Computer algebra system, CAS calculator

Capable of producing symbolic results. Can manipulate algebraic expressions, performing operations such as factor, expand, and simplify.

Functions: --- Vectorial --------- CROSS DOT POLY Numeric ------- ABS EXP FLOOR LN LOG LOGTEN LOGTWO ROUND SIGN SQR Complex ------- ARG CONJ IM NORM RE Trigonometric ------------- ACOS ACOSH ACOT ACOTH ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATANH COS COSH COT COTH CSC CSCH SEC SECH SIN SINH TAN TANH Polynomial ---------- FACTOR GCD LAGRANGIANINTERPOLATION LCM MOD ORTHOG RESIDUE ROOTS Other ----- EULERS ISOLATE LIM Matrix ------ ADJ COF DET ECHELON EGV EGVL EIGENVALUES EIGENVECTORS IDENTITY JACOBIAN JORDAN RANK TRACE TRANSPOSE TRN Examples: ---Basic operations:--- 2×3+4 2^3^2 √(2+2) 1600/((1-(1+1/4)^30)/(1-(1+1/4))) m!/(n!*(m-n)!)@m=5@n=3 gcd(12;36;6;24) ' Greatest common divisor lcm(12;18;60) ' Least common multiple ---Custom functions:--- P(x)/Q(x)?P(x)=(x+1)*(x-1)|Q(x)=x+1 y^2?y=(x+i)*(x-i) f(3,1)?f(x,y)=y-x f(2,-2)?f(x,y)=y-x;x+y|x*y;-2*x*y ---Evaluating:--- x^2-9*x+20@x=5 x^2-9x+20@x=4.5 2+x/(y*z)@x=12|y=4|z=-3 ---Hexadecimal, octal, binary, decimal: &h0F+&o17+&b1111+&d15 ---Logical operators: (&h0ff OR &h0f) AND &b111 ---Modulus: ((x5+3x3+4)*(6x6+4x3))%11 (x7+x6+x5+x4+x3+x2)mod(x5+x) ---POLYNOMIALS: ---Find polynomial given zeros: POLY(1;i;-i) ' find polynomial of given roots 1, i and -i POLY(2;5) ' find polynomial of given roots 2 and 5 ---Add, subs., multiply, divide: (x-1)+(x+1) (x-1)-(x+1) (x-1)*(x+1) (x^2-1)/(x+1) gcd((3x2-3)(x+2);-(3x-3)(x+2);(2x+4))' Greatest common divisor poly(-1;2) ' find a polynomial given the roots ---Root finder: roots(x16-1) factors(x16-1) (x-1)*(x+1)=0 (5*x+2)*(3*x-1)=0 x^2-9x+20=0 ---Partial fraction descomposition: partialfractions((-4s+8)/(s2+6s+8)) partialfractions((s-2)/((s-1)(s+2)(s-3))) ---Orthogonality: orthog(-1;1;2*t;3*t^2+5) ---Interpolation:--- lagrangianinterpolation(-2;1|0;-1|2;1) lagrangianinterpolation(-1;1;10;abs(x))' 10 intervals at [-1,1] with Chebyshev nodes for f(x)=abs(x) ---Derivatives:--- Dx(cosh(x)) Dy(sin(x^2*y^2+y)) Dy(z)?z=x+y|x=y^2 ---2nd.derivative:--- D2x(3x^2-2x+5) ---Jacobian:--- jacobian(1,000x^2-2x+5;sin(x2)|xsinh(y);xasinh(y)) ---Vector operation: dot(3;-3;1|4;9;2) cross(3;-3;1|4;9;2) ---LIMITS: lim((x2-16)/(x-4);x;4) lim(sin(x)/x;x;0) lim(ln(x)/x;x;0) lim((5t4-4t2-1)/(10-t-9t3);t;1) lim(x*e^x;x;-infinity) lim(exp(x)/x^2;x;∞) lim(x*ln(x);x;0) lim(x^(1/x);x;infinity) ---MATRIX operations: (1;0|0;-1|^|-1)|*|1;0|0;-1 (1;2|3;4|+|1;0|0;1)|*|-1;0|0;1 ((1;0|0;3|-|5;0|3;-2)|^|-1)|*|(-4;0|-3;5) (x;0|0;1|^|-1)|*|a?a=x;0|0;1 x+1;0|0;-1|^|-1|*|a?a=(x+1);0|0;-1 A+(-B*C)?A=1;2|3;-1||B=A|C=1;0|0;1 Dx(x^2-sin(x);-6*x^2-x+3|tan(x)+x^2;sinh(x)) integral(A)dy @ A = x^2*y-y^2;-6*x*y^2-x+3|1/(y+1);sinh(y) ---Inverse matrix: A^-1?A=1;2|3;-1 A^-1*A?A=1;2|3;-1 A^-1*A?A=x;y|2;-3 