TI-89 Titanium CAS commands, with examples

Commands marked ⁺ are Calc89 additions in TI-Nspire CAS style and are not on the TI-89 Titanium handheld.

Algebra · Calculus · Matrix · List · Trigonometry · Number functions · Special functions · Units · Variables and memory · Conversions · Probability · Distributions · Statistics · Finance · Strings

Algebra

• approx(Evaluates an expression numerically and returns a decimal approximation, even when the…
• cFactor(Factors an expression over the complex numbers, so factors with non-real coefficients…
• comDenom(Combines a sum of fractions into one reduced fraction over a common denominator.
• completeSquare(⁺Rewrites a quadratic expression in completed square form.
• cPolyRoots(⁺Returns all roots of a polynomial as a list, including non-real complex roots.
• cSolve(Solves an equation over the complex numbers and returns both real and non-real solutions.
• cZeros(Returns the real and non-real zeros of an expression as a list.
• domain(⁺Returns the domain of an expression with respect to a variable as a condition, for…
• exact(Converts a decimal or approximate value into an exact rational form where possible.
• expand(Multiplies out products and powers in an expression and returns a sum of terms.
• exp▶list(Extracts the values from a solution such as x=1 or x=2 and returns them as a list.
• factor(Factors an expression over the rational numbers, for example a polynomial into linear and…
• getDenom(Returns the denominator of a fraction after the expression has been reduced to a common…
• getNum(Returns the numerator of a fraction after the expression has been reduced to a common…
• left(Returns the left side of an equation or inequality.
• linSolve(⁺Solves a system of linear equations and returns the values of the variables as a list.
• nSolve(Finds one real solution of an equation numerically.
• piecewise(⁺Defines a piecewise function from pairs of values and conditions; each value applies…
• polyCoeffs(⁺Returns the coefficients of a polynomial as a list, starting with the highest power.
• polyDegree(⁺Returns the degree of a polynomial, the highest power of the variable that occurs.
• polyGcd(⁺Returns the greatest common divisor of two polynomials.
• polyQuotient(⁺Divides one polynomial by another and returns the quotient, as in polynomial long…
• polyRemainder(⁺Divides one polynomial by another and returns the remainder, as in polynomial long…
• polyRoots(⁺Returns the real roots of a polynomial as a list.
• propFrac(Rewrites a fraction as a proper fraction: a whole part plus a remainder fraction.
• right(Returns the right side of an equation or inequality.
• solve(Solves an equation or inequality for a variable and returns the real solutions, joined…
• tCollect(Collects products and integer powers of sines and cosines into sines and cosines of…
• tExpand(Expands sines and cosines of sums and multiple angles into products of sines and cosines…
• when(Returns one of several values depending on whether a condition is true, false or…
• zeros(Returns the real values of the variable that make an expression zero, as a list.

Calculus

• arcLen(Returns the arc length of the graph of an expression between two values of the variable.
• d(Differentiates an expression symbolically with respect to a variable.
• deSolve(Solves first and second order ordinary differential equations symbolically.
• dominantTerm(⁺Returns the term of an expression that dominates near a point, for example as the…
• euler(⁺Solves a differential equation numerically with Euler's method and returns a matrix with…
• fMax(Returns the value of the variable at which an expression reaches its maximum, as a…
• fMin(Returns the value of the variable at which an expression reaches its minimum, as a…
• impDif(Computes the derivative dy/dx of an equation that defines y implicitly in terms of x.
• limit(Computes the limit of an expression as the variable approaches a point, including ∞.
• nDeriv(Approximates the derivative of an expression numerically with a central difference…
• nDerivative(⁺Computes the numerical derivative of an expression at a given value of the variable.
• nfMax(⁺Finds the location of a maximum of an expression numerically within an interval.
• nfMin(⁺Finds the location of a minimum of an expression numerically within an interval.
• nInt(Approximates a definite integral numerically.
• normalLine(⁺Returns the equation of the normal line to the graph of an expression at a point, the…
• rk23(⁺Solves a differential equation numerically with an adaptive Runge Kutta method and…
• series(⁺Returns a power series expansion of an expression up to a given order.
• tangentLine(⁺Returns the equation of the tangent line to the graph of an expression at a point.
• taylor(Returns the Taylor polynomial of an expression up to a given order, around 0 or around a…
• Π(Computes the product of an expression as the variable runs from a lower to an upper value.
• Σ(Computes the sum of an expression as the variable runs from a lower to an upper value.
• ∫(Integrates an expression with respect to a variable.

