Built-in Functions

The following is an alphabetical list of the functions built-into Derive (see Built-in Functions and ConstantsBuilt_in_Functions_and_Constants).

ABSPiecewise_Continuous_Functions(x) absolute value of real x

ABSComplex_Variable_Functions(z) magnitude (modulus) of complex z

ABSVector_Operations(v) magnitude (length) of vector v

ACOSInverse_Trigonometric_Functions(z) angle whose cosine is z

ACOSHInverse_Hyperbolic_Functions(z) inverse hyperbolic cosine of z

ACOTInverse_Trigonometric_Functions(x,y) angle of the point (x,y)

ACOTInverse_Trigonometric_Functions(z) angle whose cotangent is z

ACOTHInverse_Hyperbolic_Functions(z) inverse hyperbolic cotangent of z

ACSCInverse_Trigonometric_Functions(z) angle whose cosecant is z

ACSCHInverse_Hyperbolic_Functions(z) inverse hyperbolic cosecant of z

ADJOINVector_Manipulation_Functions(u,v) adjoin u to the front of vector v

APPENDVector_Manipulation_Functions(v,w) vector of elements of v followed by elements of w

APPROX1LCSBCN(u) approximate u using the current digits of precision

APPROX1LCSBCN(u,n) approximate u using n digits of precision

ASECInverse_Trigonometric_Functions(z) angle whose secant is z

ASECHInverse_Hyperbolic_Functions(z) inverse hyperbolic secant of z

ASINInverse_Trigonometric_Functions(z) angle whose sine is z

ASINHInverse_Hyperbolic_Functions(z) inverse hyperbolic sine of z

ASSIGNProgramming_Functions(v,u) if the value of v is a variable, assigns that variable the value u

ATANInverse_Trigonometric_Functions(y,x) angle of the point (x,y)

ATANInverse_Trigonometric_Functions(z) angle whose tangent is z

ATANHInverse_Hyperbolic_Functions(z) inverse hyperbolic tangent of z

AVERAGEStatistical_Functions(z1,...,zn) arithmetic mean (average) of z1, ..., zn

CEILINGPiecewise_Continuous_Functions(m) smallest integer ≥ m

CEILINGPiecewise_Continuous_Functions(m,n) smallest integer ≥ m/n

CHARPOLYEigenvalues(A,v) characteristic polynomial of square matrix A in terms of variable v

CHIPiecewise_Continuous_Functions(a,x,b) if a<x<b, returns 1; if x<a or x>b, returns 0

CHIPiecewise_Continuous_Functions(a,x,b,c) if x=a, returns c; if x=b, returns 1-c; else returns CHI(a,x,b)

CHIPiecewise_Continuous_Functions(a,x,b,c,d) if x=a, returns c; if x=b, returns d; else returns CHI(a,x,b)

CODES_TO_NAMEString_Processing_Functions(v) string or integer corresponding to ASCII codes in vector v

COMBProbability_Functions(z,w) combinations of z things taken w at a time

CONJComplex_Variable_Functions(z) complex conjugate of z

COSTrigonometric_Functions(z) cosine of z radians

COSHHyperbolic_Functions(z) hyperbolic cosine of z

COTTrigonometric_Functions(z) cotangent of z radians

COTHHyperbolic_Functions(z) hyperbolic cotangent of z

CSCTrigonometric_Functions(z) cosecant of z radians

CSCHHyperbolic_Functions(z) hyperbolic cosecant of z

CURLDifferential_Vector_Calculus(v) curl of 2 or 3 element vector v wrt variables x, y, and z

CURLDifferential_Vector_Calculus(v,w) curl of 2 or 3 element vector v wrt variables in vector w

CURLDifferential_Vector_Calculus(v,A) curl of 2 or 3 element vector v using coordinate geometry matrix A

