:Abs:Abs(x):absolute value or modulus of complex number:
:Add:Add(val1, val2, ...):find sum of a list of values:
:Add:Add({list})::
:Append:Append(list, expr):append an entry at the end of a list:
:Apply:Apply(fn, arglist):apply a function to arguments:
:ArcCos:ArcCos(x):inverse trigonometric function arc-cosine:
:ArcSin:ArcSin(x):inverse trigonometric function arc-sine:
:ArcTan:ArcTan(x):inverse trigonometric function arc-tangent:
:Arg:Arg(x):argument of a complex number:
:Array'Create:Array'Create(size,init):create array:
:Array'CreateFromList:Array'CreateFromList(list):convert list to array:
:Array'Get:Array'Get(array,index):fetch array element:
:Array'Set:Array'Set(array,index,element):set array element:
:Array'Size:Array'Size(array):get array size:
:Array'ToList:Array'ToList(array):convert array to list:
:Assert:Assert("str") pred::
:Assert:Assert("str", expr) pred:signal "soft" custom error:
:Assert:Assert() pred::
:Assoc:Assoc(key, alist):return element stored in association list:
:AssocDelete:AssocDelete(alist, "key"):delete an entry in an association list:
:AssocDelete:AssocDelete(alist, {key, value})::
:AssocIndices:AssocIndices(alist):return the keys in an association list:
:Atom:Atom("string"):convert string to atom:
:BaseVector:BaseVector(k, n):base vector:
:Bernoulli:Bernoulli(index):Bernoulli numbers and polynomials:
:Bernoulli:Bernoulli(index, x)::
:BernoulliDistribution:BernoulliDistribution(p):Bernoulli distribution:
:BigOh:BigOh(poly, var, degree):drop all terms of a certain order in a polynomial:
:Bin:Bin(n, m):binomial coefficients:
:BinSplitData:BinSplitData(n1,n2, a, b, c, d):computations of series by the binary splitting method:
:BinSplitFinal:BinSplitFinal({P,Q,B,T}):computations of series by the binary splitting method:
:BinSplitNum:BinSplitNum(n1, n2, a, b, c, d):computations of series by the binary splitting method:
:BinomialDistribution:BinomialDistribution(p,n):binomial distribution:
:BitAnd:BitAnd(n,m):bitwise and operation:
:BitOr:BitOr(n,m):bitwise or operation:
:BitXor:BitXor(n,m):bitwise xor operation:
:Bodied:Bodied("op", precedence):define function syntax (bodied function):
:BracketRational:BracketRational(x, eps):find optimal rational approximations:
:BubbleSort:BubbleSort(list, compare):sort a list:
:Builtin'Precision'Get:Builtin'Precision'Get():get the current precision:
:Builtin'Precision'Set:Builtin'Precision'Set(n):set the precision:
:CForm:CForm(expr):export expression to C++ code:
:CachedConstant:CachedConstant(cache, Cname, Cfunc):precompute multiple-precision constants:
:CanProve:CanProve(proposition):try to prove statement:
:Catalan:Catalan:Catalan's Constant:
:CatalanNumber:CatalanNumber(n):return the {n}th Catalan Number:
:Ceil:Ceil(x):round a number upwards:
:CharacteristicEquation:CharacteristicEquation(matrix,var):get characteristic polynomial of a matrix:
:Check:Check(predicate,"error text"):report "hard" errors:
:ChiSquareTest:ChiSquareTest(observed,expected):Pearson's ChiSquare test:
:ChiSquareTest:ChiSquareTest(observed,expected,params)::
:Cholesky:Cholesky(A):find the Cholesky Decomposition:
:Clear:Clear(var, ...):undo an assignment:
:ClearError:ClearError("str"):custom errors handlers:
:ClearErrors:ClearErrors():simple error handlers:
:CoFactor:CoFactor(M,i,j):cofactor of a matrix:
:Coef:Coef(expr, var, order):coefficient of a polynomial:
:Complex:Complex(r, c):construct a complex number:
:Concat:Concat(list1, list2, ...):concatenate lists:
:ConcatStrings:ConcatStrings(strings):concatenate strings:
:Conjugate:Conjugate(x):complex conjugate:
:ContFrac:ContFrac(x):continued fraction expansion:
:ContFrac:ContFrac(x, depth)::
:ContFracEval:ContFracEval(list):manipulate continued fractions:
:ContFracEval:ContFracEval(list, rest)::
:ContFracList:ContFracList(frac):manipulate continued fractions:
:ContFracList:ContFracList(frac, depth)::
:Contains:Contains(list, expr):test whether a list contains a certain element:
:Content:Content(expr):content of a univariate polynomial:
:Cos:Cos(x):trigonometric cosine function:
:Count:Count(list, expr):count the number of occurrences of an expression:
:CrossProduct:CrossProduct(a,b):outer product of vectors:
:Curl:Curl(vector, basis):curl of a vector field:
:CurrentFile:CurrentFile():return current input file:
:CurrentLine:CurrentLine():return current line number on input:
:Cyclotomic:Cyclotomic(n,x):construct the cyclotomic polynomial:
:D:D(list) expression::
:D:D(variable) expression:take derivative of expression with respect to variable:
:D:D(variable,n) expression::
:Decimal:Decimal(frac):decimal representation of a rational:
:DefLoad:DefLoad(name):load a {.def} file:
:DefMacroRuleBase:DefMacroRuleBase(name,params):define a function as a macro:
:DefMacroRuleBaseListed:DefMacroRuleBaseListed("name", params):define macro with variable number of arguments:
:DefaultTokenizer:DefaultTokenizer():select the default syntax tokenizer for parsing the input:
:Degree:Degree(expr):degree of a polynomial:
:Degree:Degree(expr, var)::
:Delete:Delete(list, n):delete an element from a list:
:Denom:Denom(expr):denominator of an expression:
:DestructiveAppend:DestructiveAppend(list, expr):destructively append an entry to a list:
:DestructiveDelete:DestructiveDelete(list, n):delete an element destructively from a list:
:DestructiveInsert:DestructiveInsert(list, n, expr):insert an element destructively into a list:
:DestructiveReplace:DestructiveReplace(list, n, expr):replace an entry destructively in a list:
:DestructiveReverse:DestructiveReverse(list):reverse a list destructively:
:Determinant:Determinant(M):determinant of a matrix:
:Diagonal:Diagonal(A):extract the diagonal from a matrix:
:DiagonalMatrix:DiagonalMatrix(d):construct a diagonal matrix:
:Difference:Difference(l1, l2):return the difference of two lists:
:Div:Div(x,y):Determine divisor of two mathematical objects:
:Diverge:Diverge(vector, basis):divergence of a vector field:
:Divisors:Divisors(n):number of divisors:
:DivisorsList:DivisorsList(n):the list of divisors:
:DivisorsSum:DivisorsSum(n):the sum of  divisors:
:Dot:Dot(t1,t2):get dot product of tensors:
:Drop:Drop(list, -n)::
:Drop:Drop(list, n):drop a range of elements from a list:
:Drop:Drop(list, {m,n})::
:DumpErrors:DumpErrors():simple error handlers:
:Echo:Echo(item):high-level printing routine:
:Echo:Echo(item,item,item,...)::
:Echo:Echo(list)::
:EigenValues:EigenValues(matrix):get eigenvalues of a matrix:
:EigenVectors:EigenVectors(A,eigenvalues):get eigenvectors of a matrix:
:Eliminate:Eliminate(var, value, expr):substitute and simplify:
:EndOfFile:EndOfFile:end-of-file marker:
:Equals:Equals(a,b):check equality:
:Euler:Euler(index):Euler numbers and polynomials:
:Euler:Euler(index,x)::
:Eulerian:Eulerian(n,m):Eulerian numbers:
:Eval:Eval(expr):force evaluation of expression:
:EvalFormula:EvalFormula(expr):print an evaluation nicely with ASCII art:
:EvaluateHornerScheme:EvaluateHornerScheme(coeffs,x):fast evaluation of polynomials:
:Exp:Exp(x):exponential function:
:Expand:Expand(expr):transform a polynomial to an expanded form:
:Expand:Expand(expr, var)::
:Expand:Expand(expr, varlist)::
:ExpandBrackets:ExpandBrackets(expr):expand all brackets:
:ExtraInfo'Get:ExtraInfo'Get(expr):annotate objects with additional information:
:ExtraInfo'Set:ExtraInfo'Set(expr,tag):annotate objects with additional information:
:Factor:Factor(x):factorization, in pretty form:
:FactorialSimplify:FactorialSimplify(expression):Simplify hypergeometric expressions containing factorials:
:Factorize:Factorize(list):product of a list of values:
:Factorize:Factorize(var, from, to, body)::
:Factors:Factors(x):factorization:
:False:False:boolean constant representing false:
:FermatNumber:FermatNumber(n):return the {n}th Fermat Number:
:FillList:FillList(expr, n):fill a list with a certain expression:
:Find:Find(list, expr):get the index at which a certain element occurs:
:FindFile:FindFile(name):find a file in the current path:
:FindFunction:FindFunction(function):find the library file where a function is defined:
:FindRealRoots:FindRealRoots(p):find the real roots of a polynomial:
:FlatCopy:FlatCopy(list):copy the top level of a list:
:Flatten:Flatten(expression,operator):flatten expression w.r.t. some operator:
:Floor:Floor(x):round a number downwards:
:For:For(init, pred, incr) body:C-style {for} loop:
:ForEach:ForEach(var, list) body:loop over all entries in list:
:FromBase:FromBase(base,"string"):conversion of a number from non-decimal base to decimal base:
:FromFile:FromFile(name) body:connect current input to a file:
:FromString:FromString(str) body;:connect current input to a string:
:FullForm:FullForm(expr):print an expression in LISP-format:
:FuncList:FuncList(expr):list of functions used in an expression:
:FuncListArith:FuncListArith(expr):list of functions used in an expression:
:FuncListSome:FuncListSome(expr, list):list of functions used in an expression:
:Function:Function("op", {arglist, ...}) body::
:Function:Function("op", {arglist}) body::
:Function:Function() func(arglist):declare or define a function:
:Function:Function() func(arglist, ...)::
:Gamma:Gamma(x):Euler's Gamma function:
:GarbageCollect:GarbageCollect():do garbage collection on unused memory:
:GaussianFactors:GaussianFactors(z):factorization in Gaussian integers:
:GaussianGcd:GaussianGcd(z,w):greatest common divisor in Gaussian integers:
:GaussianNorm:GaussianNorm(z):norm of a Gaussian integer:
:Gcd:Gcd(list)::
:Gcd:Gcd(n,m):greatest common divisor:
:GenericTypeName:GenericTypeName(object):get type name:
:GetCoreError:GetCoreError():get "hard" error string:
:GetError:GetError("str"):custom errors handlers:
:GetErrorTableau:GetErrorTableau():custom errors handlers:
:GetTime:GetTime(expr):measure the time taken by an evaluation:
:GlobalPop:GlobalPop()::
:GlobalPop:GlobalPop(var):restore variables using a global stack:
:GlobalPush:GlobalPush(expr):save variables using a global stack:
:GoldenRatio:GoldenRatio:the Golden Ratio:
:GreaterThan:GreaterThan(a,b):comparison predicate:
:GuessRational:GuessRational(x):find optimal rational approximations:
:GuessRational:GuessRational(x, digits)::
:HarmonicNumber:HarmonicNumber(n):return the {n}th Harmonic Number:
:HarmonicNumber:HarmonicNumber(n,r)::
:HasExpr:HasExpr(expr, x):check for expression containing a subexpression:
:HasExprArith:HasExprArith(expr, x):check for expression containing a subexpression:
:HasExprSome:HasExprSome(expr, x, list):check for expression containing a subexpression:
:HasFunc:HasFunc(expr, func):check for expression containing a function:
:HasFuncArith:HasFuncArith(expr, func):check for expression containing a function:
:HasFuncSome:HasFuncSome(expr, func, list):check for expression containing a function:
:Head:Head(list):the first element of a list:
:HeapSort:HeapSort(list, compare):sort a list:
:HessianMatrix:HessianMatrix(function,var):create the Hessian matrix:
:HilbertInverseMatrix:HilbertInverseMatrix(n):create a Hilbert inverse matrix:
:HilbertMatrix:HilbertMatrix(n):create a Hilbert matrix:
:HilbertMatrix:HilbertMatrix(n,m)::
:Hold:Hold(expr):keep expression unevaluated:
:HoldArg:HoldArg("operator",parameter):mark argument as not evaluated:
:HoldArgNr:HoldArgNr("function", arity, argNum):specify argument as not evaluated:
:Horner:Horner(expr, var):convert a polynomial into the Horner form:
:I:I:imaginary unit:
:Identity:Identity(n):make identity matrix:
:If:If(pred, then):branch point:
:If:If(pred, then, else)::
:Im:Im(x):imaginary part of a complex number:
:InNumericMode:InNumericMode():determine if currently in numeric mode:
:InProduct:InProduct(a,b):inner product of vectors (deprecated):
:InVerboseMode:InVerboseMode():set verbose output mode:
:Infinity:Infinity:constant representing mathematical infinity:
:Infix:Infix("op"):define function syntax (infix operator):
:Infix:Infix("op", precedence)::
:Insert:Insert(list, n, expr):insert an element into a list:
:IntLog:IntLog(n, base):integer part of logarithm:
:IntNthRoot:IntNthRoot(x, n):integer part of $n$-th root:
:IntPowerNum:IntPowerNum(x, n, mult, unity):optimized computation of integer powers:
:Integrate:Integrate(var) expr::
:Integrate:Integrate(var, x1, x2) expr:integration:
:Intersection:Intersection(l1, l2):return the intersection of two lists:
:Inverse:Inverse(M):get inverse of a matrix:
:InverseTaylor:InverseTaylor(var, at, order) expr:Taylor expansion of inverse:
:IsAmicablePair:IsAmicablePair(m,n):test for a pair of amicable numbers:
:IsAtom:IsAtom(expr):test for an atom:
:IsBodied:IsBodied("op"):check for function syntax:
:IsBoolean:IsBoolean(expression):test for a Boolean value:
:IsBound:IsBound(var):test for a bound variable:
:IsCFormable:IsCFormable(expr):check possibility to export expression to C++ code:
:IsCFormable:IsCFormable(expr, funclist)::
:IsCarmichaelNumber:IsCarmichaelNumber(n):test for a Carmichael number:
:IsComposite:IsComposite(n):test for a composite number:
:IsConstant:IsConstant(expr):test for a constant:
:IsCoprime:IsCoprime(list)::
:IsCoprime:IsCoprime(m,n):test if integers are coprime :
:IsDiagonal:IsDiagonal(A):test for a diagonal matrix:
:IsError:IsError("str")::
:IsError:IsError():check for custom error:
:IsEven:IsEven(n):test for an even integer:
:IsEvenFunction:IsEvenFunction(expression,variable):Return true if function is an even function, False otherwise:
:IsFreeOf:IsFreeOf(var, expr):test whether expression depends on variable:
:IsFreeOf:IsFreeOf({var, ...}, expr)::
:IsFunction:IsFunction(expr):test for a composite object:
:IsGaussianInteger:IsGaussianInteger(z):test for a Gaussian integer:
:IsGaussianPrime:IsGaussianPrime(z):test for a Gaussian prime:
:IsGaussianUnit:IsGaussianUnit(z):test for a Gaussian unit:
:IsGeneric:IsGeneric(object):check for generic object:
:IsHermitian:IsHermitian(A):test for a Hermitian matrix:
:IsIdempotent:IsIdempotent(A):test for an idempotent matrix:
:IsInfinity:IsInfinity(expr):test for an infinity:
:IsInfix:IsInfix("op"):check for function syntax:
:IsIrregularPrime:IsIrregularPrime(n):test for an irregular prime:
:IsList:IsList(expr):test for a list:
:IsLowerTriangular:IsLowerTriangular(A):test for a lower triangular matrix:
:IsMatrix:IsMatrix(expr):test for a matrix:
:IsMatrix:IsMatrix(pred,expr)::
:IsNegativeInteger:IsNegativeInteger(n):test for a negative integer:
:IsNegativeNumber:IsNegativeNumber(n):test for a negative number:
:IsNegativeReal:IsNegativeReal(expr):test for a numerically negative value:
:IsNonObject:IsNonObject(expr):test whether argument is not an {Object()}:
:IsNonZeroInteger:IsNonZeroInteger(n):test for a nonzero integer:
:IsNotZero:IsNotZero(n):test for a nonzero number:
:IsNumber:IsNumber(expr):test for a number:
:IsNumericList:IsNumericList({list}):test for a list of numbers:
:IsOdd:IsOdd(n):test for an odd integer:
:IsOddFunction:IsOddFunction(expression,variable):Return true if function is an odd function, False otherwise:
:IsOrthogonal:IsOrthogonal(A):test for an orthogonal matrix:
:IsPositiveInteger:IsPositiveInteger(n):test for a positive integer:
:IsPositiveNumber:IsPositiveNumber(n):test for a positive number:
:IsPositiveReal:IsPositiveReal(expr):test for a numerically positive value:
:IsPostfix:IsPostfix("op"):check for function syntax:
:IsPrefix:IsPrefix("op"):check for function syntax:
:IsPrime:IsPrime(n):test for a prime number:
:IsPrimePower:IsPrimePower(n):test for a power of a prime number:
:IsPromptShown:IsPromptShown():test for the Yacas prompt option:
:IsQuadraticResidue:IsQuadraticResidue(m,n):functions related to finite groups:
:IsRational:IsRational(expr):test whether argument is a rational:
:IsScalar:IsScalar(expr):test for a scalar:
:IsSkewSymmetric:IsSkewSymmetric(A):test for a skew-symmetric matrix:
:IsSmallPrime:IsSmallPrime(n):test for a (small) prime number:
:IsSquareFree:IsSquareFree(n):test for a square-free number:
:IsSquareMatrix:IsSquareMatrix(expr):test for a square matrix:
:IsSquareMatrix:IsSquareMatrix(pred,expr)::
:IsString:IsString(expr):test for an string:
:IsSymmetric:IsSymmetric(A):test for a symmetric matrix:
:IsTwinPrime:IsTwinPrime(n):test for a twin prime:
:IsUnitary:IsUnitary(A):test for a unitary matrix:
:IsUpperTriangular:IsUpperTriangular(A):test for an upper triangular matrix:
:IsVector:IsVector(expr):test for a vector:
:IsVector:IsVector(pred,expr)::
:IsZero:IsZero(n):test whether argument is zero:
:IsZeroVector:IsZeroVector(list):test whether list contains only zeroes:
:JacobiSymbol:JacobiSymbol(m,n):functions related to finite groups:
:JacobianMatrix:JacobianMatrix(functions,variables):calculate the Jacobian matrix of $n$ functions in $n$ variables:
:KnownFailure:KnownFailure(test):Mark a test as a known failure:
:LagrangeInterpolant:LagrangeInterpolant(xlist, ylist, var):polynomial interpolation:
:LambertW:LambertW(x):Lambert's $W$ function:
:LaplaceTransform:LaplaceTransform(t,s,func)	:Laplace Transform:
:Lcm:Lcm(list)::
:Lcm:Lcm(n,m):least common multiple:
:LeadingCoef:LeadingCoef(poly):leading coefficient of a polynomial:
:LeadingCoef:LeadingCoef(poly, var)::
:LeftPrecedence:LeftPrecedence("op",precedence):set operator precedence:
:LegendreSymbol:LegendreSymbol(m,n):functions related to finite groups:
:Length:Length(object):the length of a list or string:
:LessThan:LessThan(a,b):comparison predicate:
:LeviCivita:LeviCivita(list):totally anti-symmetric Levi-Civita symbol:
:Limit:Limit(var, val) expr:limit of an expression:
:Limit:Limit(var, val, dir) expr::
:LispRead:LispRead():read expressions in LISP syntax:
:LispReadListed:LispReadListed():read expressions in LISP syntax:
:List:List(expr1, expr2, ...):construct a list:
:Listify:Listify(expr):convert a function application to a list:
:Ln:Ln(x):natural logarithm:
:LnCombine:LnCombine(expr):combine logarithmic expressions using standard logarithm rules:
:LnExpand:LnExpand(expr):expand a logarithmic expression using standard logarithm rules:
:Load:Load(name):evaluate all expressions in a file:
:Local:Local(var, ...):declare new local variables:
:LocalSymbols:LocalSymbols(var1, var2, ...) body:create unique local symbols with given prefix:
:LogicTest:LogicTest(variables,expr1,expr2):verifying equivalence of two expressions:
:LogicVerify:LogicVerify(question,answer):verifying equivalence of two expressions:
:Macro:Macro("op", {arglist, ...}) body::
:Macro:Macro("op", {arglist}) body::
:Macro:Macro() func(arglist):declare or define a macro:
:Macro:Macro() func(arglist, ...)::
:MakeVector:MakeVector(var,n):vector of uniquely numbered variable names:
:Map:Map(fn, list):apply an $n$-ary function to all entries in a list:
:MapArgs:MapArgs(expr, fn):apply a function to all top-level arguments:
:MapSingle:MapSingle(fn, list):apply a unary function to all entries in a list:
:MatchLinear:MatchLinear(x,expr):match an expression to a polynomial of degree one in a variable:
:MathAbs:MathAbs(x)     (absolute value of x, or |x| )::
:MathAdd:MathAdd(x,y)      (add two numbers)::
:MathAnd:MathAnd(...):built-in logical "and":
:MathArcCos:MathArcCos(x)   (inverse cosine)::
:MathArcCosh:MathArcCosh(x)  (inverse hyperbolic cosine)::
:MathArcSin:MathArcSin(x)   (inverse sine)::
:MathArcSinh:MathArcSinh(x)  (inverse hyperbolic sine)::
:MathArcTan:MathArcTan(x)   (inverse tangent)::
:MathArcTanh:MathArcTanh(x)  (inverse hyperbolic tangent)::
:MathCeil:MathCeil(x)    (smallest integer not smaller than x)::
:MathCos:MathCos(x)     (cosine)::
:MathCosh:MathCosh(x)     (hyperbolic cosine)::
:MathDiv:MathDiv(x,y)    (integer division, result is an integer)::
:MathDivide:MathDivide(x,y)   (divide two numbers)::
:MathExp:MathExp(x)     (exponential, base 2.718...)::
:MathFloor:MathFloor(x)   (largest integer not larger than x)::
:MathGcd:MathGcd(n,m)      (Greatest Common Divisor)::
:MathGetExactBits:MathGetExactBits(x):manipulate precision of floating-point numbers:
:MathLog:MathLog(x)     (natural logarithm, for x>0)::
:MathMod:MathMod(x,y)    (remainder of division, or x mod y)::
:MathMultiply:MathMultiply(x,y) (multiply two numbers)::
:MathNot:MathNot(expression):built-in logical "not":
:MathOr:MathOr(...):built-in logical "or":
:MathPower:MathPower(x,y) (power, x ^ y)::
:MathSetExactBits:MathSetExactBits(x,bits):manipulate precision of floating-point numbers:
:MathSin:MathSin(x)     (sine)::
:MathSinh:MathSinh(x)     (hyperbolic sine)::
:MathSqrt:MathSqrt(x)    (square root, must be x>=0)::
:MathSubtract:MathSubtract(x,y) (subtract two numbers)::
:MathTan:MathTan(x)     (tangent)::
:MathTanh:MathTanh(x)     (hyperbolic tangent)::
:MatrixPower:MatrixPower(mat,n):get nth power of a square matrix:
:MatrixSolve:MatrixSolve(A,b):solve a system of equations:
:Max:Max(list)::
:Max:Max(x,y):maximum of a number of values:
:MaxEvalDepth:MaxEvalDepth(n):set the maximum evaluation depth:
:MaximumBound:MaximumBound(p):return upper bounds on the absolute values of real roots of a polynomial:
:Min:Min(list)::
:Min:Min(x,y):minimum of a number of values:
:MinimumBound:MinimumBound(p):return lower bounds on the absolute values of real roots of a polynomial:
:Minor:Minor(M,i,j):get principal minor of a matrix:
:Mod:Mod(x,y):Determine remainder of two mathematical objects after dividing one by the other:
:Moebius:Moebius(n):the Moebius function:
:MoebiusDivisorsList:MoebiusDivisorsList(n):the list of divisors and Moebius values:
:Monic:Monic(poly):monic part of a polynomial:
:Monic:Monic(poly, var)::
:MultiplyNum:MultiplyNum(x,y):optimized numerical multiplication:
:MultiplyNum:MultiplyNum(x,y,z,...)::
:MultiplyNum:MultiplyNum({x,y,z,...})::
:N:N(expression):try determine numerical approximation of expression:
:N:N(expression, precision)::
:NFunction:NFunction("newname","funcname", {arglist}):make wrapper for numeric functions:
:NearRational:NearRational(x):find optimal rational approximations:
:NearRational:NearRational(x, digits)::
:NewLine:NewLine():print one or more newline characters:
:NewLine:NewLine(nr)::
:Newton:Newton(expr, var, initial, accuracy):solve an equation numerically with Newton's method:
:Newton:Newton(expr, var, initial, accuracy,min,max)::
:NewtonNum:NewtonNum(func, x0)::
:NewtonNum:NewtonNum(func, x0, prec0)::
:NewtonNum:NewtonNum(func, x0, prec0, order):low-level optimized Newton's iterations:
:NextPrime:NextPrime(i):generate a prime following a number:
:Nl:Nl():the newline character:
:NonN:NonN(expr):calculate part in non-numeric mode:
:Normalize:Normalize(v):normalize a vector:
:Not:Not expr:logical negation:
:NrArgs:NrArgs(expr):return number of top-level arguments:
:Nth:Nth(list, n):return the $n$-th element of a list:
:NthRoot:NthRoot(m,n):calculate/simplify nth root of an integer:
:NumRealRoots:NumRealRoots(p):return the number of real roots of a polynomial:
:Numer:Numer(expr):numerator of an expression:
:OMDef:OMDef(yacasForm, cd, name):define translations from Yacas to OpenMath and vice-versa.:
:OMDef:OMDef(yacasForm, cd, name, yacasToOM)::
:OMDef:OMDef(yacasForm, cd, name, yacasToOM, omToYacas)::
:OMForm:OMForm(expression):convert Yacas expression to OpenMath:
:OMRead:OMRead():convert expression from OpenMath to Yacas expression:
:Object:Object("pred", exp):create an incomplete type:
:OdeOrder:OdeOrder(eqn):return order of an ODE:
:OdeSolve:OdeSolve(expr1==expr2):general ODE solver:
:OdeTest:OdeTest(eqn,testsol):test the solution of an ODE:
:OldSolve:OldSolve(eq, var):old version of {Solve}:
:OldSolve:OldSolve(eqlist, varlist)::
:OpLeftPrecedence:OpLeftPrecedence("op"):get operator precedence:
:OpPrecedence:OpPrecedence("op"):get operator precedence:
:OpRightPrecedence:OpRightPrecedence("op"):get operator precedence:
:OrthoG:OrthoG(n, a, x);:Gegenbauer orthogonal polynomials:
:OrthoGSum:OrthoGSum(c, a, x);:sums of series of orthogonal polynomials:
:OrthoH:OrthoH(n, x);:Hermite orthogonal polynomials:
:OrthoHSum:OrthoHSum(c, x);:sums of series of orthogonal polynomials:
:OrthoL:OrthoL(n, a, x);:Laguerre orthogonal polynomials:
:OrthoLSum:OrthoLSum(c, a, x);:sums of series of orthogonal polynomials:
:OrthoP:OrthoP(n, a, b, x);::
:OrthoP:OrthoP(n, x);:Legendre and Jacobi orthogonal polynomials:
:OrthoPSum:OrthoPSum(c, a, b, x);::
:OrthoPSum:OrthoPSum(c, x);:sums of series of orthogonal polynomials:
:OrthoPoly:OrthoPoly(name, n, par, x):internal function for constructing orthogonal polynomials:
:OrthoPolySum:OrthoPolySum(name, c, par, x):internal function for computing series of orthogonal polynomials:
:OrthoT:OrthoT(n, x);:Chebyshev polynomials:
:OrthoTSum:OrthoTSum(c, x);:sums of series of orthogonal polynomials:
:OrthoU:OrthoU(n, x);:Chebyshev polynomials:
:OrthoUSum:OrthoUSum(c, x);:sums of series of orthogonal polynomials:
:OrthogonalBasis:OrthogonalBasis(W):create an orthogonal basis :
:OrthonormalBasis:OrthonormalBasis(W):create an orthonormal basis :
:Outer:Outer(t1,t2):get outer tensor product:
:PAdicExpand:PAdicExpand(n, p):p-adic expansion:
:PDF:PDF(dist,x):probability density function:
:PSolve:PSolve(poly, var):solve a polynomial equation:
:Partition:Partition(list, n):partition a list in sublists of equal length:
:PatchLoad:PatchLoad(name):execute commands between {<?} and {?>} in file:
:PatchString:PatchString(string):execute commands between {<?} and {?>} in strings:
:Permutations:Permutations(list):get all permutations of a list:
:Pi:Pi:mathematical constant, $pi$:
:Plot2D:Plot2D(f(x)):adaptive two-dimensional plotting:
:Plot2D:Plot2D(f(x), a b)::
:Plot2D:Plot2D(f(x), a b, option=value)::
:Plot2D:Plot2D(f(x), a b, option=value, ...)::
:Plot2D:Plot2D(list, ...)::
:Plot3DS:Plot3DS(f(x,y)):three-dimensional (surface) plotting:
:Plot3DS:Plot3DS(f(x,y), a b, c d)::
:Plot3DS:Plot3DS(f(x,y), a b, c d, option=value)::
:Plot3DS:Plot3DS(f(x,y), a b, c d, option=value, ...)::
:Plot3DS:Plot3DS(list, ...)::
:Pop:Pop(stack, n):remove an element from a stack:
:PopBack:PopBack(stack):remove an element from the bottom of a stack:
:PopFront:PopFront(stack):remove an element from the top of a stack:
:Postfix:Postfix("op"):define function syntax (postfix operator):
:Postfix:Postfix("op", precedence)::
:Prefix:Prefix("op"):define function syntax (prefix operator):
:Prefix:Prefix("op", precedence)::
:PrettyForm:PrettyForm(expr):print an expression nicely with ASCII art:
:PrimitivePart:PrimitivePart(expr):primitive part of a univariate polynomial:
:PrintList:PrintList(list):print list with padding:
:PrintList:PrintList(list, padding);::
:Prog:Prog(statement1, statement2, ...):block of statements:
:ProperDivisors:ProperDivisors(n):the number of proper divisors:
:ProperDivisorsSum:ProperDivisorsSum(n):the sum of proper divisors:
:Pslq:Pslq(xlist,precision):search for integer relations between reals:
:Push:Push(stack, expr):add an element on top of a stack:
:RadSimp:RadSimp(expr):simplify expression with nested radicals:
:RamanujanSum:RamanujanSum(k,n):compute the "Ramanujan sum":
:RandVerifyArithmetic:RandVerifyArithmetic(n):Special purpose arithmetic verifiers:
:Random:Random():(pseudo-) random number generator:
:RandomIntegerMatrix:RandomIntegerMatrix(rows,cols,from,to):generate a matrix of random integers:
:RandomIntegerVector:RandomIntegerVector(nr, from, to):generate a vector of random integers:
:RandomPoly:RandomPoly(var,deg,coefmin,coefmax):construct a random polynomial:
:RandomSeed:RandomSeed(init):(pseudo-) random number generator:
:Rationalize:Rationalize(expr):convert floating point numbers to fractions:
:Re:Re(x):real part of a complex number:
:Read:Read():read an expression from current input:
:ReadCmdLineString:ReadCmdLineString(prompt):read an expression from command line and return in string:
:ReadToken:ReadToken():read a token from current input:
:RemoveDuplicates:RemoveDuplicates(list):remove any duplicates from a list:
:Replace:Replace(list, n, expr):replace an entry in a list:
:Retract:Retract("function",arity):erase rules for a function:
:Reverse:Reverse(list):return the reversed list (without touching the original):
:ReversePoly:ReversePoly(f, g, var, newvar, degree):solve $h(f(x)) = g(x) + O(x^n)$ for $h$:
:RightAssociative:RightAssociative("op"):declare associativity:
:RightPrecedence:RightPrecedence("op",precedence):set operator precedence:
:Rng:Rng(r):manipulate random number generators as objects:
:RngCreate:RngCreate():manipulate random number generators as objects:
:RngCreate:RngCreate(init)::
:RngCreate:RngCreate(option==value,...)::
:RngSeed:RngSeed(r, init):manipulate random number generators as objects:
:Round:Round(x):round a number to the nearest integer:
:RoundTo:RoundTo(number,precision):Round a real-valued result to a set number of digits:
:Rule:Rule("operator", arity,:define a rewrite rule:
:RuleBase:RuleBase(name,params):define function with a fixed number of arguments:
:RuleBaseArgList:RuleBaseArgList("operator", arity):obtain list of arguments:
:RuleBaseListed:RuleBaseListed("name", params):define function with variable number of arguments:
:Secure:Secure(body):guard the host OS:
:Select:Select(pred, list):select entries satisfying some predicate:
:Set:Set(var, exp):assignment:
:SetGlobalLazyVariable:SetGlobalLazyVariable(var,value):global variable is to be evaluated lazily:
:ShiftLeft:ShiftLeft(expr,bits)::
:ShiftRight:ShiftRight(expr,bits)::
:Sign:Sign(x):sign of a number:
:Simplify:Simplify(expr):try to simplify an expression:
:Sin:Sin(x):trigonometric sine function:
:Solve:Solve(eq, var):solve an equation:
:SolveMatrix:SolveMatrix(M,v):solve a linear system:
:Space:Space():print one or more spaces:
:Space:Space(nr)::
:Sparsity:Sparsity(matrix):get the sparsity of a matrix:
:Sqrt:Sqrt(x):square root:
:SquareFree:SquareFree(p):return the square-free part of polynomial:
:SquareFreeDivisorsList:SquareFreeDivisorsList(n):the list of square-free divisors:
:StirlingNumber1:StirlingNumber1(n,m):return the {n,m}th Stirling Number of the first kind:
:String:String(atom):convert atom to string:
:StringMid'Get:StringMid'Get(index,length,string):retrieve a substring:
:StringMid'Set:StringMid'Set(index,substring,string):change a substring:
:Subfactorial:Subfactorial(m):factorial and related functions:
:Subst:Subst(from, to) expr:perform a substitution:
:SuchThat:SuchThat(expr, var):special purpose solver:
:Sum:Sum(var, from, to, body):find sum of a sequence:
:SumForDivisors:SumForDivisors(var,n,expr):loop over divisors:
:SumTaylorNum:SumTaylorNum(x, NthTerm, TermFactor, order)::
:SumTaylorNum:SumTaylorNum(x, NthTerm, order):optimized numerical evaluation of Taylor series:
:SumTaylorNum:SumTaylorNum(x, ZerothTerm, TermFactor, order)::
:Swap:Swap(list, i1, i2):swap two elements in a list:
:SylvesterMatrix:SylvesterMatrix(poly1,poly2,variable):calculate the Sylvester matrix of two polynomials:
:SystemCall:SystemCall(str):pass a command to the shell:
:Table:Table(body, var, from, to, step):evaluate while some variable ranges over interval:
:TableForm:TableForm(list):print each entry in a list on a line:
:Tail:Tail(list):returns a list without its first element:
:Take:Take(list, -n)::
:Take:Take(list, n):take a sublist from a list, dropping the rest:
:Take:Take(list, {m,n})::
:Tan:Tan(x):trigonometric tangent function:
:Taylor:Taylor(var, at, order) expr:univariate Taylor series expansion:
:TeXForm:TeXForm(expr):export expressions to $LaTeX$:
:TestYacas:TestYacas(question,answer):verifying equivalence of two expressions:
:Time:Time(expr):measure the time taken by a function:
:ToBase:ToBase(base, number):conversion of a number in decimal base to non-decimal base:
:ToFile:ToFile(name) body:connect current output to a file:
:ToStdout:ToStdout() body:select initial output stream for output:
:ToString:ToString() body:connect current output to a string:
:ToeplitzMatrix:ToeplitzMatrix(N):create a Toeplitz matrix:
:Trace:Trace(M):trace of a matrix:
:TraceExp:TraceExp(expr):evaluate with tracing enabled:
:TraceRule:TraceRule(template) expr:turn on tracing for a particular function:
:TraceStack:TraceStack(expression):show calling stack after an error occurs:
:Transpose:Transpose(M):get transpose of a matrix:
:TrapError:TrapError(expression,errorHandler):trap "hard" errors:
:TrigSimpCombine:TrigSimpCombine(expr):combine products of trigonometric functions:
:True:True:boolean constant representing true:
:TruncRadian:TruncRadian(r):remainder modulo $2*Pi$:
:Type:Type(expr):return the type of an expression:
:UnFence:UnFence("operator",arity):change local variable scope for a function:
:UnFlatten:UnFlatten(list,operator,identity):inverse operation of Flatten:
:UnList:UnList(list):convert a list to a function application:
:Undefined:Undefined:constant signifying an undefined result:
:Union:Union(l1, l2):return the union of two lists:
:UniqueConstant:UniqueConstant():create a unique identifier:
:Until:Until(pred) body:loop until a condition is met:
:Use:Use(name):load a file, but not twice:
:V:V(expression):set verbose output mode:
:VandermondeMatrix:VandermondeMatrix(vector):create the Vandermonde matrix:
:VarList:VarList(expr):list of variables appearing in an expression:
:VarListArith:VarListArith(expr):list of variables appearing in an expression:
:VarListSome:VarListSome(expr, list):list of variables appearing in an expression:
:Verify:Verify(question,answer):verifying equivalence of two expressions:
:VerifyArithmetic:VerifyArithmetic(x,n,m):Special purpose arithmetic verifiers:
:VerifyDiv:VerifyDiv(u,v):Special purpose arithmetic verifiers:
:While:While(pred) body:loop while a condition is met:
:WithValue:WithValue(var, val, expr):temporary assignment during an evaluation:
:WithValue:WithValue({var,...}, {val,...}, expr)::
:Write:Write(expr, ...):low-level printing routine:
:WriteString:WriteString(string):low-level printing routine for strings:
:WronskianMatrix:WronskianMatrix(func,var):create the Wronskian matrix:
:XmlExplodeTag:XmlExplodeTag(xmltext):convert XML strings to tag objects:
:XmlTokenizer:XmlTokenizer():select an XML syntax tokenizer for parsing the input:
:ZeroMatrix:ZeroMatrix(n):make a zero matrix:
:ZeroMatrix:ZeroMatrix(n, m)::
:ZeroVector:ZeroVector(n):create a vector with all zeroes:
:Zeta:Zeta(x):Riemann's Zeta function:
:::::::