Matrix

• .*Multiplies two matrices element by element, unlike the normal matrix product.
• .+Adds element by element: each entry of the first matrix is added to the matching entry of…
• .-Subtracts element by element: the matching entry of the second matrix, or a single value…
• ./Divides element by element: each entry is divided by the matching entry of the second…
• .^Raises each entry of a matrix to a power element by element, instead of computing a…
• augment(Joins two matrices side by side, appending the columns of the second to the first.
• charPoly(⁺Returns the characteristic polynomial of a square matrix in the given variable.
• colAugment(⁺Stacks two matrices vertically, appending the rows of the second below the first.
• colDim(Returns the number of columns of a matrix.
• colNorm(Returns the column norm of a matrix, the largest sum of the absolute values of the…
• constructMat(⁺Builds a matrix by evaluating an expression in two index variables for every row and…
• crossP(Returns the cross product of two vectors.
• det(Returns the determinant of a square matrix.
• diag(Returns the main diagonal of a square matrix as a row vector.
• dim(Returns the dimensions of a matrix as {rows, columns}, or the number of elements of a…
• dotP(Returns the dot product of two vectors.
• eigVc(Returns the eigenvectors of a square matrix as the columns of a matrix.
• eigVl(Returns the eigenvalues of a square matrix as a list.
• FillReplaces every element of an existing list or matrix variable with the same value.
• identity(Returns the identity matrix of size n by n.
• inverse(⁺Returns the inverse of a square matrix, the same result as raising it to the power −1.
• list▶mat(Converts a list into a matrix, filling it row by row with the given number of columns.
• LUComputes the LU decomposition of a matrix with partial pivoting and stores the lower…
• mat▶list(Returns the entries of a matrix as one list, row by row.
• mRow(Multiplies one row of a matrix by a value, one of the elementary row operations of…
• mRowAdd(Multiplies one row of a matrix by a value and adds the result to another row, the key…
• newMat(Returns a matrix of zeros with the given number of rows and columns.
• norm(Returns the Frobenius norm of a matrix; for a vector this is its length.
• QRComputes the QR factorization of a matrix and stores the orthogonal matrix q and the…
• randMat(Returns a matrix of the given size filled with random integers.
• ref(Returns the row echelon form of a matrix, the result of forward Gaussian elimination.
• rowAdd(Adds one row of a matrix to another row and returns the new matrix.
• rowDim(Returns the number of rows of a matrix.
• rowNorm(Returns the row norm of a matrix, the largest sum of the absolute values of the entries…
• rowSwap(Swaps two rows of a matrix and returns the new matrix.
• rref(Returns the reduced row echelon form of a matrix.
• simult(Solves a system of linear equations given as a coefficient matrix and a column of…
• subMat(Returns the part of a matrix between a start row and column and an end row and column.
• trace(Returns the trace of a square matrix, the sum of the entries on its main diagonal.
• transpose(⁺Returns the transpose of a matrix, with rows and columns swapped.
• unitV(Returns the unit vector in the direction of a vector, the vector divided by its length.

List

• cumSum(Returns a list of the running totals of a list's elements.
• deltaList(Returns a list of the differences between consecutive elements of a list.
• product(Returns the product of the elements of a list.
• seq(Builds a list by evaluating an expression as a variable runs from a low to a high value.
• SortASorts a list variable in ascending order and stores the result back in the variable.
• SortDSorts a list variable in descending order and stores the result back in the variable.
• sum(Returns the sum of the elements of a list.