DELETEVector_Manipulation_Functions(v,n) delete element n from vector v

DENOMINATORExpression_Decomposition_Functions(u) syntactic denominator of u

DETMatrix_Operations(A) determinant of matrix A

DIF12746IV(u,x) derivative of u(x) wrt x

DIF12746IV(u,x,n) nth order derivative of u(x) wrt x

DIF12746IV(u,x,-n) nth-order antiderivative of u(x) wrt x

DIGAMMAProbability_Functions(x) digamma function ψ(x)

DIMVector_Operations(v) number of elements of vector v

DISPLAYProgramming_Functions(u,n) display u using up to n lines of text in a new text box

DIVDifferential_Vector_Calculus(v) divergence of vector v wrt variables x, y, and z

DIVDifferential_Vector_Calculus(v,w) divergence of vector v wrt variables in vector w

DIVDifferential_Vector_Calculus(v,A) divergence of vector v using coordinate geometry matrix A

EIGENVALUESEigenvalues(A,v) eigenvalues of square matrix A in terms of variable v

ELEMENTVector_Manipulation_Functions(v,n) nth element of vector v

ELEMENTVector_Manipulation_Functions(A,j,k) element in jth row and kth column of matrix A

ERFError_Functions(z) error function of z

ERFError_Functions(z,w) generalized error function of z and w

ERFCError_Functions(z) complementary error function of z

EVEN?Expression_Type_Functions(k) if k is an even number, return true; otherwise return false

EVERYBoolean_Functions(u,x,c) if u(x) is true for every x in c, return true; otherwise return false

EVERYBoolean_Functions(u,k,m,n,s) if u(k) is true for every k=m to n in steps of s, return true; otherwise return false

EXPExponential_Functions(z) exponential of z (that is e^z)

EXPAND984VML(u,amount,x,y,...) expand u by amount wrt variables x,y,...

FACTORU08MH3(u,amount,x,y,...) factor u by amount wrt variables x,y,...

FACTORSExpression_Decomposition_Functions(n) vector of pairs of primes and their powers of factorization of integer n

FACTORSExpression_Decomposition_Functions(u) vector of pairs of syntactic factors and their powers of expression u

FIRSTVector_Manipulation_Functions(v) first element of vector v

FITStatistical_Functions(v,A) least squares fit of label vector v to data matrix A

FLOORPiecewise_Continuous_Functions(m) integer part of m

FLOORPiecewise_Continuous_Functions(m,n) greatest integer ≤ m/n

FVALFinancial_Functions(i,nper,pmt,pval,time) future value of contract

GAMMAProbability_Functions(z) gamma function of z

GCDNumber_Theory_Functions(m,n,...) greatest common divisor of m, n, ...

GRADDifferential_Vector_Calculus(u) gradient of expression u wrt variables x, y, and z

GRADDifferential_Vector_Calculus(u,w) gradient of expression u wrt variables in vector w

GRADDifferential_Vector_Calculus(u,A) gradient of expression u using coordinate geometry matrix A

GROEBNER_BASISGROEBNER_BASIS(polys,vars) Gröbner basis of polys based on lexicographic ordering vars

HEX1338PND(n) nth hex (i.e. 6-sided centered) number

IDENTICAL?Expression_Type_Functions(u,v) if u is identical to v, return true; otherwise return false

IDENTITY_MATRIXGenerating_Vectors_and_Matrices(n) n by n identity matrix

IFIF_Expressions(r) if r is true, return 1; if r is false, return 0

IFIF_Expressions(r,t,f) if r is true, return expression t; if r is false, return expression f

IFIF_Expressions(r,t,f,u) if r is true, return expression t; if false, return expression f; if unknown, return u

IMComplex_Variable_Functions(z) imaginary part of z

INSERTVector_Manipulation_Functions(u,v,n) insert u before the nth element of v

INTARB2JQ(u,x) antiderivative of u(x) wrt x

INTARB2JQ(u,x,a,b) definite integral of u(x) from x=a to b

INTEGER?Expression_Type_Functions(k) if k is an integer, return true; otherwise return false

INTEGER_TYPE?Expression_Type_Functions(u) if expression u is of integer type, return true; otherwise return false

INVERSE_MODNumber_Theory_Functions(a,m) inverse of a mod m if it exists, and a question mark otherwise

ITERATEThe_ITERATE_Function(u,x,x0) 1st repeated element of sequence x0, u(x0), u(u(x0)), ...

