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Computer algebra system, CAS calculator
Capable of producing symbolic results. Can manipulate algebraic expressions, performing operations such as factor, expand, and simplify.
Updated:
2024/09/10
v10.0.47
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 = value (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)
Result:
CustomValidator