Trigonometry

• cos(Returns the cosine of an angle, interpreted in the current angle mode.
• cosh(Returns the hyperbolic cosine of a value.
• cosh⁻¹(Returns the inverse hyperbolic cosine of a value.
• cos⁻¹(Returns the angle whose cosine is the given value, in the current angle mode.
• cot(Returns the cotangent of an angle, interpreted in the current angle mode.
• coth(Returns the hyperbolic cotangent of a value.
• coth⁻¹(Returns the inverse hyperbolic cotangent of a value.
• cot⁻¹(Returns the angle whose cotangent is the given value, in the current angle mode.
• csc(Returns the cosecant of an angle, interpreted in the current angle mode.
• csch(Returns the hyperbolic cosecant of a value.
• csch⁻¹(Returns the inverse hyperbolic cosecant of a value.
• csc⁻¹(Returns the angle whose cosecant is the given value, in the current angle mode.
• P▶Rx(Converts polar coordinates to the rectangular x coordinate, x=r·cos(θ).
• P▶Ry(Converts polar coordinates to the rectangular y coordinate, y=r·sin(θ).
• R▶Pr(Converts rectangular coordinates to the polar radius r, the distance of the point from…
• R▶Pθ(Converts rectangular coordinates to the polar angle θ, in the current angle mode.
• sec(Returns the secant of an angle, interpreted in the current angle mode.
• sech(Returns the hyperbolic secant of a value.
• sech⁻¹(Returns the inverse hyperbolic secant of a value.
• sec⁻¹(Returns the angle whose secant is the given value, in the current angle mode.
• sin(Returns the sine of an angle, interpreted in the current angle mode.
• sinh(Returns the hyperbolic sine of a value.
• sinh⁻¹(Returns the inverse hyperbolic sine of a value.
• sin⁻¹(Returns the angle whose sine is the given value, in the current angle mode.
• tan(Returns the tangent of an angle, interpreted in the current angle mode.
• tanh(Returns the hyperbolic tangent of a value.
• tanh⁻¹(Returns the inverse hyperbolic tangent of a value.
• tan⁻¹(Returns the angle whose tangent is the given value, in the current angle mode.

Number functions

• abs(Returns the absolute value of a number, or the modulus of a complex number.
• angle(Returns the argument of a complex number, the angle of its point in the complex plane.
• ans(Recalls a previous answer from the home screen history: ans(1) is the last answer, ans(2)…
• ceiling(Returns the smallest integer that is greater than or equal to a value.
• conj(Returns the complex conjugate of a number, with the sign of the imaginary part changed.
• entry(Recalls a previous entry from the home screen history so it can be evaluated again.
• floor(Returns the largest integer that is less than or equal to a value.
• fPart(Returns the fractional part of a number, the part after the decimal point.
• gcd(Returns the greatest common divisor of two integers.
• imag(Returns the imaginary part of a complex number.
• iPart(Returns the integer part of a number, truncated toward zero.
• lcm(Returns the least common multiple of two integers.
• ln(Returns the natural logarithm of a value, the logarithm to base ℯ.
• log(Returns the common logarithm of a value, or the logarithm to a given base.
• max(Returns the larger of two values, or the largest element of a list.
• min(Returns the smaller of two values, or the smallest element of a list.
• mod(Returns a modulo b, the remainder of the division with the sign of b.
• real(Returns the real part of a complex number.
• remain(Returns the remainder of a divided by b, with the sign of a.
• root(⁺Returns the n-th root of a value, for example the cube root for n=3.
• round(Rounds a value to a given number of decimal places.
• sign(Returns the sign of a value: 1 for positive and −1 for negative numbers.
• √(Returns the square root of a value.

Special functions

• Chi(⁺Returns the hyperbolic cosine integral of a value.
• Ci(⁺Returns the cosine integral of a value.
• dilog(⁺Returns the dilogarithm of a value; dilog(1) is π^2/6.
• Ei(⁺Returns the exponential integral of a value.
• erf(⁺Returns the error function of a value, which is closely related to the normal…
• erfc(⁺Returns the complementary error function, 1 minus erf of the value.
• erfi(⁺Returns the imaginary error function of a value.
• fresnelC(⁺Returns the Fresnel cosine integral of a value.
• fresnelS(⁺Returns the Fresnel sine integral of a value.
• gamma(⁺Returns the gamma function of a value; for a positive integer n, gamma(n) equals (n−1)!.
• gammaInc(⁺Returns the incomplete gamma function of a and x.
• li(⁺Returns the logarithmic integral of a value.
• polylog(⁺Returns the polylogarithm of order n of a value.
• Shi(⁺Returns the hyperbolic sine integral of a value.
• Si(⁺Returns the sine integral of a value.