ITERATEThe_ITERATE_Function(u,x,x0,n) element n+1 of sequence x0, u(x0), u(u(x0)), ...

ITERATEThe_ITERATE_Function(u,[x1,x2,...],[x01, x02,...]) 1st repeated element of sequence [x01, x02,...],u(x01, x02,...),...

ITERATESThe_ITERATES_Function(u,x,x0) vector [x0,u(x0),u(u(x0)),...] until an element is repeated

ITERATESThe_ITERATES_Function(u,x,x0,n) 1st n+1 elements of vector [x0,u(x0),u(u(x0)),...]

LAPLACIANDifferential_Vector_Calculus(u) divergence of gradient of expression u wrt variables x, y, and z

LAPLACIANDifferential_Vector_Calculus(u,w) divergence of gradient of expression u wrt variables in vector w

LAPLACIANDifferential_Vector_Calculus(u,A) divergence of gradient of expression u using coordinate geometry matrix A

LCMNumber_Theory_Functions(m,n,...) least common multiple of m, n, ...

LHSExpression_Decomposition_Functions(r) left hand side (left operand) of relation r

LIMPGUOQ0(u,x,a) limit of u(x) as x approaches a

LIMPGUOQ0(u,x,a,1) limit of u(x) as x approaches a from above

LIMPGUOQ0(u,x,a,-1) limit of u(x) as x approaches a from below

LNLogarithmic_Functions(z) natural logarithm of z

LOAD1_O7U5P(filename) load the utility file named filename

LOGLogarithmic_Functions(z) natural logarithm of z

LOGLogarithmic_Functions(z,w) logarithm of z to the base w

LOGICAL?Expression_Type_Functions(k) if k is a truth-value (i.e. true or false), return true; otherwise return false

LOGICAL_TYPE?Expression_Type_Functions(u) if expression u is of truth-value type, return true; otherwise return false

LOOPProcedural_Programming(s1,...,sn) repeatedly simplify statements s1 through sn until a RETURN or EXIT statement encountered

MAPProgramming_Functions(u,x,c) evaluates u(x) for x equal to elements of collection c and returns true

MAPProgramming_Functions(u,k,m,n,s) evaluates u(k) for k=m to n in steps of size s and returns true

MAP_LISTProgramming_Functions(u,x,c) evaluates u(x) for x equal to elements of collection c and returns result as a collection

MAP_LISTProgramming_Functions(u,k,m,n,s) evaluates u(k) for k=m to n in steps of size s and returns result as a vector

MATRIX?Expression_Type_Functions(u) if u is a matrix, return true; otherwise return false

MAXPiecewise_Continuous_Functions(x1,x2,...) maximum of x1, x2, ...

MAXPiecewise_Continuous_Functions(v) maximum element of vector v

MEMBER?Vector_Operations(u,v) if u is a member of v, return true; otherwise return false

MINPiecewise_Continuous_Functions(x1,x2,...) minimum of x1, x2, ...

MINPiecewise_Continuous_Functions(v) minimum element of vector v

MODPiecewise_Continuous_Functions(m) fractional part of m

MODPiecewise_Continuous_Functions(m,n) m modulo n (nonnegative remainder of m/n)

MODSPiecewise_Continuous_Functions(m,n) symmetric m modulo n

NAME_TO_CODESString_Processing_Functions(v) vector of ASCII codes corresponding to the characters in string or integer s

NEXT_PRIMENumber_Theory_Functions(n) next prime larger than n

NORMALError_Functions(z) cumulative distribution function of z

NORMALError_Functions(z,m,s) normal distribution function of z with mean m and standard deviation s

