T

T (transpose)	Catalog >
Matrix1T ⇒ matrix Returns the complex conjugate transpose of Matrix1. Note: You can insert this operator from the computer keyboard by typing @t.

T (transpose)

Catalog >

Matrix1T ⇒ matrix

Returns the complex conjugate transpose of Matrix1.

Note: You can insert this operator from the computer keyboard by typing @t.

tan()	µ key
tan(Value1) ⇒ value tan(List1) ⇒ list tan(Value1) returns the tangent of the argument. tan(List1) returns a list of the tangents of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use °, g or r to override the angle mode setting temporarily.	In Degree angle mode: In Gradian angle mode: In Radian angle mode:
tan(squareMatrix1) ⇒ squareMatrix Returns the matrix tangent of squareMatrix1. This is not the same as calculating the tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.	In Radian angle mode:

tan()

µ key

tan(Value1) ⇒ value
tan(List1) ⇒ list

tan(Value1) returns the tangent of the argument.

tan(List1) returns a list of the tangents of all elements in List1.

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use °, g or r to override the angle mode setting temporarily.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

tan(squareMatrix1) ⇒ squareMatrix

Returns the matrix tangent of squareMatrix1. This is not the same as calculating the tangent of each element. For information about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

tan-1()	µ key
tan-1(Value1) ⇒ value tan-1(List1) ⇒ list tan-1(Value1) returns the angle whose tangent is Value1. tan-1(List1) returns a list of the inverse tangents of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arctan(...).	In Degree angle mode: In Gradian angle mode: In Radian angle mode:
tan-1(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse tangent of squareMatrix1. This is not the same as calculating the inverse tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.	In Radian angle mode:

tan-1()

µ key

tan-1(Value1) ⇒ value

tan-1(List1) ⇒ list

tan-1(Value1) returns the angle whose tangent is Value1.

tan-1(List1) returns a list of the inverse tangents of each element of List1.

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arctan(...).

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

tan-1(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse tangent of squareMatrix1. This is not the same as calculating the inverse tangent of each element. For information about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

tanh()	Catalog >
tanh(Value1) ⇒ value tanh(List1) ⇒ list tanh(Value1) returns the hyperbolic tangent of the argument. tanh(List1) returns a list of the hyperbolic tangents of each element of List1.
tanh(squareMatrix1) ⇒ squareMatrix Returns the matrix hyperbolic tangent of squareMatrix1. This is not the same as calculating the hyperbolic tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.	In Radian angle mode:

tanh()

Catalog >

tanh(Value1) ⇒ value

tanh(List1) ⇒ list

tanh(Value1) returns the hyperbolic tangent of the argument.

tanh(List1) returns a list of the hyperbolic tangents of each element of List1.

tanh(squareMatrix1) ⇒ squareMatrix

Returns the matrix hyperbolic tangent of squareMatrix1. This is not the same as calculating the hyperbolic tangent of each element. For information about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

tanh-1()	Catalog >
tanh-1(Value1) ⇒ value tanh-1(List1) ⇒ list tanh-1(Value1) returns the inverse hyperbolic tangent of the argument. tanh-1(List1) returns a list of the inverse hyperbolic tangents of each element of List1. Note: You can insert this function from the keyboard by typing arctanh(...).	In Rectangular complex format: To see the entire result, press 5 and then use 7 and 8 to move the cursor.
tanh-1(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse hyperbolic tangent of squareMatrix1. This is not the same as calculating the inverse hyperbolic tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.	In Radian angle mode and Rectangular complex format: To see the entire result, press 5 and then use 7 and 8 to move the cursor.

tanh-1()

Catalog >

tanh-1(Value1) ⇒ value
tanh-1(List1) ⇒ list

tanh-1(Value1) returns the inverse hyperbolic tangent of the argument.

tanh-1(List1) returns a list of the inverse hyperbolic tangents of each element of List1.

Note: You can insert this function from the keyboard by typing arctanh(...).

