ Tan[v]=Divide[Sin[u + v],Cos[u]*Cos[v]] |
Successful | Successful | - | - | |
4.21.E10 | tan(u)- tan(v)=(sin(u - v))/(cos(u)*cos(v)) |
Tan[u]- Tan[v]=Divide[Sin[u - v],Cos[u]*Cos[v]] |
Successful | Successful | - | - | |
4.21.E11 | cot(u)+ cot(v)=(sin(v + u))/(sin(u)*sin(v)) |
Cot[u]+ Cot[v]=Divide[Sin[v + u],Sin[u]*Sin[v]] |
Successful | Successful | - | - | |
4.21.E11 | cot(u)- cot(v)=(sin(v - u))/(sin(u)*sin(v)) |
Cot[u]- Cot[v]=Divide[Sin[v - u],Sin[u]*Sin[v]] |
Successful | Successful | - | - | |
4.21.E12 | (sin(z))^(2)+ (cos(z))^(2)= 1 |
(Sin[z])^(2)+ (Cos[z])^(2)= 1 |
Successful | Successful | - | - | |
4.21.E13 | (sec(z))^(2)= 1 + (tan(z))^(2) |
(Sec[z])^(2)= 1 + (Tan[z])^(2) |
Successful | Successful | - | - | |
4.21.E14 | (csc(z))^(2)= 1 + (cot(z))^(2) |
(Csc[z])^(2)= 1 + (Cot[z])^(2) |
Successful | Successful | - | - | |
4.21.E15 | 2*sin(u)*sin(v)= cos(u - v)- cos(u + v) |
2*Sin[u]*Sin[v]= Cos[u - v]- Cos[u + v] |
Successful | Successful | - | - | |
4.21.E16 | 2*cos(u)*cos(v)= cos(u - v)+ cos(u + v) |
2*Cos[u]*Cos[v]= Cos[u - v]+ Cos[u + v] |
Successful | Successful | - | - | |
4.21.E17 | 2*sin(u)*cos(v)= sin(u - v)+ sin(u + v) |
2*Sin[u]*Cos[v]= Sin[u - v]+ Sin[u + v] |
Successful | Successful | - | - | |
4.21.E18 | (sin(u))^(2)- (sin(v))^(2)= sin(u + v)*sin(u - v) |
(Sin[u])^(2)- (Sin[v])^(2)= Sin[u + v]*Sin[u - v] |
Successful | Successful | - | - | |
4.21.E19 | (cos(u))^(2)- (cos(v))^(2)= - sin(u + v)*sin(u - v) |
(Cos[u])^(2)- (Cos[v])^(2)= - Sin[u + v]*Sin[u - v] |
Successful | Successful | - | - | |
4.21.E20 | (cos(u))^(2)- (sin(v))^(2)= cos(u + v)*cos(u - v) |
(Cos[u])^(2)- (Sin[v])^(2)= Cos[u + v]*Cos[u - v] |
Successful | Successful | - | - | |
4.21.E21 | sin((z)/(2))= +((1 - cos(z))/(2))^(1/ 2) |
Sin[Divide[z,2]]= +(Divide[1 - Cos[z],2])^(1/ 2) |
Failure | Failure | Fail -1.637854044-1.167010648*I <- {z = -2^(1/2)-I*2^(1/2)} -1.637854044+1.167010648*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.6378540442140963, -1.1670106484252494] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.6378540442140963, 1.1670106484252494] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.21.E21 | sin((z)/(2))= -((1 - cos(z))/(2))^(1/ 2) |
Sin[Divide[z,2]]= -(Divide[1 - Cos[z],2])^(1/ 2) |
Failure | Failure | Fail 1.637854044+1.167010648*I <- {z = 2^(1/2)+I*2^(1/2)} 1.637854044-1.167010648*I <- {z = 2^(1/2)-I*2^(1/2)} |
Fail
Complex[1.6378540442140963, 1.1670106484252494] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.6378540442140963, -1.1670106484252494] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} | |
4.21.E22 | cos((z)/(2))= +((1 + cos(z))/(2))^(1/ 2) |
Cos[Divide[z,2]]= +(Divide[1 + Cos[z],2])^(1/ 2) |
Failure | Failure | Successful | Successful | |
4.21.E22 | cos((z)/(2))= -((1 + cos(z))/(2))^(1/ 2) |
Cos[Divide[z,2]]= -(Divide[1 + Cos[z],2])^(1/ 2) |