NPERFinancial_Functions(i,pmt,pval,fval,time) number of payment periods

NSOLUTIONSSolving_Equations_Numerically(u,x) vector of approximate solutions of equation u=0 for variable x

NSOLUTIONSSolving_Equations_Numerically(B,x) vector of approximate solutions of Boolean B for variable x

NSOLUTIONSSolving_Equations_Numerically(B,x,Real) vector of approximate real solutions of Boolean B for variable x

NSOLUTIONSSolving_Equations_Numerically(B,v) vector of vectors of simultaneous solutions of Boolean B for variables in vector v

NSOLUTIONSSolving_Equations_Numerically(w,v) vector of vectors of simultaneous solutions of Booleans in vector w for variables in vector v

NSOLVESolving_Equations_Numerically(u,x) approximate solution of equation u=0 for variable x expressed as a Boolean equivalent to u=0

NSOLVESolving_Equations_Numerically(B,x) approximate solution of Boolean B for variable x expressed as a Boolean equivalent to B

NSOLVESolving_Equations_Numerically(B,x,Real) approximate real solution of Boolean B for variable x expressed as a Boolean equivalent to B

NSOLVESolving_Equations_Numerically(B,v) solution of Boolean B for variables in vector v expressed as a Boolean equivalent to B

NSOLVESolving_Equations_Numerically(w,v) solution of Booleans in vector w for variables in vector v expressed as a vector of Booleans whose disjunction is equivalent to the conjunction of the Booleans in vector w

NUMBER?Expression_Type_Functions(k) if k is a real or complex number, return true; otherwise return false

NUMBER_TYPE?Expression_Type_Functions(u) if expression u is real or complex, return true; otherwise return false

NUMERATORExpression_Decomposition_Functions(u) syntactic numerator of u

ODD?Expression_Type_Functions(k) if k is an odd number, return true; otherwise return false

PERMProbability_Functions(z,w) permutations of z things taken w at a time

PHASEComplex_Variable_Functions(z) phase angle of z

PMTFinancial_Functions(i,nper,pval,fval,time) periodic payment

POLY_GCDExpression_Decomposition_Functions(u,v) polynomial gcd of u and v

POLY_MODPiecewise_Continuous_Functions(u,n) polynomial whose coefficients are those of polynomial u reduced by modulus n

POLY_MODSPiecewise_Continuous_Functions(u,n) polynomial whose coefficients are those of polynomial u reduced by symetric modulus n

POSITIONVector_Manipulation_Functions(e,v,n) position of expression e in vector v after the nth element

POTENTIALIntegral_Vector_Calculus(v) scalar potential of vector v starting at (0,0,0) wrt variables x, y, and z

POTENTIALIntegral_Vector_Calculus(v,w) scalar potential of vector v starting at coordinates in vector w wrt variables x, y, and z

POTENTIALIntegral_Vector_Calculus(v,w,u) scalar potential of vector v starting at coordinates in vector w wrt variables in vector u

POTENTIALIntegral_Vector_Calculus(v,w,A) scalar potential of vector v starting at coordinates in vector w using geometry matrix A

POWER?Expression_Type_Functions(u) if expression u is a power, return true; otherwise return false

POWER_MODNumber_Theory_Functions(n,d,m) n^d mod m

POWER_SETSet_Operators(s) all subsets of s

PREVIOUS_PRIMENumber_Theory_Functions(n) first prime smaller than n

PRIME?Number_Theory_Functions(n) if n is prime, return true; otherwise return false

PRODUCT1NW3ZP_(c) product of the elements of collection c

PRODUCT1NW3ZP_(u,k) antiquotient of u(k) wrt k

PRODUCT1NW3ZP_(u,k,c) product of u(k) for k an element of collection c

PRODUCT1NW3ZP_(u,k,m,n) definite product of u(k) from k=m to n

PRODUCT?Expression_Type_Functions(u) if expression u is a product, return true; otherwise return false