In Rectangular complex format:

To see the entire result,
press 5 and then use 7 and 8 to move the cursor.

tanh-1(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse hyperbolic tangent of squareMatrix1. This is not the same as calculating the inverse hyperbolic tangent of each element. For information about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular complex format:

To see the entire result,
press 5 and then use 7 and 8 to move the cursor.

tCdf()	Catalog >
tCdf(lowBound,upBound,df) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the Student-t distribution probability between lowBound and upBound for the specified degrees of freedom df. For P(X ≤ upBound), set lowBound = -9E999.

tCdf()

Catalog >

tCdf(lowBound,upBound,df) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists

Computes the Student-t distribution probability between lowBound and upBound for the specified degrees of freedom df.

For P(X ≤ upBound), set lowBound = -9E999.

Text

Catalog >

TextpromptString[, DispFlag]

Programming command: Pauses the program and displays the character string promptString in a dialog box.

When the user selects OK, program execution continues.

The optional flag argument can be any expression.

•

If DispFlag is omitted or evaluates to 1, the text message is added to the Calculator history.

•

If DispFlag evaluates to 0, the text message is not added to the history.

If the program needs a typed response from the user, refer to Request, here, or RequestStr, here.

Note: You can use this command within a user-defined program but not within a function.

Define a program that pauses to display each of five random numbers in a dialog box.

Within the Prgm...EndPrgm template, complete each line by pressing @ instead of ·. On the computer keyboard, hold down Alt and press Enter.

Define text_demo()=Prgm
  For i,1,5
    strinfo:=”Random number “ & string(rand(i))
    Text strinfo
  EndFor
EndPrgm

Run the program:

text_demo()

Sample of one dialog box:

Then	See If, here.

tInterval	Catalog >
tInterval List[, Freq[, CLevel]] (Data list input) tInterval v, sx, n[, CLevel] (Summary stats input) Computes a t confidence interval. A summary of results is stored in the stat.results variable. (See here.) For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

tInterval

Catalog >

tInterval List[, Freq[, CLevel]]

(Data list input)

tInterval v, sx, n[, CLevel]

(Summary stats input)

Computes a t confidence interval. A summary of results is stored in the stat.results variable. (See here.)

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.CLower, stat.CUpper	Confidence interval for an unknown population mean
stat.v	Sample mean of the data sequence from the normal random distribution
stat.ME	Margin of error
stat.df	Degrees of freedom
stat.σx	Sample standard deviation
stat.n	Length of the data sequence with sample mean

tInterval_2Samp	Catalog >
tInterval_2Samp List1,List2[,Freq1[,Freq2[,CLevel[,Pooled]]]] (Data list input) tInterval_2Samp v1,sx1,n1,v2,sx2,n2[,CLevel[,Pooled]] (Summary stats input) Computes a two-sample t confidence interval. A summary of results is stored in the stat.results variable. (See here.) Pooled=1 pools variances; Pooled=0 does not pool variances. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

tInterval_2Samp

Catalog >

tInterval_2Samp List1,List2[,Freq1[,Freq2[,CLevel[,Pooled]]]]

(Data list input)

tInterval_2Samp v1,sx1,n1,v2,sx2,n2[,CLevel[,Pooled]]

(Summary stats input)

Computes a two-sample t confidence interval. A summary of results is stored in the stat.results variable. (See here.)

Pooled=1 pools variances; Pooled=0 does not pool variances.

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.CLower, stat.CUpper	Confidence interval containing confidence level probability of distribution
stat.v1-v2	Sample means of the data sequences from the normal random distribution
stat.ME	Margin of error
stat.df	Degrees of freedom
stat.v1, stat.v2	Sample means of the data sequences from the normal random distribution
stat.σx1, stat.σx2	Sample standard deviations for List 1 and List 2
stat.n1, stat.n2	Number of samples in data sequences
stat.sp	The pooled standard deviation. Calculated when Pooled = YES

tPdf()	Catalog >
tPdf(XVal,df) ⇒ number if XVal is a number, list if XVal is a list Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df.

tPdf()

Catalog >

tPdf(XVal,df) ⇒ number if XVal is a number, list if XVal is a list

Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df.

trace()	Catalog >
trace(squareMatrix) ⇒ value Returns the trace (sum of all the elements on the main diagonal) of squareMatrix.

trace()

Catalog >

trace(squareMatrix) ⇒ value

Returns the trace (sum of all the elements on the main diagonal) of squareMatrix.