a*a^-1|*|a|-|a?a=cos(x);-sin(x)|sin(x);cos(x) A*A^-1?A=(3;a;a;a;a|a;3;a;a;a|a;a;3;a;a|a;a;a;3;a|a;a;a;a;3) ---Determinant: det(A)?A=(1-x;2|3;2-x) roots(det(A))?A=(1-x;2|3;2-x) det(A)=0?A=(1-x;2|3;2-x) roots(det(A))@A=(3;a;a;a;a|a;3;a;a;a|a;a;3;a;a|a;a;a;3;a|a;a;a;a;3) det(A)|-|(4a+3)*(3-a)^4?A=(3;a;a;a;a|a;3;a;a;a|a;a;3;a;a|a;a;a;3;a|a;a;a;a;3) det(A-B)=0?A=(1;2|3;2)|B=λ*(1;0|0;1) ---Identity matrix: Identity(3) ' 3x3 Identity matrix Identity(3;4) ' 3x4 Identity matrix ---Trace: trace(1-x;2|3;2-x) ---Transpose: transpose(1-x;2|3;2-x) ---Cofactor: cof(1;3;1|1;1;2|2;3;4) ---Adjoint: Adj(1;3;1|1;1;2|2;3;4) ---Echelon: Echelon(1;2;1|-2;-3;1|3;5;0) /* see https://en.wikipedia.org/wiki/Row_echelon_form */ ---Rank: Rank(1;2;1|-2;-3;1|3;5;0) /* see https://en.wikipedia.org/wiki/Rank_(linear_algebra) */ ---EigenValues: eigenvalues(2;1|1;2) ---Eigenvectors: eigenvectors(2;1|1;2) ---Jordan form: A*T-T*jordan(A)?A=2;0;1|0;2;0|1;0;2|T=eigenvectors(A) ---SYSTEM OF EQUATIONS:--- ---Linear:--- &var1 Xc=1/(2*pi*f*C)?Xc=50|f=10e6 x+y=2|x-y=1 ---Non-Linear:--- x2-10x+y2+8=0|x*y2+x-10y+8=0 ---INTEGRATION: ---Integration of polynomials: integral(6x-2) integral(3x2+y)dx ∫(x2+y)dy ∫(√x+(1/√x))^2|∫((√x+(1/√x))^2)dx|(√x+(1/√x))^2 ---Inmediate integrals: ∫(sin(x))dx ∫(ln(x))dx ---Trigonometric integrals: ∫(sin2(x)*cos(x))dx ∫(tan2(x))dx ---Definite integrals: integral(1,2,x)dx integral(1,2,x*y)dy ∫(1,2,x)dx ∫(a,b,x*y)dx?a=1|b=2 ∫(a,b,S(x))dx,pi(10^(3/2)-1)/27?a=0|b=1|f(x)=x3|S(x)=2*pi*f(x)*sqr(1+(Dx(f(x)))^2) ---Partial fractions integration: ∫[1/(x(x-2)^2)]dx (x(x-2)^2)*Dx(∫1/(x(x-2)^2)dx) ---Trigonometric integration: ∫(sec(x)*tan2(x))dx ---Integration by parts: 13*∫(sin(3*x)*exp(2*x))dx ---Improper integrals lim(integral(0;b;1/(1+x2))dx,b,infinity) ---DIFFERENTIAL EQUATIONS: ---First order linear: Dt(y)=9.8-0.196y@y(0)=48 t*Dt(y)+2*y=t^2-t+1@y(1)=0.5 2*Dt(y)-y=4*sin(3t)@y(0)=_y0 ---First order separable: Dx(y)=6y^2x@y(1)=1/25 Dx(y)=(3x2+4x-4)/(2y-4)@y(1)=3 Dx(y)=exp(-y)*(2x-4)@y(5)=0 1/(exp(-y)*(2x-4))*Dx(y)=1@y(5)=0 Dθ(r)=r^2/θ@r(1)=2 Dt(y)=exp(y-t)*sec(y)*(1+t^2)@y(0)=0 ---First order exact: 2xy-9x2+(2y+x2+1)*Dx(y)=0@y(0)=-3 2xy2+4=2*(3-x2y)*Dx(y)@y(-1)=8 (2xy2+4)/(2*(3-x2y)*Dx(y))=1@ y(-1)=8 ---First order Bernoulli: Dx(y)+(4/x)*y = x3*y2@y(2)=-1 Dx(y)=5y+exp(-2x)*y^-2@y(0)=2 6*Dx(y)-2y = xy4 @ y(0)=-2 Dx(y)+y/x-sqr(y)=0 @ y(1)=0 ---First order substitution: xyDx(y)+4x2+y2=0 @ y(2)=-7 Dx(y)=exp(9y-x) @ y(0)=0 ---Euler's method: Eulers(_step;N;Dt(y)-y=-1/2*exp(t/2)*sin(5t)+5*exp(t/2)*cos(5t))?_step=0.1|N=10|y(0)=0 ---MISCELLANEOUS:--- isolate(C,w*L=1/(w*C)) isolate(x,x-y+3=-1) Expression to operate: Variable(s) (if any): Decimals: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 i  j Eng. Binary Detail Fractions Octal Decimal Hexadecimal Variables' name 1 character long Math10 User's guide (.pdf)

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