PROGProcedural_Programming(s1,...,sn) simplify statements s1 through sn unless a RETURN(u) or EXIT statement encountered

PVALFinancial_Functions(i,nper,pmt,fval,time) present value of contract

QUOTIENTExpression_Decomposition_Functions(u,v) polynomial quotient of u divided by v

RANDOMProbability_Functions(n) if n=0, initialize seed based on current time

RANDOMProbability_Functions(n) if n=1, a random number in the interval [0,1)

RANDOMProbability_Functions(n) if n>1, a random integer in the interval [0,n)

RANDOMProbability_Functions(n) if n<1, initialize random number seed to n

RANKRow_Echelon_Form(A) rank of matrix A

RATEFinancial_Functions(nper,pmt,pval,fval,time,min,max) periodic interest rate

RATIONAL?Expression_Type_Functions(k) if k is a rational number, return true; otherwise return false

REComplex_Variable_Functions(z) real part of z

REAL_TYPE?Expression_Type_Functions(u) if expression u is real, return true; otherwise return false

REMAINDERExpression_Decomposition_Functions(u,v) polynomial remainder of u divided by v

REPLACEVector_Manipulation_Functions(u,v,n) replace the nth element of v with u

RESTVector_Manipulation_Functions(v) returns a vector of all but the first element of v

RETURNProcedural_Programming(u) immediately exit function and return u as its value

REVERSEVector_Manipulation_Functions(v) reverse elements of vector v

RHSExpression_Decomposition_Functions(r) right hand side (right operand) of relation r

RMSStatistical_Functions(z1,...,zn) root mean square of z1 through zn

ROUNDPiecewise_Continuous_Functions(m,n) nearest integer to m/n (n defaults to 1)

ROW_REDUCERow_Echelon_Form(A) row echelon form of A

ROW_REDUCERow_Echelon_Form(A,B) row echelon form of A augmented by B

SECTrigonometric_Functions(z) secant of z radians

SECHHyperbolic_Functions(z) hyperbolic secant of z

SELECTVector_Manipulation_Functions(u,k,m,n,s) vector of k as k goes from m thru n in steps of s for which u(k) is true

SELECTVector_Manipulation_Functions(u,k,c) collection of those elements of collection c for which u(k) is true

SET?Expression_Type_Functions(u) if u is a set, return true; otherwise return false

SET_TYPE?Expression_Type_Functions(u) if expression u is of set type, return true; otherwise return false

SIGNPiecewise_Continuous_Functions(x) sign of x

SIGNComplex_Variable_Functions(z) radial projection of z on unit circle

SINTrigonometric_Functions(z) sine of z radians

SINTrigonometric_Functions(z·deg) sine of z degrees

SINHHyperbolic_Functions(z) hyperbolic sine of z

SOLUTIONSSolving_Equations_and_Inequalities_Algebraically(u,x) vector of solutions of equation u=0 for variable x

SOLUTIONSSolving_Equations_and_Inequalities_Algebraically(B,x) vector of solutions of Boolean B for variable x

SOLUTIONSSolving_Equations_and_Inequalities_Algebraically(B,x,Real) vector of real solutions of Boolean B for variable x

SOLUTIONSSolving_Systems_of_Equations(B,v) vector of vectors of simultaneous solutions of Boolean B for variables in vector v

SOLUTIONSSolving_Systems_of_Equations(w,v) vector of vectors of simultaneous solutions of Booleans in vector w for variables in vector v

SOLVESolving_Equations_and_Inequalities_Algebraically(u,x) solution of equation u=0 for variable x expressed as a Boolean equivalent to u=0

SOLVESolving_Equations_and_Inequalities_Algebraically(B,x) solution of Boolean B for variable x expressed as a Boolean equivalent to B

SOLVESolving_Equations_and_Inequalities_Algebraically(B,x,Real) real solution of Boolean B for variable x expressed as a Boolean equivalent to B