Try	Catalog >
Try block1 Else block2 EndTry Executes block1 unless an error occurs. Program execution transfers to block2 if an error occurs in block1. System variable errCode contains the error code to allow the program to perform error recovery. For a list of error codes, see “Error codes and messages,” here. block1 and block2 can be either a single statement or a series of statements separated with the “:” character. Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
To see the commands Try, ClrErr, and PassErr in operation, enter the eigenvals() program shown at the right. Run the program by executing each of the following expressions. Note: See also ClrErr, here, and PassErr, here.	Define eigenvals(a,b)=Prgm © Program eigenvals(A,B) displays eigenvalues of A•B Try Disp "A= ",a Disp "B= ",b Disp " " Disp "Eigenvalues of A•B are:",eigVl(a*b) Else If errCode=230 Then Disp "Error: Product of A•B must be a square matrix" ClrErr Else PassErr EndIf EndTry EndPrgm

Try

Catalog >

Try
block1
Else
block2
EndTry

Executes block1 unless an error occurs. Program execution transfers to block2 if an error occurs in block1. System variable errCode contains the error code to allow the program to perform error recovery. For a list of error codes, see “Error codes and messages,” here.

block1 and block2 can be either a single statement or a series of statements separated with the “:” character.

Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.

To see the commands Try, ClrErr, and PassErr in operation, enter the eigenvals() program shown at the right. Run the program by executing each of the following expressions.

Note: See also ClrErr, here, and PassErr, here.

Define eigenvals(a,b)=Prgm
© Program eigenvals(A,B) displays eigenvalues of A•B

Try
    Disp "A= ",a
    Disp "B= ",b
    Disp " "

Disp "Eigenvalues of A•B are:",eigVl(a*b)

Else
    If errCode=230 Then
        Disp "Error: Product of A•B must be a square matrix"
        ClrErr
    Else
        PassErr
    EndIf
EndTry

EndPrgm

tTest	Catalog >
tTest μ0,List[,Freq[,Hypoth]] (Data list input) tTest μ0,v,sx,n,[Hypoth] (Summary stats input) Performs a hypothesis test for a single unknown population mean μ when the population standard deviation σ is unknown. A summary of results is stored in the stat.results variable. (See here.) Test H0: μ = μ0, against one of the following: For Ha: μ < μ0, set Hypoth<0 For Ha: μ ≠ μ0 (default), set Hypoth=0 For Ha: μ > μ0, set Hypoth>0 For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

tTest

Catalog >

tTest μ0,List[,Freq[,Hypoth]]

(Data list input)

tTest μ0,v,sx,n,[Hypoth]

(Summary stats input)

Performs a hypothesis test for a single unknown population mean μ when the population standard deviation σ is unknown. A summary of results is stored in the stat.results variable. (See here.)

Test H0: μ = μ0, against one of the following:

For Ha: μ < μ0, set Hypoth<0
For Ha: μ ≠ μ0 (default), set Hypoth=0
For Ha: μ > μ0, set Hypoth>0

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.t	(v − μ0) / (stdev / sqrt(n))
stat.PVal	Smallest level of significance at which the null hypothesis can be rejected
stat.df	Degrees of freedom
stat.v	Sample mean of the data sequence in List
stat.sx	Sample standard deviation of the data sequence
stat.n	Size of the sample

tTest_2Samp	Catalog >
tTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth[,Pooled]]]] (Data list input) tTest_2Samp v1,sx1,n1,v2,sx2,n2[,Hypoth[,Pooled]] (Summary stats input) Computes a two-sample t test. A summary of results is stored in the stat.results variable. (See here.) Test H0: μ1 = μ2, against one of the following: For Ha: μ1< μ2, set Hypoth<0 For Ha: μ1≠ μ2 (default), set Hypoth=0 For Ha: μ1> μ2, set Hypoth>0 Pooled=1 pools variances Pooled=0 does not pool variances For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

tTest_2Samp

Catalog >

tTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth[,Pooled]]]]

(Data list input)

tTest_2Samp v1,sx1,n1,v2,sx2,n2[,Hypoth[,Pooled]]

(Summary stats input)

Computes a two-sample t test. A summary of results is stored in the stat.results variable. (See here.)