Units

• tmpCnv(Converts a temperature from one unit to another, for example from °C to °F, including the…
• ΔtmpCnv(Converts a temperature difference from one unit to another; only the scale changes, the…

Variables and memory

• DefineDefines a user function or variable that can be used in later calculations, for example…
• DelVarDeletes variables from memory so they are undefined again.
• getLockInfo(⁺Returns 1 if a variable is locked and 0 if it is not.
• LockLocks variables so they cannot be changed or deleted until they are unlocked.
• NewProbStarts a new problem by clearing single letter variables, so values stored earlier do not…
• unLockUnlocks variables that were locked with Lock, so they can be changed or deleted again.

Conversions

• ▶approxFraction(⁺Converts a decimal value into a fraction that approximates it within a tolerance.
• ▶cos⁺Rewrites an expression in terms of cosine, for example sin(x)^2 as 1−cos(x)^2.
• ▶CylindDisplays a three element vector in cylindrical form, with radius, angle and height.
• ▶DDConverts an angle to decimal degrees.
• ▶Decimal⁺Displays a result as a decimal number instead of an exact value.
• ▶DMSDisplays an angle in degrees, minutes and seconds.
• ▶exp⁺Rewrites an expression in terms of the natural exponential ℯ^x, for example hyperbolic…
• ▶GradConverts an angle to gradians.
• ▶ln⁺Rewrites logarithms in an expression in terms of the natural logarithm ln.
• ▶logbase(⁺Rewrites logarithms in an expression in terms of logarithms to a given base.
• ▶PolarDisplays a vector or complex number in polar form, with length and angle.
• ▶RadConverts an angle to radians.
• ▶RectDisplays a vector or complex number in rectangular form.
• ▶sin⁺Rewrites an expression in terms of sine, for example cos(x)^2 as 1−sin(x)^2.
• ▶SphereDisplays a three element vector in spherical form, with length and two angles.

Probability

• nCr(Returns the number of combinations, the ways to choose r items from n when order does not…
• nPr(Returns the number of permutations, the ways to arrange r items chosen from n when order…
• rand(Returns a random number between 0 and 1, or a list of such numbers.
• randBin(Returns a random number of successes from a binomial distribution, or a list of them.
• randInt(Returns a random integer between two bounds, or a list of them.
• randNorm(Returns a random number from a normal distribution, or a list of them.
• randSamp(Draws a random sample of elements from a list.
• RandSeedSets the seed of the random number generator, so a sequence of random results can be…

Distributions

• binomCdf(Returns a cumulative binomial probability, the chance of a number of successes within a…
• binomPdf(Returns the binomial probability of exactly a given number of successes.
• chi2Cdf(Returns the χ² distribution probability between two bounds.
• chi2Pdf(Returns the probability density of the χ² distribution at a value.
• FCdf(Returns the F distribution probability between two bounds.
• FPdf(Returns the probability density of the F distribution at a value.
• geomCdf(Returns the cumulative geometric probability that the first success occurs within a range…
• geomPdf(Returns the geometric probability that the first success occurs on a given trial.
• invBinom(⁺Inverse cumulative binomial distribution: finds the number of successes at which the…
• invBinomN(⁺Finds the number of trials at which the cumulative binomial probability for a given…
• invChi2(Inverse χ² distribution: returns the value with a given area to its left.
• invF(Inverse F distribution: returns the value with a given area to its left.
• invNorm(Inverse normal distribution: returns the value with a given area to its left.
• invt(Inverse Student t distribution: returns the value with a given area to its left, used for…
• normCdf(Returns the probability that a normally distributed value lies between two bounds.
• normPdf(Returns the probability density of the normal distribution at a value.
• poissCdf(Returns the cumulative Poisson probability for a range of counts.
• poissPdf(Returns the Poisson probability of exactly a given count.
• tCdf(Returns the Student t distribution probability between two bounds.
• tPdf(Returns the probability density of the Student t distribution at a value.