SOLVESolving_Systems_of_Equations(B,v) solution of Boolean B for variables in vector v expressed as a Boolean equivalent to B

SOLVESolving_Systems_of_Equations(w,v) solution of Booleans in vector w for variables in vector v expressed as a vector of Booleans whose disjunction is equivalent to the conjunction of the Booleans in vector w

SOMEBoolean_Functions(u,x,c) if u(x) is true for some x in c, return true; otherwise return false

SOMEBoolean_Functions(u,k,m,n,s) if u(k) is true for some k=m to n in steps of s, return true; otherwise return false

SORTVector_Manipulation_Functions(v) function to sort the elements of a vector or set v, and return the result as a vector

SQRTExponential_Functions(z) square root of z

STDEVStatistical_Functions(z1,...,zn) standard deviation of z1 through zn

STEPPiecewise_Continuous_Functions(x) step function of x

STRINGString_Processing_Functions(v) string variable having same display name as variable v

STRING?Expression_Type_Functions(u) if expression u is a string variable, return true; otherwise return false

SUBSTGP2.L1(u,old,new) substitute new for old in u

SUM15A5MUZ(c) sum of the elements of collection c

SUM15A5MUZ(u,k) antidifference of u(k) wrt k

SUM15A5MUZ(u,k,c) sum of u(k) for k an element of collection c

SUM15A5MUZ(u,k,m,n) definite sum of u(k) from k=m to n

SUM?Expression_Type_Functions(u) if expression u is a sum, return true; otherwise return false

TABLETX0JH_(u,k,m,n,s) table of (n-m+1)/s rows of u(k) simplified with k=m to n in steps of size s

TANTrigonometric_Functions(z) tangent of z radians

TANHHyperbolic_Functions(z) hyperbolic tangent of z

TAYLORMRJ3J4(u,x,a,n) nth order Taylor approximation of u(x) about x=a

TERMSExpression_Decomposition_Functions(u) vector of syntactic terms of u

TRACEMatrix_Operations(A) trace of matrix A (sum of diagonal elements)

TRUTH_TABLETruth_Table_Functions(p1,p2,...,bool1,bool2,...) truth table matrix for Boolean expressions bool1, bool2, ...

VARIABLE?Expression_Type_Functions(u) if u is a variable, return true; otherwise return false

VARIABLESExpression_Decomposition_Functions(u) a vector of the free variables in u

VARIANCEStatistical_Functions(z1,...,zn) variance of z1, ..., zn

VECTOR.WK1F5(u,k,v) vector of u(k) applied to elements of vector v

VECTOR.WK1F5(u,k,n) vector of u(k) as k goes from 1 thru n in steps of 1

VECTOR.WK1F5(u,k,m,n) vector of u(k) as k goes from m thru n in steps of 1

VECTOR.WK1F5(u,k,m,n,s) vector of u(k) as k goes from m thru n in steps of s

VECTOR?Expression_Type_Functions(u) if u is a vector, return true; otherwise return false

VECTOR_POTENTIALIntegral_Vector_Calculus(v) vector potential of vector v starting at (0,0,0) wrt variables x, y, and z

VECTOR_POTENTIALIntegral_Vector_Calculus(v,w) vector potential of vector v starting at vector w wrt variables x, y, and z

VECTOR_POTENTIALIntegral_Vector_Calculus(v,w,u) vector potential of vector v starting at vector w wrt variables in vector u

VECTOR_POTENTIALIntegral_Vector_Calculus(v,w,A) vector potential of vector v starting at vector w using geometry matrix A

VECTOR_TYPE?Expression_Type_Functions(u) if expression u is of vector type, return true; otherwise return false

WRITEProgramming_Functions(u) write u as a line of text on the Algebra window status line

ZETAZeta_Functions(s) the Riemann zeta function ζ(s)

ZETAZeta_Functions(s,z) the Hurwitz zeta function ζ(s,z)