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Algebra & Functions Commands

The templates, functions, commands, and operators available for evaluating math expressions within CAS (Home and Y= tabs) and Spreadsheet (and Data Analysis Data Sheets) are listed below in alphabetical order.

Alphabetical Listing of Available Commands

Items whose names are not alphabetical (such as +, !, and /) are listed at the end. In general, when interpreting the table below, note that:

  1. All commands that begin with a 'command(' must end with a ')' to ensure proper syntax; and
  2. The mode (e.g., Degree/Radian) should be set prior to executing commands.
Command Explanation Example(s)
abs(Expr) The absolute value of an expression abs(-15) returns 15
y=abs(x)+5
ans(1) Return the result of the previous calculation sqrt(16) returns 4.0 then sqrt(ans(1)) returns 2.0
average(x1,x2,x3,...,xn)
average(
ColARow1:ColARowN)
Return the arithmetic average of a list of data (x1, ..., xn, OR from Column A Row 1 to Column A Row N) average(1,2,3) returns 2
=average(A1:A25) returns 70 with Apartment Temperatures data in Column A (rows 1 through 25) of a data sheet
binomcdf(n,p,x) The probability of the sum of the events up to x given n trials with an event probability of p binomcdf(5,.8,4) returns 0.6723 with Auto Numeric On
binompdf(n,p,x) The probability of x given n trials with an event probability of p binompdf(5,.8,1) returns 0.0064 with Auto Numeric On
ceil(Expr) Returns the smallest integer not less than the given expression ceil(2.3) returns 3
y=ceil(x)
chisqcdf(x,y,df) The area between x and y based on the degrees of freedom df chisqcdf(0,1.145,5) returns 0.05 with Auto Numeric On
chisqpdf(x,df) The area to the right of x based on the degrees of freedom df chisqpdf(1,5) returns 0.0807 with Auto Numeric On
col(Matrix,n) Show the nth column of a given matrix col([[1,2],[3,4]],1) returns [[1,2]]
r:=[[4,8,1],[3,8,9],[4,7,9]]
col(r,2)
returns [[3,8,9]], the 2nd column of matrix r
comb(n,k) Compute the number of different combinations of k objects taken from n objects comb(5,2) returns 10
complex(a,b) When in Complex Numbers mode, take an ordered pair of real numbers, (ab), and return a complex number, a + bi or bi + a   complex(-5,7) returns 7i-5
complex(2,-3) returns 2-3i
conj(Expr) When in Complex Numbers mode, compute the complex conjugate of the given expression conj(4+i) returns 4-i
cos(Expr) Evaluate the cosine of the given expression cos(pi) returns -1 in Radian mode
y=cos(x/2)
count(x1,x2,...,xn)
count(ColARow1:ColBRowN)
Gives the number of elements in a list of data count(a,b,c,d,e) returns 5
=count(B1:C22)
returns 44 within 100-meter Freestyle data sheet
der(Expr,Var) Evaluate the derivative of an expression with respect a variable der(x^2,x) returns 2x
y:=der(x^3+x^2+x,x) returns y:=3x^2+2x+1
det(Matrix) Calculate the determinant of a given matrix det([[2,0],[4,2]]) returns 4
t:=[[7,3],[2,1]]
det(t)
returns 1
exp(Expr) Gives the special number 'e' and can be used as a base in expressions for exponential functions ln(exp(x)) returns x
solve(exp(x)=20,x) returns x=ln(20)
expand(Expr) Rewrites an expression in an equivalent form that does not contain parentheses expand((6-(45/3))^2) returns 81
expand((6*x^2)*(4*x+12)) returns 24*x^3+72*x^2
fact(n) Compute the factorial of a natural number fact(5) returns 120; equivalent to 5*4*3*2*1
factor(Expr) Rewrites an expression in factored form, when possible factor(3*x^2+6*x-24) returns -3*(2-x)*(x+4)
Fcdf(x,y,dfNum,dfDenom) The area between x and y given the degrees of freedom of the numerator and denominator Fcdf(0,2.1,25,20) returns 0.9528 with Auto Numeric On
Fpdf(x,dfNum,dfDenom) The area to the right of x given the degrees of freedom of the numerator and denominator Fpdf(5,25,20) returns 0.0004 with Auto Numeric On
floor(Expr) Returns the largest integer less than or equal to the given expression floor(6.7) returns 6
y=floor(x)
i Defined as sqrt(-1) with Complex Numbers on sqrt(-1) returns i
id(n) Show the nxn identity matrix in matrix form id(3) returns [[1,0,0],[0,1,0],[0,0,1]] in matrix form
imag(Expr) Returns the imaginary part of a complex number imag(6i+42) returns 6i

int(Expr,Var,lowBound,upBound)