Test H0: μ1 = μ2, against one of the following:

For Ha: μ1< μ2, set Hypoth<0
For Ha: μ1≠ μ2 (default), set Hypoth=0
For Ha: μ1> μ2, set Hypoth>0

Pooled=1 pools variances
Pooled=0 does not pool variances

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.t	Standard normal value computed for the difference of means
stat.PVal	Smallest level of significance at which the null hypothesis can be rejected
stat.df	Degrees of freedom for the t-statistic
stat.v1, stat.v2	Sample means of the data sequences in List 1 and List 2
stat.sx1, stat.sx2	Sample standard deviations of the data sequences in List 1 and List 2
stat.n1, stat.n2	Size of the samples
stat.sp	The pooled standard deviation. Calculated when Pooled=1.

tvmFV()	Catalog >
tvmFV(N,I,PV,Pmt,[PpY],[CpY],[PmtAt]) ⇒ value Financial function that calculates the future value of money. Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmFV()

Catalog >

tvmFV(N,I,PV,Pmt,[PpY],[CpY],[PmtAt]) ⇒ value

Financial function that calculates the future value of money.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmI()	Catalog >
tvmI(N,PV,Pmt,FV,[PpY],[CpY],[PmtAt]) ⇒ value Financial function that calculates the interest rate per year. Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmI()

Catalog >

tvmI(N,PV,Pmt,FV,[PpY],[CpY],[PmtAt]) ⇒ value

Financial function that calculates the interest rate per year.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmN()	Catalog >
tvmN(I,PV,Pmt,FV,[PpY],[CpY],[PmtAt]) ⇒ value Financial function that calculates the number of payment periods. Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmN()

Catalog >

tvmN(I,PV,Pmt,FV,[PpY],[CpY],[PmtAt]) ⇒ value

Financial function that calculates the number of payment periods.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmPmt()	Catalog >
tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt]) ⇒ value Financial function that calculates the amount of each payment. Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmPmt()

Catalog >

tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt]) ⇒ value

Financial function that calculates the amount of each payment.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmPV()	Catalog >
tvmPV(N,I,Pmt,FV,[PpY],[CpY],[PmtAt]) ⇒ value Financial function that calculates the present value. Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

tvmPV()

Catalog >

tvmPV(N,I,Pmt,FV,[PpY],[CpY],[PmtAt]) ⇒ value

Financial function that calculates the present value.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, here. See also amortTbl(), here.

TVM argument*	Description	Data type
N	Number of payment periods	real number
I	Annual interest rate	real number
PV	Present value	real number
Pmt	Payment amount	real number
FV	Future value	real number
PpY	Payments per year, default=1	integer > 0
CpY	Compounding periods per year, default=1	integer > 0
PmtAt	Payment due at the end or beginning of each period, default=end	integer (0=end, 1=beginning)

* These time-value-of-money argument names are similar to the TVM variable names (such as tvm.pv and tvm.pmt) that are used by the Calculator application’s finance solver. Financial functions, however, do not store their argument values or results to the TVM variables.

TwoVar	Catalog >
TwoVar X, Y[, [Freq][, Category, Include]] Calculates the TwoVar statistics. A summary of results is stored in the stat.results variable. (See here.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of numeric category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see here.

TwoVar

Catalog >

TwoVar X, Y[, [Freq][, Category, Include]]

Calculates the TwoVar statistics. A summary of results is stored in the stat.results variable. (See here.)

All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0.

Category is a list of numeric category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see here.

Output variable	Description
stat.v	Mean of x values
stat.Σx	Sum of x values
stat.Σx2	Sum of x2 values
stat.sx	Sample standard deviation of x
stat.σx	Population standard deviation of x
stat.n	Number of data points
stat.w	Mean of y values
stat.Σy	Sum of y values
stat.Σy2	Sum of y2 values
stat.sy	Sample standard deviation of y
stat.σy	Population standard deviation of y
stat.Σxy	Sum of x•y values
stat.r	Correlation coefficient
stat.MinX	Minimum of x values
stat.Q1X	1st Quartile of x
stat.MedianX	Median of x
stat.Q3X	3rd Quartile of x
stat.MaxX	Maximum of x values
stat.MinY	Minimum of y values
stat.Q1Y	1st Quartile of y
stat.MedY	Median of y
stat.Q3Y	3rd Quartile of y
stat.MaxY	Maximum of y values
stat.Σ(x-v)2	Sum of squares of deviations from the mean of x
stat.Σ(y-w)2	Sum of squares of deviations from the mean of y