Failure | Failure | Fail 1.916716266-.9972227728*I <- {z = 2^(1/2)+I*2^(1/2)} 1.916716266+.9972227728*I <- {z = 2^(1/2)-I*2^(1/2)} 1.916716266-.9972227728*I <- {z = -2^(1/2)-I*2^(1/2)} 1.916716266+.9972227728*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.916716265666014, -0.9972227733456656] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.916716265666014, 0.9972227733456656] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[1.916716265666014, -0.9972227733456656] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.916716265666014, 0.9972227733456656] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.21.E23 | tan((z)/(2))= +((1 - cos(z))/(1 + cos(z)))^(1/ 2) |
Tan[Divide[z,2]]= +(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2) |
Failure | Failure | Fail -.8463685478-1.658064547*I <- {z = -2^(1/2)-I*2^(1/2)} -.8463685478+1.658064547*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.8463685477398917, -1.6580645472823399] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.8463685477398917, 1.6580645472823399] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.21.E23 | tan((z)/(2))= -((1 - cos(z))/(1 + cos(z)))^(1/ 2) |
Tan[Divide[z,2]]= -(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2) |
Failure | Failure | Fail .8463685478+1.658064547*I <- {z = 2^(1/2)+I*2^(1/2)} .8463685478-1.658064547*I <- {z = 2^(1/2)-I*2^(1/2)} |
Fail
Complex[0.8463685477398917, 1.6580645472823399] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.8463685477398917, -1.6580645472823399] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} | |
4.21.E23 | +((1 - cos(z))/(1 + cos(z)))^(1/ 2)=(1 - cos(z))/(sin(z)) |
+(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2)=Divide[1 - Cos[z],Sin[z]] |
Failure | Failure | Skip | Fail
Complex[0.8463685477398916, 1.6580645472823403] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.8463685477398916, -1.6580645472823403] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} | |
4.21.E23 | -((1 - cos(z))/(1 + cos(z)))^(1/ 2)=(1 - cos(z))/(sin(z)) |
-(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2)=Divide[1 - Cos[z],Sin[z]] |
Failure | Failure | Skip | Fail
Complex[-0.8463685477398916, -1.6580645472823403] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.8463685477398916, 1.6580645472823403] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} | |
4.21.E23 | (1 - cos(z))/(sin(z))=(sin(z))/(1 + cos(z)) |
Divide[1 - Cos[z],Sin[z]]=Divide[Sin[z],1 + Cos[z]] |
Successful | Successful | - | - | |
4.21.E24 | sin(- z)= - sin(z) |
Sin[- z]= - Sin[z] |
Successful | Successful | - | - | |
4.21.E25 | cos(- z)= cos(z) |
Cos[- z]= Cos[z] |
Successful | Successful | - | - | |
4.21.E26 | tan(- z)= - tan(z) |
Tan[- z]= - Tan[z] |
Successful | Successful | - | - | |
4.21.E27 | sin(2*z)= 2*sin(z)*cos(z) |
Sin[2*z]= 2*Sin[z]*Cos[z] |
Successful | Successful | - | - | |
4.21.E27 | 2*sin(z)*cos(z)=(2*tan(z))/(1 + (tan(z))^(2)) |
2*Sin[z]*Cos[z]=Divide[2*Tan[z],1 + (Tan[z])^(2)] |
Successful | Successful | - | - | |
4.21.E28 | cos(2*z)= 2*(cos(z))^(2)- 1 |
Cos[2*z]= 2*(Cos[z])^(2)- 1 |
Successful | Successful | - | - | |
4.21.E28 |