Compute the definite integral of an expression from lower to upper bound values int(sin(x),x,pi,2*pi) returns 1-cos(2*pi) and -2 in auto simplify mode
inv(Matrix) Calculate the inverse of a matrix inv([[2,2],[1,2]]) returns [[1,-1],[-1/2,1]]
n:=[[1,1],[1,0]]
inv(n)
returns [[0,1],[1,-1]] in matrix form
invcos(Expr) The inverse cosine of an expression invcos(1.) returns 0
y=invcos(x+pi)
invNorm(percentile,xbar,s) The value given the percentile rank with mean x-bar and standard deviation s invNorm(0.05,25,6) returns 15.1309 with Auto Numeric On
invsin(Expr) The inverse sine of an expression invsin(1.) returns 90
y=invsin(2*x-pi)
invT(pvalue,df) The t-value given a p-value and degrees of freedom df invT(.05,61) returns 1.9996 with Auto Numeric On
invtan(Expr) The inverse tangent of an expression invtan(1) returns 45 in Degree mode
y=invtan((x/2)*pi)
ln(Expr) Take the natural log (base e) of an expression ln(exp(2)) returns 2
y=ln(x)
log(Expr) Take the log (base 10) of an expression log(100) returns 2
y=log(6*x)
matrix(r,c,Expr,Expr,...Expr) Define a matrix with r rows, c columns, and its entries by row matrix(2,3,1,2,3,4,5,6) is a 2x3 matrix with row entries 1,2,3 and 4,5,6
m:=matrix(2,2,1,0,0,1) then m returns the 2x2 identity matrix
[[col 1],[col 2], ..., [col k]] Define a matrix by its column entries separated by commas [[2,3,0],[1,2,1]] returns a 3x2 matrix with column entries 2,3,0 and 1,2,1
k:=[[4,5],[7,9]] then k returns a 2x2 matrix with row entries 4,7 and 5,9
max(x1,x2,...,xn)
max(
ColARow1:ColBRowN)
Determine the greatest value in a list of data max(7,3,5,2,1) returns 7
=max(B1:C22) returns 82.2 within 100-meter Freestyle data sheet
normalcdf(x,y,xbar,s) The area between x and y with mean x-bar and standard deviation s normalcdf(-infinity,19.2,25,6) returns 0.1669 with Auto Numeric On
normalpdf(x,xbar,s) The area to the right of x with mean x-bar and standard deviation s normalpdf(5,25,6) returns 0.0003 with Auto Numeric On
perm(n,k) Compute the number of different permutations of k objects taken from n objects perm(5,2) returns 20
piecewise(Expr,Expr,...) Create a piecewise function y=piecewise(cos(x),x<0,1.5^x,0<=x AND x<=4) returns the two-part piecewise function on the specified domain
prod(Expr,Expr,...,Expr) Multiply a list of numerical values prod(5,4,3,2) returns 120
prod(2*x,x^2,x^3) returns 2.0*x^6
prod(Expr,Var,Start,End)