Statistics

• ANOVAPerforms a one way analysis of variance to compare the means of several groups.
• ANOVA2wayPerforms a two way analysis of variance on several lists of data.
• chi22wayPerforms a χ² test for association on a two way table of observed counts.
• chi2GOFPerforms a χ² goodness of fit test that compares observed counts with expected counts.
• CubicRegFits a cubic polynomial y=a·x^3+b·x^2+c·x+d to data with least squares regression.
• ExpRegFits an exponential model y=a·b^x to data with least squares regression.
• FTest_2Samp⁺Performs a two sample F test that compares the variances of two populations.
• LinRegBx⁺Fits a line y=a+b·x to data with least squares regression.
• LinRegMx⁺Fits a line y=m·x+b to data with least squares regression.
• LinRegtIntervalsComputes confidence intervals for a linear regression, for the slope or for a predicted…
• LinRegtTestPerforms a t test on the slope of a linear regression and the correlation of the data.
• LnRegFits a logarithmic model y=a+b·ln(x) to data with least squares regression.
• LogisticFits a logistic growth model y=c/(1+a·ℯ^(−b·x)) to data.
• LogisticD⁺Fits a logistic model with an added constant d to data.
• mean(Returns the arithmetic mean of the elements of a list.
• median(Returns the median of the elements of a list.
• MedMedFits a median median line to data, a line that is resistant to outliers.
• MultRegPerforms a multiple linear regression of one y list on several x lists.
• MultRegIntervalsComputes a confidence interval for a predicted value from a multiple linear regression.
• MultRegTestsPerforms the F test and t tests of a multiple linear regression.
• OneVarComputes one variable statistics of a list, such as mean, standard deviation and…
• PowerRegFits a power model y=a·x^b to data with least squares regression.
• QuadRegFits a quadratic y=a·x^2+b·x+c to data with least squares regression.
• QuartRegFits a quartic polynomial y=a·x^4+b·x^3+c·x^2+d·x+e to data with least squares regression.
• SinRegFits a sinusoidal model y=a·sin(b·x+c)+d to data.
• stDevPop(Returns the population standard deviation of a list.
• stDevSamp(⁺Returns the sample standard deviation of a list.
• tIntervalComputes a t confidence interval for a population mean when σ is unknown.
• tInterval_2Samp⁺Computes a t confidence interval for the difference of two population means.
• tTestPerforms a one sample t test on a population mean when σ is unknown.
• tTest_2Samp⁺Performs a two sample t test on the difference of two population means.
• TwoVarComputes two variable statistics of paired data, such as means, sums and the correlation.
• varPop(Returns the population variance of a list.
• varSamp(⁺Returns the sample variance of a list.
• zIntervalComputes a z confidence interval for a population mean when σ is known.
• zInterval_1Prop⁺Computes a z confidence interval for a population proportion.
• zInterval_2Prop⁺Computes a z confidence interval for the difference of two proportions.
• zInterval_2Samp⁺Computes a z confidence interval for the difference of two population means with known σ.
• zTestPerforms a one sample z test on a population mean when σ is known.
• zTest_1Prop⁺Performs a one proportion z test.
• zTest_2Prop⁺Performs a two proportion z test that compares two population proportions.
• zTest_2Samp⁺Performs a two sample z test on the difference of two population means with known σ.
• χ²2way⁺Performs a χ² test for association on a two way table of observed counts; it is the same…
• χ²GOF⁺Performs a χ² goodness of fit test that compares observed counts with expected counts; it…

Finance

• amortTbl(⁺Returns an amortization table as a matrix, with payment number, interest, principal and…
• bal(Returns the remaining loan balance after a given payment.
• dbd(Returns the number of days between two dates.
• eff(⁺Converts a nominal annual interest rate into the effective annual rate.
• irr(Returns the internal rate of return of a series of cash flows, the rate at which the net…
• mirr(⁺Returns the modified internal rate of return, which uses separate finance and…
• nom(⁺Converts an effective annual interest rate into the nominal annual rate.
• npv(Returns the net present value of a series of cash flows at a given interest rate.
• tvmFV(Time value of money: returns the future value of a loan or savings plan.
• tvmI(Time value of money: returns the annual interest rate in percent.
• tvmN(Time value of money: returns the number of payment periods.
• tvmPmt(Time value of money: returns the payment per period, for example a monthly loan payment.
• tvmPV(Time value of money: returns the present value of a loan or savings plan.
• ΣInt(Returns the total interest paid over a range of loan payments.
• ΣPrn(Returns the total principal paid over a range of loan payments.

Strings

• &Joins two strings into one.
• expr(Evaluates the expression contained in a string and returns its result.
• mid(Returns a part of a string or list, starting at a given position.
• string(Simplifies an expression and returns the result as a string.

The full reference as plain text for AI assistants: /commands/llms.txt.