Find the product of a variable expression for the specified variable for a range of numerical values from Start to End

prod(3*x,x,1,4) returns 1944 which equals (3*1)*(3*2)*(3*3)*(3*4)
real(Expr) Returns the real part of a complex number real(-3i+10) returns 10
regeq(1) As long as a regression of some sort has already been performed on bivariate data, this will return the regression equation itself regeq(1) returns y=<the regression equation>
y=regeq(x) creates an equation in the Y= tab, but does not display the specific equation
root(Expr,n) Take the nth root of an expression root(27,3) returns 3.0
y=root(x,4)
row(Matrix,n) Show the nth row of a given matrix row([[3,0],[0,5],[7,0]],1); returns first entries of each column, namely the row [3,0,7]
w:=[[2,2],[3,4],[5,1]] then
row(w,2)
returns [2,4,1]
simplify(Expr) Rewrites an expression in an equivalent, simplified form simplify(6+10) returns 16
simplify((5x+3)*(2x+3)) returns 10*x^2+21*x+9
sin(Expr) The sine of an expression sin(3*pi/2) returns -1.0 in Radian mode
y=sin(x+3)
size(Matrix) Calculate the (row , column) size of a matrix size([[1,3,5],[7,9,11]]) returns [3 2]
n:=[[2,2],[4,4],[6,6]] then
size(n)
returns [2 3]
solve(Equation,Var) Solve an equation or inequality for the specified variable solve(30=5*x^2+2*x+6,x) returns x=-12/5 or x=2
sqr(Expr) The square of an expression sqr(17) returns 289
y=sqr(11*x)
sqrt(Expr) The square root of an expression sqrt(225) returns 15
y=sqrt(36*x^2+1)
stdev(x1,x2,...,xn)
stdev(
ColARow1:ColBRowN)
Computes the standard deviation of a list of data stdev(1,2,3) returns 1
=stdev(A1:A25)
returns 2.16 within Apartment Temperatures data sheet
sum(Expr,Expr,...,Expr) Sum a list of numerical values or expressions sum(5,6,7,8) returns 26.0
sum(x,2x,-4x,17x,8x) returns 24*x+0.0
sum(Expr,Var,Start,End) Find the sum of a variable expression with respect to the variable for a range of numerical values from Start to End sum(x-4,x,1,4) returns -6
tan(Expr) Evaluate the tangent of an expression tan(45) returns 1 in Degree mode
y=tan(pi/x)
tcdf(t1,t2,df) The area between t1 and t2 based on the degrees of freedom df tcdf(-2,2,61) returns 0.95 with Auto Numeric On
tpdf(t,df) The area to the right of t based on the degrees of freedom df tpdf(1,61) returns 0.24 with Auto Numeric On
tr(Matrix) Transpose a given matrix tr([[1,2],[3,4]]) returns [[1,3],[2,4]] in matrix form
P:=[[1,1,1],[2,2,2],[3,3,3]]
then tr(P) returns [[1,2,3],[1,2,3],[1,2,3]] in matrix form
Expr+Expr Add; Returns the sum of two expressions 147+56 returns 203
y=5*x+3
Expr at Var=Value
Expr @ Var=Value
At; Evaluate the expression at the indicated value of the variable y=-x+3 at x=2 returns y=1
y=-x+3 @ x=2 returns y=1
Expr/Expr Divide; Returns the quotient of two expressions -135/27.0 returns -5.0
y=1/x
Expr=Expr Equal to 23^2=529 returns true evaluation
y=x
Expr>Expr Greater than 16*24/3>129 returns false evaluation
y>2*x
Expr>=Expr Greater than or equal to 47*13>=649 returns false evaluation
y>=6*x+4
Expr<Expr Less than 23*13<300 returns true evaluation
y<10*x+2
Expr<=Expr Less than or equal to 65*7<=490 returns true evaluation
y<=2*x-5
Expr%Expr Modulo 27%12 returns 3
Expr*Expr Multiply, take the product of 167*14 returns 2338
y=6*x
Expr!=Expr Not equal to 9/167!=0.1 returns true evaluation
y!=10+x
Expr^Expr Raise to the power of 36^4 returns 1679616
y=2^(x+1)
Expr-Expr Subtract; negative value 64-13 returns 51
y=3x^2-2x-1

Math Toolbar

Choose Math Toolbar in the CAS Home tab Options menu to view the Typing Palette. From the typing palette, click on an available button to utilize it's functionality in the Command line.
Icon
Command
Icon
Command
Expr/Expr
<
^2
<=
sqrt()
>=
root(Expr,n)
>
sum(Expr,Var, Start,End)
!=
prod(Expr,Var,Start,End)